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</div> <div class="control"> <button class="button is-small is-link">Go</button> </div> </div> </form> </div> </div> <ol class="breathe-horizontal" start="1"> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2407.08696">arXiv:2407.08696</a> <span> [<a href="https://arxiv.org/pdf/2407.08696">pdf</a>, <a href="https://arxiv.org/format/2407.08696">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> </div> <p class="title is-5 mathjax"> Reducing the Resources Required by ADAPT-VQE Using Coupled Exchange Operators and Improved Subroutines </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Ram%C3%B4a%2C+M">Mafalda Ram么a</a>, <a href="/search/quant-ph?searchtype=author&query=Anastasiou%2C+P+G">Panagiotis G. Anastasiou</a>, <a href="/search/quant-ph?searchtype=author&query=Santos%2C+L+P">Luis Paulo Santos</a>, <a href="/search/quant-ph?searchtype=author&query=Mayhall%2C+N+J">Nicholas J. Mayhall</a>, <a href="/search/quant-ph?searchtype=author&query=Barnes%2C+E">Edwin Barnes</a>, <a href="/search/quant-ph?searchtype=author&query=Economou%2C+S+E">Sophia E. Economou</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2407.08696v1-abstract-short" style="display: inline;"> Adaptive variational quantum algorithms arguably offer the best prospects for quantum advantage in the NISQ era. Since the inception of the first such algorithm, ADAPT-VQE, many improvements have appeared in the literature. We combine the key improvements along with a novel operator pool -- which we term Coupled Exchange Operator (CEO) pool -- to assess the cost of running state-of-the-art ADAPT-V… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2407.08696v1-abstract-full').style.display = 'inline'; document.getElementById('2407.08696v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2407.08696v1-abstract-full" style="display: none;"> Adaptive variational quantum algorithms arguably offer the best prospects for quantum advantage in the NISQ era. Since the inception of the first such algorithm, ADAPT-VQE, many improvements have appeared in the literature. We combine the key improvements along with a novel operator pool -- which we term Coupled Exchange Operator (CEO) pool -- to assess the cost of running state-of-the-art ADAPT-VQE on hardware in terms of measurement counts and circuit depth. We show a dramatic reduction of these quantum resources compared to the early versions of the algorithm. We also find that our state-of-the-art CEO-ADAPT-VQE outperforms UCCSD, the most widely regarded static VQE ansatz, in all relevant metrics. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2407.08696v1-abstract-full').style.display = 'none'; document.getElementById('2407.08696v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 11 July, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2406.10913">arXiv:2406.10913</a> <span> [<a href="https://arxiv.org/pdf/2406.10913">pdf</a>, <a href="https://arxiv.org/format/2406.10913">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> </div> <p class="title is-5 mathjax"> Minimal evolution times for fast, pulse-based state preparation in silicon spin qubits </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Long%2C+C+K">Christopher K. Long</a>, <a href="/search/quant-ph?searchtype=author&query=Mayhall%2C+N+J">Nicholas J. Mayhall</a>, <a href="/search/quant-ph?searchtype=author&query=Economou%2C+S+E">Sophia E. Economou</a>, <a href="/search/quant-ph?searchtype=author&query=Barnes%2C+E">Edwin Barnes</a>, <a href="/search/quant-ph?searchtype=author&query=Barnes%2C+C+H+W">Crispin H. W. Barnes</a>, <a href="/search/quant-ph?searchtype=author&query=Martins%2C+F">Frederico Martins</a>, <a href="/search/quant-ph?searchtype=author&query=Arvidsson-Shukur%2C+D+R+M">David R. M. Arvidsson-Shukur</a>, <a href="/search/quant-ph?searchtype=author&query=Mertig%2C+N">Normann Mertig</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2406.10913v1-abstract-short" style="display: inline;"> Standing as one of the most significant barriers to reaching quantum advantage, state-preparation fidelities on noisy intermediate-scale quantum processors suffer from quantum-gate errors, which accumulate over time. A potential remedy is pulse-based state preparation. We numerically investigate the minimal evolution times (METs) attainable by optimizing (microwave and exchange) pulses on silicon… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2406.10913v1-abstract-full').style.display = 'inline'; document.getElementById('2406.10913v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2406.10913v1-abstract-full" style="display: none;"> Standing as one of the most significant barriers to reaching quantum advantage, state-preparation fidelities on noisy intermediate-scale quantum processors suffer from quantum-gate errors, which accumulate over time. A potential remedy is pulse-based state preparation. We numerically investigate the minimal evolution times (METs) attainable by optimizing (microwave and exchange) pulses on silicon hardware. We investigate two state preparation tasks. First, we consider the preparation of molecular ground states and find the METs for H$_2$, HeH$^+$, and LiH to be 2.4 ns, 4.4 ns, and 27.2 ns, respectively. Second, we consider transitions between arbitrary states and find the METs for transitions between arbitrary four-qubit states to be below 50 ns. For comparison, connecting arbitrary two-qubit states via one- and two-qubit gates on the same silicon processor requires approximately 200 ns. This comparison indicates that pulse-based state preparation is likely to utilize the coherence times of silicon hardware more efficiently than gate-based state preparation. Finally, we quantify the effect of silicon device parameters on the MET. We show that increasing the maximal exchange amplitude from 10 MHz to 1 GHz accelerates the METs, e.g., for H$_2$ from 84.3 ns to 2.4 ns. This demonstrates the importance of fast exchange. We also show that increasing the maximal amplitude of the microwave drive from 884 kHz to 56.6 MHz shortens state transitions, e.g., for two-qubit states from 1000 ns to 25 ns. Our results bound both the state-preparation times for general quantum algorithms and the execution times of variational quantum algorithms with silicon spin qubits. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2406.10913v1-abstract-full').style.display = 'none'; document.getElementById('2406.10913v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 16 June, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">9 + (7) pages, 6 figs, comments are welcomed</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2405.15166">arXiv:2405.15166</a> <span> [<a href="https://arxiv.org/pdf/2405.15166">pdf</a>, <a href="https://arxiv.org/format/2405.15166">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> </div> <p class="title is-5 mathjax"> Parameterization and optimizability of pulse-level VQEs </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Sherbert%2C+K+M">Kyle M Sherbert</a>, <a href="/search/quant-ph?searchtype=author&query=Amer%2C+H">Hisham Amer</a>, <a href="/search/quant-ph?searchtype=author&query=Economou%2C+S+E">Sophia E Economou</a>, <a href="/search/quant-ph?searchtype=author&query=Barnes%2C+E">Edwin Barnes</a>, <a href="/search/quant-ph?searchtype=author&query=Mayhall%2C+N+J">Nicholas J Mayhall</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2405.15166v1-abstract-short" style="display: inline;"> In conventional variational quantum eigensolvers (VQEs), trial states are prepared by applying series of parameterized gates to a reference state, with the gate parameters being varied to minimize the energy of the target system. Recognizing that the gates are intermediates which are ultimately compiled into a set of control pulses to be applied to each qubit in the lab, the recently proposed ctrl… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2405.15166v1-abstract-full').style.display = 'inline'; document.getElementById('2405.15166v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2405.15166v1-abstract-full" style="display: none;"> In conventional variational quantum eigensolvers (VQEs), trial states are prepared by applying series of parameterized gates to a reference state, with the gate parameters being varied to minimize the energy of the target system. Recognizing that the gates are intermediates which are ultimately compiled into a set of control pulses to be applied to each qubit in the lab, the recently proposed ctrl-VQE algorithm takes the amplitudes, frequencies, and phases of the pulse as the variational parameters used to minimize the molecular energy. In this work, we explore how all three degrees of freedom interrelate with one another. To this end, we consider several distinct strategies to parameterize the control pulses, assessing each one through numerical simulations of a transmon-like device. For each parameterization, we contrast the pulse duration required to prepare a good ansatz, and the difficulty to optimize that ansatz from a well-defined initial state. We deduce several guiding heuristics to implement practical ctrl-VQE in hardware, which we anticipate will generalize for generic device architectures. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2405.15166v1-abstract-full').style.display = 'none'; document.getElementById('2405.15166v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 May, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">13 pages (10 of main text), 6 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2403.09624">arXiv:2403.09624</a> <span> [<a href="https://arxiv.org/pdf/2403.09624">pdf</a>, <a href="https://arxiv.org/format/2403.09624">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1021/acs.jctc.4c00329">10.1021/acs.jctc.4c00329 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Physically motivated improvements of Variational Quantum Eigensolvers </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Vaquero-Sabater%2C+N">Nonia Vaquero-Sabater</a>, <a href="/search/quant-ph?searchtype=author&query=Carreras%2C+A">Abel Carreras</a>, <a href="/search/quant-ph?searchtype=author&query=Or%C3%BAs%2C+R">Rom谩n Or煤s</a>, <a href="/search/quant-ph?searchtype=author&query=Mayhall%2C+N+J">Nicholas J. Mayhall</a>, <a href="/search/quant-ph?searchtype=author&query=Casanova%2C+D">David Casanova</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2403.09624v2-abstract-short" style="display: inline;"> The Adaptive Derivative-Assembled Pseudo-Trotter Variational Quantum Eigensolver (ADAPT-VQE) has emerged as a pivotal promising approach for electronic structure challenges in quantum chemistry with noisy quantum devices. Nevertheless, to surmount existing technological constraints, this study endeavors to enhance ADAPT-VQE's efficacy. Leveraging insights from electronic structure theory, we conce… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2403.09624v2-abstract-full').style.display = 'inline'; document.getElementById('2403.09624v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2403.09624v2-abstract-full" style="display: none;"> The Adaptive Derivative-Assembled Pseudo-Trotter Variational Quantum Eigensolver (ADAPT-VQE) has emerged as a pivotal promising approach for electronic structure challenges in quantum chemistry with noisy quantum devices. Nevertheless, to surmount existing technological constraints, this study endeavors to enhance ADAPT-VQE's efficacy. Leveraging insights from electronic structure theory, we concentrate on optimizing state preparation without added computational burden and guiding ansatz expansion to yield more concise wavefunctions with expedited convergence toward exact solutions. These advancements culminate in shallower circuits and, as demonstrated, reduced measurement requirements. This research delineates these enhancements and assesses their performance across mono, di, and tridimensional arrangements of H4 models, as well as in the water molecule. Ultimately, this work attests to the viability of physically-motivated strategies in fortifying ADAPT-VQE's efficiency, marking a significant stride in quantum chemistry simulations. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2403.09624v2-abstract-full').style.display = 'none'; document.getElementById('2403.09624v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 2 September, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 14 March, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J. Chem. Theory Comput. 2024, 20, 5133-5144 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2401.05172">arXiv:2401.05172</a> <span> [<a href="https://arxiv.org/pdf/2401.05172">pdf</a>, <a href="https://arxiv.org/format/2401.05172">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1088/2058-9565/ad904e">10.1088/2058-9565/ad904e <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Reducing measurement costs by recycling the Hessian in adaptive variational quantum algorithms </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Ram%C3%B4a%2C+M">Mafalda Ram么a</a>, <a href="/search/quant-ph?searchtype=author&query=Santos%2C+L+P">Luis Paulo Santos</a>, <a href="/search/quant-ph?searchtype=author&query=Mayhall%2C+N+J">Nicholas J. Mayhall</a>, <a href="/search/quant-ph?searchtype=author&query=Barnes%2C+E">Edwin Barnes</a>, <a href="/search/quant-ph?searchtype=author&query=Economou%2C+S+E">Sophia E. Economou</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2401.05172v2-abstract-short" style="display: inline;"> Adaptive protocols enable the construction of more efficient state preparation circuits in variational quantum algorithms (VQAs) by utilizing data obtained from the quantum processor during the execution of the algorithm. This idea originated with ADAPT-VQE, an algorithm that iteratively grows the state preparation circuit operator by operator, with each new operator accompanied by a new variation… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2401.05172v2-abstract-full').style.display = 'inline'; document.getElementById('2401.05172v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2401.05172v2-abstract-full" style="display: none;"> Adaptive protocols enable the construction of more efficient state preparation circuits in variational quantum algorithms (VQAs) by utilizing data obtained from the quantum processor during the execution of the algorithm. This idea originated with ADAPT-VQE, an algorithm that iteratively grows the state preparation circuit operator by operator, with each new operator accompanied by a new variational parameter, and where all parameters acquired thus far are optimized in each iteration. In ADAPT-VQE and other adaptive VQAs that followed it, it has been shown that initializing parameters to their optimal values from the previous iteration speeds up convergence and avoids shallow local traps in the parameter landscape. However, no other data from the optimization performed at one iteration is carried over to the next. In this work, we propose an improved quasi-Newton optimization protocol specifically tailored to adaptive VQAs. The distinctive feature in our proposal is that approximate second derivatives of the cost function are recycled across iterations in addition to parameter values. We implement a quasi-Newton optimizer where an approximation to the inverse Hessian matrix is continuously built and grown across the iterations of an adaptive VQA. The resulting algorithm has the flavor of a continuous optimization where the dimension of the search space is augmented when the gradient norm falls below a given threshold. We show that this inter-optimization exchange of second-order information leads the Hessian in the state of the optimizer to better approximate the exact Hessian. As a result, our method achieves a superlinear convergence rate even in situations where the typical quasi-Newton optimizer converges only linearly. Our protocol decreases the measurement costs in implementing adaptive VQAs on quantum hardware as well as the runtime of their classical simulation. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2401.05172v2-abstract-full').style.display = 'none'; document.getElementById('2401.05172v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 18 November, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 10 January, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Quantum Sci. Technol. 10 (2024) 015031 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2306.03227">arXiv:2306.03227</a> <span> [<a href="https://arxiv.org/pdf/2306.03227">pdf</a>, <a href="https://arxiv.org/format/2306.03227">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> </div> <p class="title is-5 mathjax"> How to really measure operator gradients in ADAPT-VQE </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Anastasiou%2C+P+G">Panagiotis G. Anastasiou</a>, <a href="/search/quant-ph?searchtype=author&query=Mayhall%2C+N+J">Nicholas J. Mayhall</a>, <a href="/search/quant-ph?searchtype=author&query=Barnes%2C+E">Edwin Barnes</a>, <a href="/search/quant-ph?searchtype=author&query=Economou%2C+S+E">Sophia E. Economou</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2306.03227v2-abstract-short" style="display: inline;"> ADAPT-VQE is one of the leading VQE algorithms which circumvents the choice-of-ansatz conundrum by iteratively growing compact and arbitrarily accurate problem-tailored ans盲tze. However, for hardware-efficient operator pools, the gradient-measurement step of the algorithm requires the estimation of $O(N^8)$ observables, which may represent a bottleneck for relevant system sizes on real devices. We… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2306.03227v2-abstract-full').style.display = 'inline'; document.getElementById('2306.03227v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2306.03227v2-abstract-full" style="display: none;"> ADAPT-VQE is one of the leading VQE algorithms which circumvents the choice-of-ansatz conundrum by iteratively growing compact and arbitrarily accurate problem-tailored ans盲tze. However, for hardware-efficient operator pools, the gradient-measurement step of the algorithm requires the estimation of $O(N^8)$ observables, which may represent a bottleneck for relevant system sizes on real devices. We present an efficient strategy for measuring the pool gradients based on simultaneously measuring commuting observables. We argue that our approach is relatively robust to shot-noise effects, and show that measuring the pool gradients is in fact only $O(N)$ times as expensive as a naive VQE iteration. Our proposed measurement strategy significantly ameliorates the measurement overhead of ADAPT-VQE and brings us one step closer to practical implementations on real devices. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2306.03227v2-abstract-full').style.display = 'none'; document.getElementById('2306.03227v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 29 September, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 5 June, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">8 pages, 2 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2301.06260">arXiv:2301.06260</a> <span> [<a href="https://arxiv.org/pdf/2301.06260">pdf</a>, <a href="https://arxiv.org/format/2301.06260">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Chemical Physics">physics.chem-ph</span> </div> </div> <p class="title is-5 mathjax"> Quantum simulation of molecular response properties </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Kumar%2C+A">Ashutosh Kumar</a>, <a href="/search/quant-ph?searchtype=author&query=Asthana%2C+A">Ayush Asthana</a>, <a href="/search/quant-ph?searchtype=author&query=Abraham%2C+V">Vibin Abraham</a>, <a href="/search/quant-ph?searchtype=author&query=Crawford%2C+T+D">T. Daniel Crawford</a>, <a href="/search/quant-ph?searchtype=author&query=Mayhall%2C+N+J">Nicholas J. Mayhall</a>, <a href="/search/quant-ph?searchtype=author&query=Zhang%2C+Y">Yu Zhang</a>, <a href="/search/quant-ph?searchtype=author&query=Cincio%2C+L">Lukasz Cincio</a>, <a href="/search/quant-ph?searchtype=author&query=Tretiak%2C+S">Sergei Tretiak</a>, <a href="/search/quant-ph?searchtype=author&query=Dub%2C+P+A">Pavel A. Dub</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2301.06260v1-abstract-short" style="display: inline;"> Accurate modeling of the response of molecular systems to an external electromagnetic field is challenging on classical computers, especially in the regime of strong electronic correlation. In this paper, we develop a quantum linear response (qLR) theory to calculate molecular response properties on near-term quantum computers. Inspired by the recently developed variants of the quantum counterpart… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2301.06260v1-abstract-full').style.display = 'inline'; document.getElementById('2301.06260v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2301.06260v1-abstract-full" style="display: none;"> Accurate modeling of the response of molecular systems to an external electromagnetic field is challenging on classical computers, especially in the regime of strong electronic correlation. In this paper, we develop a quantum linear response (qLR) theory to calculate molecular response properties on near-term quantum computers. Inspired by the recently developed variants of the quantum counterpart of equation of motion (qEOM) theory, the qLR formalism employs "killer condition" satisfying excitation operator manifolds that offers a number of theoretical advantages along with reduced quantum resource requirements. We also used the qEOM framework in this work to calculate state-specific response properties. Further, through noise-less quantum simulations, we show that response properties calculated using the qLR approach are more accurate than the ones obtained from the classical coupled-cluster based linear response models due to the improved quality of the ground-state wavefunction obtained using the ADAPT-VQE algorithm. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2301.06260v1-abstract-full').style.display = 'none'; document.getElementById('2301.06260v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 January, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> LA-UR-22-29739 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2209.10562">arXiv:2209.10562</a> <span> [<a href="https://arxiv.org/pdf/2209.10562">pdf</a>, <a href="https://arxiv.org/format/2209.10562">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevResearch.6.013254">10.1103/PhysRevResearch.6.013254 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> TETRIS-ADAPT-VQE: An adaptive algorithm that yields shallower, denser circuit ans盲tze </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Anastasiou%2C+P+G">Panagiotis G. Anastasiou</a>, <a href="/search/quant-ph?searchtype=author&query=Chen%2C+Y">Yanzhu Chen</a>, <a href="/search/quant-ph?searchtype=author&query=Mayhall%2C+N+J">Nicholas J. Mayhall</a>, <a href="/search/quant-ph?searchtype=author&query=Barnes%2C+E">Edwin Barnes</a>, <a href="/search/quant-ph?searchtype=author&query=Economou%2C+S+E">Sophia E. Economou</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2209.10562v1-abstract-short" style="display: inline;"> Adaptive quantum variational algorithms are particularly promising for simulating strongly correlated systems on near-term quantum hardware, but they are not yet viable due, in large part, to the severe coherence time limitations on current devices. In this work, we introduce an algorithm called TETRIS-ADAPT-VQE, which iteratively builds up variational ans盲tze a few operators at a time in a way di… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2209.10562v1-abstract-full').style.display = 'inline'; document.getElementById('2209.10562v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2209.10562v1-abstract-full" style="display: none;"> Adaptive quantum variational algorithms are particularly promising for simulating strongly correlated systems on near-term quantum hardware, but they are not yet viable due, in large part, to the severe coherence time limitations on current devices. In this work, we introduce an algorithm called TETRIS-ADAPT-VQE, which iteratively builds up variational ans盲tze a few operators at a time in a way dictated by the problem being simulated. This algorithm is a modified version of the ADAPT-VQE algorithm in which the one-operator-at-a-time rule is lifted to allow for the addition of multiple operators with disjoint supports in each iteration. TETRIS-ADAPT-VQE results in denser but significantly shallower circuits, without increasing the number of CNOT gates or variational parameters. Its advantage over the original algorithm in terms of circuit depths increases with the system size. Moreover, the expensive step of measuring the energy gradient with respect to each candidate unitary at each iteration is performed only a fraction of the time compared to ADAPT-VQE. These improvements bring us closer to the goal of demonstrating a practical quantum advantage on quantum hardware. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2209.10562v1-abstract-full').style.display = 'none'; document.getElementById('2209.10562v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 21 September, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">10 pages, 7 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2207.04105">arXiv:2207.04105</a> <span> [<a href="https://arxiv.org/pdf/2207.04105">pdf</a>, <a href="https://arxiv.org/format/2207.04105">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Chemical Physics">physics.chem-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> </div> <p class="title is-5 mathjax"> New Local Explorations of the Unitary Coupled Cluster Energy Landscape </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Grimsley%2C+H+R">Harper R. Grimsley</a>, <a href="/search/quant-ph?searchtype=author&query=Mayhall%2C+N+J">Nicholas J. Mayhall</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2207.04105v2-abstract-short" style="display: inline;"> The recent quantum information boom has effected a resurgence of interest in unitary coupled cluster (UCC) theory. Our group's interest in local energy landscapes of unitary ans盲tze prompted us to investigate the classical approach of truncating the Taylor series expansion (instead of a perturbative expansion) of UCCSD energy at second-order. This amounts to an approach where electron correlation… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2207.04105v2-abstract-full').style.display = 'inline'; document.getElementById('2207.04105v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2207.04105v2-abstract-full" style="display: none;"> The recent quantum information boom has effected a resurgence of interest in unitary coupled cluster (UCC) theory. Our group's interest in local energy landscapes of unitary ans盲tze prompted us to investigate the classical approach of truncating the Taylor series expansion (instead of a perturbative expansion) of UCCSD energy at second-order. This amounts to an approach where electron correlation energy is estimated by taking a single Newton-Raphson step from Hartree-Fock toward UCCSD. Such an approach has been explored previously, but the accuracy was not extensively studied. In this paper, we investigate the performance and observe similar pathologies to linearized coupled cluster with singles and doubles. We introduce the use of derivatives of order three or greater to help partially recover the variational lower bound of true UCCSD, restricting these derivatives to those of the "unmixed" category in order to simplify the model. By testing the approach on several potential energy surfaces and reaction energies, we find this "diagonal" approximation to higher order terms to be effective at reducing sensitivity near singularities for strongly correlated regimes, while not significantly diminishing the accuracy of weakly correlated systems. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2207.04105v2-abstract-full').style.display = 'none'; document.getElementById('2207.04105v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 28 October, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 8 July, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">11 pages, 7 figures (including SI)</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2207.03063">arXiv:2207.03063</a> <span> [<a href="https://arxiv.org/pdf/2207.03063">pdf</a>, <a href="https://arxiv.org/ps/2207.03063">ps</a>, <a href="https://arxiv.org/format/2207.03063">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> </div> <p class="title is-5 mathjax"> Symmetry breaking slows convergence of the ADAPT Variational Quantum Eigensolver </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Bertels%2C+L+W">Luke W. Bertels</a>, <a href="/search/quant-ph?searchtype=author&query=Grimsley%2C+H+R">Harper R. Grimsley</a>, <a href="/search/quant-ph?searchtype=author&query=Economou%2C+S+E">Sophia E. Economou</a>, <a href="/search/quant-ph?searchtype=author&query=Barnes%2C+E">Edwin Barnes</a>, <a href="/search/quant-ph?searchtype=author&query=Mayhall%2C+N+J">Nicholas J. Mayhall</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2207.03063v1-abstract-short" style="display: inline;"> Because quantum simulation of molecular systems is expected to provide the strongest advantage over classical computing methods for systems exhibiting strong electron correlation, it is critical that the performance of VQEs be assessed for strongly correlated systems. For classical simulation, strong correlation often results in symmetry-breaking of the Hartree-Fock reference, leading to L枚wdin's… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2207.03063v1-abstract-full').style.display = 'inline'; document.getElementById('2207.03063v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2207.03063v1-abstract-full" style="display: none;"> Because quantum simulation of molecular systems is expected to provide the strongest advantage over classical computing methods for systems exhibiting strong electron correlation, it is critical that the performance of VQEs be assessed for strongly correlated systems. For classical simulation, strong correlation often results in symmetry-breaking of the Hartree-Fock reference, leading to L枚wdin's well-known ``symmetry dilemma'' whereby accuracy in the energy can be increased by breaking spin or spatial symmetries. Here, we explore the impact of symmetry breaking on the performance of ADAPT-VQE using two strongly correlated systems: (i) the ``fermionized" anisotropic Heisenberg model, where the anisotropy parameter controls the correlation in the system, and (ii) symmetrically-stretched linear \ce{H4}, where correlation increases with increasing H-H separation. In both of these cases, increasing the level of correlation of the system leads to spontaneous symmetry breaking (parity and $\hat{S}^{2}$, respectively) of the mean-field solutions. We analyze the role that symmetry breaking in the reference states and orbital mappings of the fermionic Hamiltonians have on the compactness and performance of ADAPT-VQE. We observe that improving the energy of the reference states by breaking symmetry has a deleterious effect on ADAPT-VQE by increasing the length of the ansatz necessary for energy convergence and exacerbating the problem of ``gradient troughs". <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2207.03063v1-abstract-full').style.display = 'none'; document.getElementById('2207.03063v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 6 July, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">16 pages, 5 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2206.14215">arXiv:2206.14215</a> <span> [<a href="https://arxiv.org/pdf/2206.14215">pdf</a>, <a href="https://arxiv.org/format/2206.14215">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Strongly Correlated Electrons">cond-mat.str-el</span> </div> </div> <p class="title is-5 mathjax"> Scaling adaptive quantum simulation algorithms via operator pool tiling </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Van+Dyke%2C+J+S">John S. Van Dyke</a>, <a href="/search/quant-ph?searchtype=author&query=Shirali%2C+K">Karunya Shirali</a>, <a href="/search/quant-ph?searchtype=author&query=Barron%2C+G+S">George S. Barron</a>, <a href="/search/quant-ph?searchtype=author&query=Mayhall%2C+N+J">Nicholas J. Mayhall</a>, <a href="/search/quant-ph?searchtype=author&query=Barnes%2C+E">Edwin Barnes</a>, <a href="/search/quant-ph?searchtype=author&query=Economou%2C+S+E">Sophia E. Economou</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2206.14215v2-abstract-short" style="display: inline;"> Adaptive variational quantum simulation algorithms use information from the quantum computer to dynamically create optimal trial wavefunctions for a given problem Hamiltonian. A key ingredient in these algorithms is a predefined operator pool from which trial wavefunctions are constructed. Finding suitable pools is critical for the efficiency of the algorithm as the problem size increases. Here, w… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2206.14215v2-abstract-full').style.display = 'inline'; document.getElementById('2206.14215v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2206.14215v2-abstract-full" style="display: none;"> Adaptive variational quantum simulation algorithms use information from the quantum computer to dynamically create optimal trial wavefunctions for a given problem Hamiltonian. A key ingredient in these algorithms is a predefined operator pool from which trial wavefunctions are constructed. Finding suitable pools is critical for the efficiency of the algorithm as the problem size increases. Here, we present a technique called operator pool tiling that facilitates the construction of problem-tailored pools for arbitrarily large problem instances. By first performing an ADAPT-VQE calculation on a smaller instance of the problem using a large, but computationally inefficient operator pool, we extract the most relevant operators and use them to design more efficient pools for larger instances. We demonstrate the method here on strongly correlated quantum spin models in one and two dimensions, finding that ADAPT automatically finds a highly effective ansatz for these systems. Given that many problems, such as those arising in condensed matter physics, have a naturally repeating lattice structure, we expect the pool tiling method to be a widely applicable technique apt for such systems. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2206.14215v2-abstract-full').style.display = 'none'; document.getElementById('2206.14215v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 November, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 28 June, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">9 pages, 4 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2206.10502">arXiv:2206.10502</a> <span> [<a href="https://arxiv.org/pdf/2206.10502">pdf</a>, <a href="https://arxiv.org/format/2206.10502">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Strongly Correlated Electrons">cond-mat.str-el</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Chemical Physics">physics.chem-ph</span> </div> </div> <p class="title is-5 mathjax"> Quantum self-consistent equation-of-motion method for computing molecular excitation energies, ionization potentials, and electron affinities on a quantum computer </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Asthana%2C+A">Ayush Asthana</a>, <a href="/search/quant-ph?searchtype=author&query=Kumar%2C+A">Ashutosh Kumar</a>, <a href="/search/quant-ph?searchtype=author&query=Abraham%2C+V">Vibin Abraham</a>, <a href="/search/quant-ph?searchtype=author&query=Grimsley%2C+H">Harper Grimsley</a>, <a href="/search/quant-ph?searchtype=author&query=Zhang%2C+Y">Yu Zhang</a>, <a href="/search/quant-ph?searchtype=author&query=Cincio%2C+L">Lukasz Cincio</a>, <a href="/search/quant-ph?searchtype=author&query=Tretiak%2C+S">Sergei Tretiak</a>, <a href="/search/quant-ph?searchtype=author&query=Dub%2C+P+A">Pavel A. Dub</a>, <a href="/search/quant-ph?searchtype=author&query=Economou%2C+S+E">Sophia E. Economou</a>, <a href="/search/quant-ph?searchtype=author&query=Barnes%2C+E">Edwin Barnes</a>, <a href="/search/quant-ph?searchtype=author&query=Mayhall%2C+N+J">Nicholas J. Mayhall</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2206.10502v2-abstract-short" style="display: inline;"> Near-term quantum computers are expected to facilitate material and chemical research through accurate molecular simulations. Several developments have already shown that accurate ground-state energies for small molecules can be evaluated on present-day quantum devices. Although electronically excited states play a vital role in chemical processes and applications, the search for a reliable and pr… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2206.10502v2-abstract-full').style.display = 'inline'; document.getElementById('2206.10502v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2206.10502v2-abstract-full" style="display: none;"> Near-term quantum computers are expected to facilitate material and chemical research through accurate molecular simulations. Several developments have already shown that accurate ground-state energies for small molecules can be evaluated on present-day quantum devices. Although electronically excited states play a vital role in chemical processes and applications, the search for a reliable and practical approach for routine excited-state calculations on near-term quantum devices is ongoing. Inspired by excited-state methods developed for the unitary coupled-cluster theory in quantum chemistry, we present an equation-of-motion-based method to compute excitation energies following the variational quantum eigensolver algorithm for ground-state calculations on a quantum computer. We perform numerical simulations on H$_2$, H$_4$, H$_2$O, and LiH molecules to test our quantum self-consistent equation-of-motion (q-sc-EOM) method and compare it to other current state-of-the-art methods. q-sc-EOM makes use of self-consistent operators to satisfy the vacuum annihilation condition, a critical property for accurate calculations. It provides real and size-intensive energy differences corresponding to vertical excitation energies, ionization potentials and electron affinities. We also find that q-sc-EOM is more suitable for implementation on NISQ devices as it is expected to be more resilient to noise compared with the currently available methods. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2206.10502v2-abstract-full').style.display = 'none'; document.getElementById('2206.10502v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 February, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 21 June, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> LA-UR-22-25463 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2205.12283">arXiv:2205.12283</a> <span> [<a href="https://arxiv.org/pdf/2205.12283">pdf</a>, <a href="https://arxiv.org/format/2205.12283">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> </div> <p class="title is-5 mathjax"> How Much Entanglement Do Quantum Optimization Algorithms Require? </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Chen%2C+Y">Yanzhu Chen</a>, <a href="/search/quant-ph?searchtype=author&query=Zhu%2C+L">Linghua Zhu</a>, <a href="/search/quant-ph?searchtype=author&query=Liu%2C+C">Chenxu Liu</a>, <a href="/search/quant-ph?searchtype=author&query=Mayhall%2C+N+J">Nicholas J. Mayhall</a>, <a href="/search/quant-ph?searchtype=author&query=Barnes%2C+E">Edwin Barnes</a>, <a href="/search/quant-ph?searchtype=author&query=Economou%2C+S+E">Sophia E. Economou</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2205.12283v2-abstract-short" style="display: inline;"> Many classical optimization problems can be mapped to finding the ground states of diagonal Ising Hamiltonians, for which variational quantum algorithms such as the Quantum Approximate Optimization Algorithm (QAOA) provide heuristic methods. Because the solutions of such classical optimization problems are necessarily product states, it is unclear how entanglement affects their performance. An Ada… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2205.12283v2-abstract-full').style.display = 'inline'; document.getElementById('2205.12283v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2205.12283v2-abstract-full" style="display: none;"> Many classical optimization problems can be mapped to finding the ground states of diagonal Ising Hamiltonians, for which variational quantum algorithms such as the Quantum Approximate Optimization Algorithm (QAOA) provide heuristic methods. Because the solutions of such classical optimization problems are necessarily product states, it is unclear how entanglement affects their performance. An Adaptive Derivative-Assembled Problem-Tailored (ADAPT) variation of QAOA improves the convergence rate by allowing entangling operations in the mixer layers whereas it requires fewer CNOT gates in the entire circuit. In this work, we study the entanglement generated during the execution of ADAPT-QAOA. Through simulations of the weighted Max-Cut problem, we show that ADAPT-QAOA exhibits substantial flexibility in entangling and disentangling qubits. By incrementally restricting this flexibility, we find that a larger amount of entanglement entropy at earlier stages coincides with faster convergence at later stages. In contrast, while the standard QAOA quickly generates entanglement within a few layers, it cannot remove excess entanglement efficiently. Our results demonstrate that the role of entanglement in quantum optimization is subtle and provide guidance for building favorable features into quantum optimization algorithms. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2205.12283v2-abstract-full').style.display = 'none'; document.getElementById('2205.12283v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 9 July, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 24 May, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">15 pages, 7 figures. Comments are welcome</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2204.07179">arXiv:2204.07179</a> <span> [<a href="https://arxiv.org/pdf/2204.07179">pdf</a>, <a href="https://arxiv.org/format/2204.07179">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Chemical Physics">physics.chem-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1038/s41534-023-00681-0">10.1038/s41534-023-00681-0 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> ADAPT-VQE is insensitive to rough parameter landscapes and barren plateaus </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Grimsley%2C+H+R">Harper R. Grimsley</a>, <a href="/search/quant-ph?searchtype=author&query=Barron%2C+G+S">George S. Barron</a>, <a href="/search/quant-ph?searchtype=author&query=Barnes%2C+E">Edwin Barnes</a>, <a href="/search/quant-ph?searchtype=author&query=Economou%2C+S+E">Sophia E. Economou</a>, <a href="/search/quant-ph?searchtype=author&query=Mayhall%2C+N+J">Nicholas J. Mayhall</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2204.07179v1-abstract-short" style="display: inline;"> Variational quantum eigensolvers (VQEs) represent a powerful class of hybrid quantum-classical algorithms for computing molecular energies. Various numerical issues exist for these methods, however, including barren plateaus and large numbers of local minima. In this work, we consider Adaptive, Problem-Tailored (ADAPT)-VQE ans盲tze, and examine how they are impacted by these local minima. We find t… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2204.07179v1-abstract-full').style.display = 'inline'; document.getElementById('2204.07179v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2204.07179v1-abstract-full" style="display: none;"> Variational quantum eigensolvers (VQEs) represent a powerful class of hybrid quantum-classical algorithms for computing molecular energies. Various numerical issues exist for these methods, however, including barren plateaus and large numbers of local minima. In this work, we consider Adaptive, Problem-Tailored (ADAPT)-VQE ans盲tze, and examine how they are impacted by these local minima. We find that while ADAPT-VQE does not remove local minima, the gradient-informed, one-operator-at-a-time circuit construction seems to accomplish two things: First, it provides an initialization strategy that is dramatically better than random initialization, and which is applicable in situations where chemical intuition cannot help with initialization, i.e., when Hartree-Fock is a poor approximation to the ground state. Second, even if an ADAPT-VQE iteration converges to a local trap at one step, it can still "burrow" toward the exact solution by adding more operators, which preferentially deepens the occupied trap. This same mechanism helps highlight a surprising feature of ADAPT-VQE: It should not suffer optimization problems due to "barren plateaus". Even if barren plateaus appear in the parameter landscape, our analysis and simulations reveal that ADAPT-VQE avoids such regions by design. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2204.07179v1-abstract-full').style.display = 'none'; document.getElementById('2204.07179v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 14 April, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2022. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2203.12757">arXiv:2203.12757</a> <span> [<a href="https://arxiv.org/pdf/2203.12757">pdf</a>, <a href="https://arxiv.org/ps/2203.12757">ps</a>, <a href="https://arxiv.org/format/2203.12757">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> </div> <p class="title is-5 mathjax"> Adaptive variational algorithms for quantum Gibbs state preparation </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Warren%2C+A">Ada Warren</a>, <a href="/search/quant-ph?searchtype=author&query=Zhu%2C+L">Linghua Zhu</a>, <a href="/search/quant-ph?searchtype=author&query=Mayhall%2C+N+J">Nicholas J. Mayhall</a>, <a href="/search/quant-ph?searchtype=author&query=Barnes%2C+E">Edwin Barnes</a>, <a href="/search/quant-ph?searchtype=author&query=Economou%2C+S+E">Sophia E. Economou</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2203.12757v1-abstract-short" style="display: inline;"> The preparation of Gibbs thermal states is an important task in quantum computation with applications in quantum simulation, quantum optimization, and quantum machine learning. However, many algorithms for preparing Gibbs states rely on quantum subroutines which are difficult to implement on near-term hardware. Here, we address this by (i) introducing an objective function that, unlike the free en… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2203.12757v1-abstract-full').style.display = 'inline'; document.getElementById('2203.12757v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2203.12757v1-abstract-full" style="display: none;"> The preparation of Gibbs thermal states is an important task in quantum computation with applications in quantum simulation, quantum optimization, and quantum machine learning. However, many algorithms for preparing Gibbs states rely on quantum subroutines which are difficult to implement on near-term hardware. Here, we address this by (i) introducing an objective function that, unlike the free energy, is easily measured, and (ii) using dynamically generated, problem-tailored ans盲tze. This allows for arbitrarily accurate Gibbs state preparation using low-depth circuits. To verify the effectiveness of our approach, we numerically demonstrate that our algorithm can prepare high-fidelity Gibbs states across a broad range of temperatures and for a variety of Hamiltonians. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2203.12757v1-abstract-full').style.display = 'none'; document.getElementById('2203.12757v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 March, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">7 pages, 3 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2203.06818">arXiv:2203.06818</a> <span> [<a href="https://arxiv.org/pdf/2203.06818">pdf</a>, <a href="https://arxiv.org/format/2203.06818">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Chemical Physics">physics.chem-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevApplied.19.064071">10.1103/PhysRevApplied.19.064071 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Minimizing state preparation times in pulse-level variational molecular simulations </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Asthana%2C+A">Ayush Asthana</a>, <a href="/search/quant-ph?searchtype=author&query=Liu%2C+C">Chenxu Liu</a>, <a href="/search/quant-ph?searchtype=author&query=Meitei%2C+O+R">Oinam Romesh Meitei</a>, <a href="/search/quant-ph?searchtype=author&query=Economou%2C+S+E">Sophia E. Economou</a>, <a href="/search/quant-ph?searchtype=author&query=Barnes%2C+E">Edwin Barnes</a>, <a href="/search/quant-ph?searchtype=author&query=Mayhall%2C+N+J">Nicholas J. Mayhall</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2203.06818v1-abstract-short" style="display: inline;"> Quantum simulation on NISQ devices is severely limited by short coherence times. A variational pulse-shaping algorithm known as ctrl-VQE was recently proposed to address this issue by eliminating the need for parameterized quantum circuits, which lead to long state preparation times. Here, we find the shortest possible pulses for ctrl-VQE to prepare target molecular wavefunctions for a given devic… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2203.06818v1-abstract-full').style.display = 'inline'; document.getElementById('2203.06818v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2203.06818v1-abstract-full" style="display: none;"> Quantum simulation on NISQ devices is severely limited by short coherence times. A variational pulse-shaping algorithm known as ctrl-VQE was recently proposed to address this issue by eliminating the need for parameterized quantum circuits, which lead to long state preparation times. Here, we find the shortest possible pulses for ctrl-VQE to prepare target molecular wavefunctions for a given device Hamiltonian describing coupled transmon qubits. We find that the time-optimal pulses that do this have a bang-bang form consistent with Pontryagin's maximum principle. We further investigate how the minimal state preparation time is impacted by truncating the transmons to two versus more levels. We find that leakage outside the computational subspace (something that is usually considered problematic) speeds up the state preparation, further reducing device coherence-time demands. This speedup is due to an enlarged solution space of target wavefunctions and to the appearance of additional channels connecting initial and target states. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2203.06818v1-abstract-full').style.display = 'none'; document.getElementById('2203.06818v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 13 March, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. Applied 19, 064071 (2023) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2109.05340">arXiv:2109.05340</a> <span> [<a href="https://arxiv.org/pdf/2109.05340">pdf</a>, <a href="https://arxiv.org/format/2109.05340">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.22331/q-2023-06-12-1040">10.22331/q-2023-06-12-1040 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Avoiding symmetry roadblocks and minimizing the measurement overhead of adaptive variational quantum eigensolvers </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Shkolnikov%2C+V+O">V. O. Shkolnikov</a>, <a href="/search/quant-ph?searchtype=author&query=Mayhall%2C+N+J">Nicholas J. Mayhall</a>, <a href="/search/quant-ph?searchtype=author&query=Economou%2C+S+E">Sophia E. Economou</a>, <a href="/search/quant-ph?searchtype=author&query=Barnes%2C+E">Edwin Barnes</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2109.05340v2-abstract-short" style="display: inline;"> Quantum simulation of strongly correlated systems is potentially the most feasible useful application of near-term quantum computers. Minimizing quantum computational resources is crucial to achieving this goal. A promising class of algorithms for this purpose consists of variational quantum eigensolvers (VQEs). Among these, problem-tailored versions such as ADAPT-VQE that build variational ans盲tz… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2109.05340v2-abstract-full').style.display = 'inline'; document.getElementById('2109.05340v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2109.05340v2-abstract-full" style="display: none;"> Quantum simulation of strongly correlated systems is potentially the most feasible useful application of near-term quantum computers. Minimizing quantum computational resources is crucial to achieving this goal. A promising class of algorithms for this purpose consists of variational quantum eigensolvers (VQEs). Among these, problem-tailored versions such as ADAPT-VQE that build variational ans盲tze step by step from a predefined operator pool perform particularly well in terms of circuit depths and variational parameter counts. However, this improved performance comes at the expense of an additional measurement overhead compared to standard VQEs. Here, we show that this overhead can be reduced to an amount that grows only linearly with the number $n$ of qubits, instead of quartically as in the original ADAPT-VQE. We do this by proving that operator pools of size $2n-2$ can represent any state in Hilbert space if chosen appropriately. We prove that this is the minimal size of such "complete" pools, discuss their algebraic properties, and present necessary and sufficient conditions for their completeness that allow us to find such pools efficiently. We further show that, if the simulated problem possesses symmetries, then complete pools can fail to yield convergent results, unless the pool is chosen to obey certain symmetry rules. We demonstrate the performance of such symmetry-adapted complete pools by using them in classical simulations of ADAPT-VQE for several strongly correlated molecules. Our findings are relevant for any VQE that uses an ansatz based on Pauli strings. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2109.05340v2-abstract-full').style.display = 'none'; document.getElementById('2109.05340v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 6 June, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 11 September, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">15+10 pages, 7 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Quantum 7, 1040 (2023) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2103.13388">arXiv:2103.13388</a> <span> [<a href="https://arxiv.org/pdf/2103.13388">pdf</a>, <a href="https://arxiv.org/format/2103.13388">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PRXQuantum.2.040329">10.1103/PRXQuantum.2.040329 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Preparing Bethe Ansatz Eigenstates on a Quantum Computer </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Van+Dyke%2C+J+S">John S. Van Dyke</a>, <a href="/search/quant-ph?searchtype=author&query=Barron%2C+G+S">George S. Barron</a>, <a href="/search/quant-ph?searchtype=author&query=Mayhall%2C+N+J">Nicholas J. Mayhall</a>, <a href="/search/quant-ph?searchtype=author&query=Barnes%2C+E">Edwin Barnes</a>, <a href="/search/quant-ph?searchtype=author&query=Economou%2C+S+E">Sophia E. Economou</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2103.13388v3-abstract-short" style="display: inline;"> Several quantum many-body models in one dimension possess exact solutions via the Bethe ansatz method, which has been highly successful for understanding their behavior. Nevertheless, there remain physical properties of such models for which analytic results are unavailable, and which are also not well-described by approximate numerical methods. Preparing Bethe ansatz eigenstates directly on a qua… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2103.13388v3-abstract-full').style.display = 'inline'; document.getElementById('2103.13388v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2103.13388v3-abstract-full" style="display: none;"> Several quantum many-body models in one dimension possess exact solutions via the Bethe ansatz method, which has been highly successful for understanding their behavior. Nevertheless, there remain physical properties of such models for which analytic results are unavailable, and which are also not well-described by approximate numerical methods. Preparing Bethe ansatz eigenstates directly on a quantum computer would allow straightforward extraction of these quantities via measurement. We present a quantum algorithm for preparing Bethe ansatz eigenstates of the spin-1/2 XXZ spin chain that correspond to real-valued solutions of the Bethe equations. The algorithm is polynomial in the number of T gates and circuit depth, with modest constant prefactors. Although the algorithm is probabilistic, with a success rate that decreases with increasing eigenstate energy, we employ amplitude amplification to boost the success probability. The resource requirements for our approach are lower than other state-of-the-art quantum simulation algorithms for small error-corrected devices, and thus may offer an alternative and computationally less-demanding demonstration of quantum advantage for physically relevant problems. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2103.13388v3-abstract-full').style.display = 'none'; document.getElementById('2103.13388v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 24 November, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 24 March, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">14 pages, 9 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> PRX Quantum 2, 040329 (2021) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2008.04302">arXiv:2008.04302</a> <span> [<a href="https://arxiv.org/pdf/2008.04302">pdf</a>, <a href="https://arxiv.org/format/2008.04302">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Strongly Correlated Electrons">cond-mat.str-el</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Chemical Physics">physics.chem-ph</span> </div> </div> <p class="title is-5 mathjax"> Gate-free state preparation for fast variational quantum eigensolver simulations: ctrl-VQE </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Meitei%2C+O+R">Oinam Romesh Meitei</a>, <a href="/search/quant-ph?searchtype=author&query=Gard%2C+B+T">Bryan T. Gard</a>, <a href="/search/quant-ph?searchtype=author&query=Barron%2C+G+S">George S. Barron</a>, <a href="/search/quant-ph?searchtype=author&query=Pappas%2C+D+P">David P. Pappas</a>, <a href="/search/quant-ph?searchtype=author&query=Economou%2C+S+E">Sophia E. Economou</a>, <a href="/search/quant-ph?searchtype=author&query=Barnes%2C+E">Edwin Barnes</a>, <a href="/search/quant-ph?searchtype=author&query=Mayhall%2C+N+J">Nicholas J. Mayhall</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2008.04302v3-abstract-short" style="display: inline;"> The variational quantum eigensolver (VQE) is currently the flagship algorithm for solving electronic structure problems on near-term quantum computers. This hybrid quantum/classical algorithm involves implementing a sequence of parameterized gates on quantum hardware to generate a target quantum state, and then measuring the expectation value of the molecular Hamiltonian. Due to finite coherence t… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2008.04302v3-abstract-full').style.display = 'inline'; document.getElementById('2008.04302v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2008.04302v3-abstract-full" style="display: none;"> The variational quantum eigensolver (VQE) is currently the flagship algorithm for solving electronic structure problems on near-term quantum computers. This hybrid quantum/classical algorithm involves implementing a sequence of parameterized gates on quantum hardware to generate a target quantum state, and then measuring the expectation value of the molecular Hamiltonian. Due to finite coherence times and frequent gate errors, the number of gates that can be implemented remains limited on current quantum devices, preventing accurate applications to systems with significant entanglement, such as strongly correlated molecules. In this work, we propose an alternative algorithm (which we refer to as ctrl-VQE) where the quantum circuit used for state preparation is removed entirely and replaced by a quantum control routine which variationally shapes a pulse to drive the initial Hartree-Fock state to the full CI target state. As with VQE, the objective function optimized is the expectation value of the qubit-mapped molecular Hamiltonian. However, by removing the quantum circuit, the coherence times required for state preparation can be drastically reduced by directly optimizing the pulses. We demonstrate the potential of this method numerically by directly optimizing pulse shapes which accurately model the dissociation curves of the hydrogen molecule (covalent bond) and helium hydride ion (ionic bond), and we compute the single point energy for LiH with four transmons. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2008.04302v3-abstract-full').style.display = 'none'; document.getElementById('2008.04302v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 10 May, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 10 August, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2020. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2005.10258">arXiv:2005.10258</a> <span> [<a href="https://arxiv.org/pdf/2005.10258">pdf</a>, <a href="https://arxiv.org/format/2005.10258">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> </div> <p class="title is-5 mathjax"> An adaptive quantum approximate optimization algorithm for solving combinatorial problems on a quantum computer </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Zhu%2C+L">Linghua Zhu</a>, <a href="/search/quant-ph?searchtype=author&query=Tang%2C+H+L">Ho Lun Tang</a>, <a href="/search/quant-ph?searchtype=author&query=Barron%2C+G+S">George S. Barron</a>, <a href="/search/quant-ph?searchtype=author&query=Calderon-Vargas%2C+F+A">F. A. Calderon-Vargas</a>, <a href="/search/quant-ph?searchtype=author&query=Mayhall%2C+N+J">Nicholas J. Mayhall</a>, <a href="/search/quant-ph?searchtype=author&query=Barnes%2C+E">Edwin Barnes</a>, <a href="/search/quant-ph?searchtype=author&query=Economou%2C+S+E">Sophia E. Economou</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2005.10258v3-abstract-short" style="display: inline;"> The quantum approximate optimization algorithm (QAOA) is a hybrid variational quantum-classical algorithm that solves combinatorial optimization problems. While there is evidence suggesting that the fixed form of the standard QAOA ansatz is not optimal, there is no systematic approach for finding better ans盲tze. We address this problem by developing an iterative version of QAOA that is problem-tai… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2005.10258v3-abstract-full').style.display = 'inline'; document.getElementById('2005.10258v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2005.10258v3-abstract-full" style="display: none;"> The quantum approximate optimization algorithm (QAOA) is a hybrid variational quantum-classical algorithm that solves combinatorial optimization problems. While there is evidence suggesting that the fixed form of the standard QAOA ansatz is not optimal, there is no systematic approach for finding better ans盲tze. We address this problem by developing an iterative version of QAOA that is problem-tailored, and which can also be adapted to specific hardware constraints. We simulate the algorithm on a class of Max-Cut graph problems and show that it converges much faster than the standard QAOA, while simultaneously reducing the required number of CNOT gates and optimization parameters. We provide evidence that this speedup is connected to the concept of shortcuts to adiabaticity. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2005.10258v3-abstract-full').style.display = 'none'; document.getElementById('2005.10258v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 July, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 20 May, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">11 pages, 7 figures; v3: additional analysis, analytical results, and simulations of larger systems</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2003.00171">arXiv:2003.00171</a> <span> [<a href="https://arxiv.org/pdf/2003.00171">pdf</a>, <a href="https://arxiv.org/ps/2003.00171">ps</a>, <a href="https://arxiv.org/format/2003.00171">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevApplied.16.034003">10.1103/PhysRevApplied.16.034003 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Preserving Symmetries for Variational Quantum Eigensolvers in the Presence of Noise </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Barron%2C+G+S">George S. Barron</a>, <a href="/search/quant-ph?searchtype=author&query=Gard%2C+B+T">Bryan T. Gard</a>, <a href="/search/quant-ph?searchtype=author&query=Altman%2C+O+J">Orien J. Altman</a>, <a href="/search/quant-ph?searchtype=author&query=Mayhall%2C+N+J">Nicholas J. Mayhall</a>, <a href="/search/quant-ph?searchtype=author&query=Barnes%2C+E">Edwin Barnes</a>, <a href="/search/quant-ph?searchtype=author&query=Economou%2C+S+E">Sophia E. Economou</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2003.00171v1-abstract-short" style="display: inline;"> One of the most promising applications of noisy intermediate-scale quantum computers is the simulation of molecular Hamiltonians using the variational quantum eigensolver. We show that encoding symmetries of the simulated Hamiltonian in the VQE ansatz reduces both classical and quantum resources compared to other, widely available ansatze. Through simulations of the H$_2$ molecule, we verify that… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2003.00171v1-abstract-full').style.display = 'inline'; document.getElementById('2003.00171v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2003.00171v1-abstract-full" style="display: none;"> One of the most promising applications of noisy intermediate-scale quantum computers is the simulation of molecular Hamiltonians using the variational quantum eigensolver. We show that encoding symmetries of the simulated Hamiltonian in the VQE ansatz reduces both classical and quantum resources compared to other, widely available ansatze. Through simulations of the H$_2$ molecule, we verify that these improvements persist in the presence of noise. This simulation is performed with IBM software using noise models from real devices. We also demonstrate how these techniques can be used to find molecular excited states of various symmetries using a noisy processor. We use error mitigation techniques to further improve the quality of our results. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2003.00171v1-abstract-full').style.display = 'none'; document.getElementById('2003.00171v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 28 February, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. Applied 16, 034003 (2021) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1911.10205">arXiv:1911.10205</a> <span> [<a href="https://arxiv.org/pdf/1911.10205">pdf</a>, <a href="https://arxiv.org/format/1911.10205">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PRXQuantum.2.020310">10.1103/PRXQuantum.2.020310 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> qubit-ADAPT-VQE: An adaptive algorithm for constructing hardware-efficient ansatze on a quantum processor </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Tang%2C+H+L">Ho Lun Tang</a>, <a href="/search/quant-ph?searchtype=author&query=Shkolnikov%2C+V+O">V. O. Shkolnikov</a>, <a href="/search/quant-ph?searchtype=author&query=Barron%2C+G+S">George S. Barron</a>, <a href="/search/quant-ph?searchtype=author&query=Grimsley%2C+H+R">Harper R. Grimsley</a>, <a href="/search/quant-ph?searchtype=author&query=Mayhall%2C+N+J">Nicholas J. Mayhall</a>, <a href="/search/quant-ph?searchtype=author&query=Barnes%2C+E">Edwin Barnes</a>, <a href="/search/quant-ph?searchtype=author&query=Economou%2C+S+E">Sophia E. Economou</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1911.10205v2-abstract-short" style="display: inline;"> Quantum simulation, one of the most promising applications of a quantum computer, is currently being explored intensely using the variational quantum eigensolver. The feasibility and performance of this algorithm depend critically on the form of the wavefunction ansatz. Recently in Nat. Commun. 10, 3007 (2019), an algorithm termed ADAPT-VQE was introduced to build system-adapted ans盲tze with subst… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1911.10205v2-abstract-full').style.display = 'inline'; document.getElementById('1911.10205v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1911.10205v2-abstract-full" style="display: none;"> Quantum simulation, one of the most promising applications of a quantum computer, is currently being explored intensely using the variational quantum eigensolver. The feasibility and performance of this algorithm depend critically on the form of the wavefunction ansatz. Recently in Nat. Commun. 10, 3007 (2019), an algorithm termed ADAPT-VQE was introduced to build system-adapted ans盲tze with substantially fewer variational parameters compared to other approaches. This algorithm relies heavily on a predefined operator pool with which it builds the ansatz. However, Nat. Commun. 10, 3007 (2019) did not provide a prescription for how to select the pool, how many operators it must contain, or whether the resulting ansatz will succeed in converging to the ground state. In addition, the pool used in that work leads to state preparation circuits that are too deep for a practical application on near-term devices. Here, we address all these key outstanding issues of the algorithm. We present a hardware-efficient variant of ADAPT-VQE that drastically reduces circuit depths using an operator pool that is guaranteed to contain the operators necessary to construct exact ans盲tze. Moreover, we show that the minimal pool size that achieves this scales linearly with the number of qubits. Through numerical simulations on $\text{H}_4$, LiH and $\text{H}_6$, we show that our algorithm ("qubit-ADAPT") reduces the circuit depth by an order of magnitude while maintaining the same accuracy as the original ADAPT-VQE. A central result of our approach is that the additional measurement overhead of qubit-ADAPT compared to fixed-ansatz variational algorithms scales only linearly with the number of qubits. Our work provides a crucial step forward in running algorithms on near-term quantum devices. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1911.10205v2-abstract-full').style.display = 'none'; document.getElementById('1911.10205v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 16 June, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 22 November, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">15 pages, 6 figures; v2 includes a new proof that the minimal operator pool size scales linearly in the number of qubits. Explicit examples of such pools are also now included</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> PRX Quantum 2, 020310 (2021) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1910.10329">arXiv:1910.10329</a> <span> [<a href="https://arxiv.org/pdf/1910.10329">pdf</a>, <a href="https://arxiv.org/format/1910.10329">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1021/acs.jctc.9b01083">10.1021/acs.jctc.9b01083 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Is the Trotterized UCCSD Ansatz chemically well-defined? </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Grimsley%2C+H+R">Harper R. Grimsley</a>, <a href="/search/quant-ph?searchtype=author&query=Claudino%2C+D">Daniel Claudino</a>, <a href="/search/quant-ph?searchtype=author&query=Economou%2C+S+E">Sophia E. Economou</a>, <a href="/search/quant-ph?searchtype=author&query=Barnes%2C+E">Edwin Barnes</a>, <a href="/search/quant-ph?searchtype=author&query=Mayhall%2C+N+J">Nicholas J. Mayhall</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1910.10329v2-abstract-short" style="display: inline;"> The variational quantum eigensolver (VQE) has emerged as one of the most promising near-term quantum algorithms that can be used to simulate many-body systems such as molecular electronic structures. Serving as an attractive ansatz in the VQE algorithm, unitary coupled cluster (UCC) theory has seen a renewed interest in recent literature. However, unlike the original classical UCC theory, implemen… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1910.10329v2-abstract-full').style.display = 'inline'; document.getElementById('1910.10329v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1910.10329v2-abstract-full" style="display: none;"> The variational quantum eigensolver (VQE) has emerged as one of the most promising near-term quantum algorithms that can be used to simulate many-body systems such as molecular electronic structures. Serving as an attractive ansatz in the VQE algorithm, unitary coupled cluster (UCC) theory has seen a renewed interest in recent literature. However, unlike the original classical UCC theory, implementation on a quantum computer requires a finite-order Suzuki-Trotter decomposition to separate the exponentials of the large sum of Pauli operators. While previous literature has recognized the non-uniqueness of different orderings of the operators in the Trotterized form of UCC methods, the question of whether or not different orderings matter at the chemical scale has not been addressed. In this letter, we explore the effect of operator ordering on the Trotterized UCCSD ansatz, as well as the much more compact $k$-UpCCGSD ansatz recently proposed by Lee et al. We observe a significant, system-dependent variation in the energies of Trotterizations with different operator orderings. The energy variations occur on a chemical scale, sometimes on the order of hundreds of kcal/mol. This letter establishes the need to define not only the operators present in the ansatz, but also the order in which they appear. This is necessary for adhering to the quantum chemical notion of a ``model chemistry'', in addition to the general importance of scientific reproducibility. As a final note, we suggest a useful strategy to select out of the combinatorial number of possibilities, a single well-defined and effective ordering of the operators. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1910.10329v2-abstract-full').style.display = 'none'; document.getElementById('1910.10329v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 February, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 22 October, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">6 pages, 2 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J. Chem. Theory Comput. 2020, 16, 1, 1-6 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1904.10910">arXiv:1904.10910</a> <span> [<a href="https://arxiv.org/pdf/1904.10910">pdf</a>, <a href="https://arxiv.org/format/1904.10910">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1038/s41534-019-0240-1">10.1038/s41534-019-0240-1 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Efficient Symmetry-Preserving State Preparation Circuits for the Variational Quantum Eigensolver Algorithm </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Gard%2C+B+T">Bryan T. Gard</a>, <a href="/search/quant-ph?searchtype=author&query=Zhu%2C+L">Linghua Zhu</a>, <a href="/search/quant-ph?searchtype=author&query=Barron%2C+G+S">George S. Barron</a>, <a href="/search/quant-ph?searchtype=author&query=Mayhall%2C+N+J">Nicholas J. Mayhall</a>, <a href="/search/quant-ph?searchtype=author&query=Economou%2C+S+E">Sophia E. Economou</a>, <a href="/search/quant-ph?searchtype=author&query=Barnes%2C+E">Edwin Barnes</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1904.10910v3-abstract-short" style="display: inline;"> The variational quantum eigensolver is one of the most promising approaches for performing chemistry simulations using noisy intermediate-scale quantum (NISQ) processors. The efficiency of this algorithm depends crucially on the ability to prepare multi-qubit trial states on the quantum processor that either include, or at least closely approximate, the actual energy eigenstates of the problem bei… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1904.10910v3-abstract-full').style.display = 'inline'; document.getElementById('1904.10910v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1904.10910v3-abstract-full" style="display: none;"> The variational quantum eigensolver is one of the most promising approaches for performing chemistry simulations using noisy intermediate-scale quantum (NISQ) processors. The efficiency of this algorithm depends crucially on the ability to prepare multi-qubit trial states on the quantum processor that either include, or at least closely approximate, the actual energy eigenstates of the problem being simulated while avoiding states that have little overlap with them. Symmetries play a central role in determining the best trial states. Here, we present efficient state preparation circuits that respect particle number, total spin, spin projection, and time-reversal symmetries. These circuits contain the minimal number of variational parameters needed to fully span the appropriate symmetry subspace dictated by the chemistry problem while avoiding all irrelevant sectors of Hilbert space. We show how to construct these circuits for arbitrary numbers of orbitals, electrons, and spin quantum numbers, and we provide explicit decompositions and gate counts in terms of standard gate sets in each case. We test our circuits in quantum simulations of the $H_2$ and $LiH$ molecules and find that they outperform standard state preparation methods in terms of both accuracy and circuit depth. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1904.10910v3-abstract-full').style.display = 'none'; document.getElementById('1904.10910v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 January, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 24 April, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">19 pages, 15 figures (v3 significant updates to match published version)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> npj Quantum Inf 6, 10 (2020) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1812.11173">arXiv:1812.11173</a> <span> [<a href="https://arxiv.org/pdf/1812.11173">pdf</a>, <a href="https://arxiv.org/format/1812.11173">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Strongly Correlated Electrons">cond-mat.str-el</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Chemical Physics">physics.chem-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1038/s41467-019-10988-2">10.1038/s41467-019-10988-2 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> An adaptive variational algorithm for exact molecular simulations on a quantum computer </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Grimsley%2C+H+R">Harper R. Grimsley</a>, <a href="/search/quant-ph?searchtype=author&query=Economou%2C+S+E">Sophia E. Economou</a>, <a href="/search/quant-ph?searchtype=author&query=Barnes%2C+E">Edwin Barnes</a>, <a href="/search/quant-ph?searchtype=author&query=Mayhall%2C+N+J">Nicholas J. Mayhall</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1812.11173v2-abstract-short" style="display: inline;"> Quantum simulation of chemical systems is one of the most promising near-term applications of quantum computers. The variational quantum eigensolver, a leading algorithm for molecular simulations on quantum hardware, has a serious limitation in that it typically relies on a pre-selected wavefunction ansatz that results in approximate wavefunctions and energies. Here we present an arbitrarily accur… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1812.11173v2-abstract-full').style.display = 'inline'; document.getElementById('1812.11173v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1812.11173v2-abstract-full" style="display: none;"> Quantum simulation of chemical systems is one of the most promising near-term applications of quantum computers. The variational quantum eigensolver, a leading algorithm for molecular simulations on quantum hardware, has a serious limitation in that it typically relies on a pre-selected wavefunction ansatz that results in approximate wavefunctions and energies. Here we present an arbitrarily accurate variational algorithm that instead of fixing an ansatz upfront, this algorithm grows it systematically one operator at a time in a way dictated by the molecule being simulated. This generates an ansatz with a small number of parameters, leading to shallow-depth circuits. We present numerical simulations, including for a prototypical strongly correlated molecule, which show that our algorithm performs much better than a unitary coupled cluster approach, in terms of both circuit depth and chemical accuracy. Our results highlight the potential of our adaptive algorithm for exact simulations with present-day and near-term quantum hardware. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1812.11173v2-abstract-full').style.display = 'none'; document.getElementById('1812.11173v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 13 July, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 28 December, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">11 pages, 3 figures; published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Nature Communications 10, 3007 (2019) </p> </li> </ol> <div class="is-hidden-tablet">  <span class="help" style="display: inline-block;"><a href="https://github.com/arXiv/arxiv-search/releases">Search v0.5.6 released 2020-02-24</a>  </span> </div> </div> </main> <footer> <div class="columns is-desktop" role="navigation" aria-label="Secondary">  <div class="column"> <div class="columns"> <div class="column"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/about">About</a></li> <li><a href="https://info.arxiv.org/help">Help</a></li> </ul> </div> <div class="column"> <ul class="nav-spaced"> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>contact arXiv</title><desc>Click here to contact arXiv</desc><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 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