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<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/2409.13510">arXiv:2409.13510</a> <span> [<a href="https://arxiv.org/pdf/2409.13510">pdf</a>, <a href="https://arxiv.org/format/2409.13510">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"> Simulating the Schwinger Model with a Regularized Variational Quantum Imaginary Time Evolution </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Li%2C+X">Xiao-Wei Li</a>, <a href="/search/quant-ph?searchtype=author&query=Li%2C+F">Fei Li</a>, <a href="/search/quant-ph?searchtype=author&query=Zhuang%2C+J">Jiapei Zhuang</a>, <a href="/search/quant-ph?searchtype=author&query=Yung%2C+M">Man-Hong Yung</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="2409.13510v1-abstract-short" style="display: inline;"> The Schwinger model serves as a benchmark for testing non-perturbative algorithms in quantum chromodynamics (QCD), emphasizing its similarities to QCD in strong coupling regimes, primarily due to the phenomena such as confinement and charge screening. However, classical algorithms encounter challenges when simulating the Schwinger model, such as the "sign problem" and the difficulty in handling la… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2409.13510v1-abstract-full').style.display = 'inline'; document.getElementById('2409.13510v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2409.13510v1-abstract-full" style="display: none;"> The Schwinger model serves as a benchmark for testing non-perturbative algorithms in quantum chromodynamics (QCD), emphasizing its similarities to QCD in strong coupling regimes, primarily due to the phenomena such as confinement and charge screening. However, classical algorithms encounter challenges when simulating the Schwinger model, such as the "sign problem" and the difficulty in handling large-scale systems. These limitations motivate the exploration of alternative simulation approaches, including quantum computing techniques, to overcome the obstacles. While existing variational quantum algorithms (VQAs) methods for simulating the Schwinger model primarily rely on mathematical gradient-based optimization, which sometimes fail to provide intuitive and physically-guided optimization pathways. In contrast, the Variational Quantum Imaginary Time Evolution (VQITE) method offers a physically-inspired optimization approach. Therefore, we introduce that VQITE holds promise as a potent tool for simulating the Schwinger model. However, the standard VQITE method is not sufficiently stable, as it encounters difficulties with the non-invertible matrix problem. To address this issue, we have proposed a regularized version of the VQITE, which we have named the Regularized-VQITE (rVQITE) method, as it incorporates a truncation-based approach. Through numerical simulations, we demonstrate that our proposed rVQITE approach achieves better performance and exhibits faster convergence compared to other related techniques. We employ the rVQITE method to simulate the phase diagrams of various physical observables in the Schwinger model, and the resulting phase boundaries are in agreement with those obtained from an exact computational approach. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2409.13510v1-abstract-full').style.display = 'none'; document.getElementById('2409.13510v1-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> 20 September, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2407.17706">arXiv:2407.17706</a> <span> [<a href="https://arxiv.org/pdf/2407.17706">pdf</a>, <a href="https://arxiv.org/format/2407.17706">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="Machine Learning">cs.LG</span> </div> </div> <p class="title is-5 mathjax"> Investigating and Mitigating Barren Plateaus in Variational Quantum Circuits: A Survey </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Cunningham%2C+J">Jack Cunningham</a>, <a href="/search/quant-ph?searchtype=author&query=Zhuang%2C+J">Jun Zhuang</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="2407.17706v1-abstract-short" style="display: inline;"> In recent years, variational quantum circuits (VQCs) have been widely explored to advance quantum circuits against classic models on various domains, such as quantum chemistry and quantum machine learning. Similar to classic machine-learning models, VQCs can be optimized through gradient-based approaches. However, the gradient variance of VQCs may dramatically vanish as the number of qubits or lay… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2407.17706v1-abstract-full').style.display = 'inline'; document.getElementById('2407.17706v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2407.17706v1-abstract-full" style="display: none;"> In recent years, variational quantum circuits (VQCs) have been widely explored to advance quantum circuits against classic models on various domains, such as quantum chemistry and quantum machine learning. Similar to classic machine-learning models, VQCs can be optimized through gradient-based approaches. However, the gradient variance of VQCs may dramatically vanish as the number of qubits or layers increases. This issue, a.k.a. Barren Plateaus (BPs), seriously hinders the scaling of VQCs on large datasets. To mitigate the exponential gradient vanishing, extensive efforts have been devoted to tackling this issue through diverse strategies. In this survey, we conduct a systematic literature review of recent works from both investigation and mitigation perspectives. Besides, we propose a new taxonomy to categorize most existing mitigation strategies. At last, we provide insightful discussion for future directions of BPs. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2407.17706v1-abstract-full').style.display = 'none'; document.getElementById('2407.17706v1-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 July, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 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">preprint, under review. Please feel free to reach out if your work fits within our scope</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2407.03116">arXiv:2407.03116</a> <span> [<a href="https://arxiv.org/pdf/2407.03116">pdf</a>, <a href="https://arxiv.org/format/2407.03116">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"> Hardware-efficient variational quantum algorithm in trapped-ion quantum computer </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Zhuang%2C+J+-">J. -Z. Zhuang</a>, <a href="/search/quant-ph?searchtype=author&query=Wu%2C+Y+-">Y. -K. Wu</a>, <a href="/search/quant-ph?searchtype=author&query=Duan%2C+L+-">L. -M. Duan</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="2407.03116v1-abstract-short" style="display: inline;"> We study a hardware-efficient variational quantum algorithm ansatz tailored for the trapped-ion quantum simulator, HEA-TI. We leverage programmable single-qubit rotations and global spin-spin interactions among all ions, reducing the dependence on resource-intensive two-qubit gates in conventional gate-based methods. We apply HEA-TI to state engineering of cluster states and analyze the scaling of… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2407.03116v1-abstract-full').style.display = 'inline'; document.getElementById('2407.03116v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2407.03116v1-abstract-full" style="display: none;"> We study a hardware-efficient variational quantum algorithm ansatz tailored for the trapped-ion quantum simulator, HEA-TI. We leverage programmable single-qubit rotations and global spin-spin interactions among all ions, reducing the dependence on resource-intensive two-qubit gates in conventional gate-based methods. We apply HEA-TI to state engineering of cluster states and analyze the scaling of required quantum resources. We also apply HEA-TI to solve the ground state problem of chemical molecules $\mathrm{H_{2}}$, $\mathrm{LiH}$ and $\mathrm{F_{2}}$. We numerically analyze the quantum computing resources required to achieve chemical accuracy and examine the performance under realistic experimental noise and statistical fluctuation. The efficiency of this ansatz is shown to be comparable to other commonly used variational ansatzes like UCCSD, with the advantage of substantially easier implementation in the trapped-ion quantum simulator. This approach showcases the hardware-efficient ansatz as a powerful tool for the application of the near-term quantum computer. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2407.03116v1-abstract-full').style.display = 'none'; document.getElementById('2407.03116v1-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> 3 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/2405.01606">arXiv:2405.01606</a> <span> [<a href="https://arxiv.org/pdf/2405.01606">pdf</a>, <a href="https://arxiv.org/format/2405.01606">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="Machine Learning">cs.LG</span> </div> </div> <p class="title is-5 mathjax"> Improving Trainability of Variational Quantum Circuits via Regularization Strategies </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Zhuang%2C+J">Jun Zhuang</a>, <a href="/search/quant-ph?searchtype=author&query=Cunningham%2C+J">Jack Cunningham</a>, <a href="/search/quant-ph?searchtype=author&query=Guan%2C+C">Chaowen Guan</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="2405.01606v1-abstract-short" style="display: inline;"> In the era of noisy intermediate-scale quantum (NISQ), variational quantum circuits (VQCs) have been widely applied in various domains, advancing the superiority of quantum circuits against classic models. Similar to classic models, regular VQCs can be optimized by various gradient-based methods. However, the optimization may be initially trapped in barren plateaus or eventually entangled in saddl… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2405.01606v1-abstract-full').style.display = 'inline'; document.getElementById('2405.01606v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2405.01606v1-abstract-full" style="display: none;"> In the era of noisy intermediate-scale quantum (NISQ), variational quantum circuits (VQCs) have been widely applied in various domains, advancing the superiority of quantum circuits against classic models. Similar to classic models, regular VQCs can be optimized by various gradient-based methods. However, the optimization may be initially trapped in barren plateaus or eventually entangled in saddle points during training. These gradient issues can significantly undermine the trainability of VQC. In this work, we propose a strategy that regularizes model parameters with prior knowledge of the train data and Gaussian noise diffusion. We conduct ablation studies to verify the effectiveness of our strategy across four public datasets and demonstrate that our method can improve the trainability of VQCs against the above-mentioned gradient issues. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2405.01606v1-abstract-full').style.display = 'none'; document.getElementById('2405.01606v1-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> 1 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">preprint, under review. TL;DR: we propose a regularization strategy to improve the trainability of VQCs</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2304.01256">arXiv:2304.01256</a> <span> [<a href="https://arxiv.org/pdf/2304.01256">pdf</a>, <a href="https://arxiv.org/format/2304.01256">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="Other Condensed Matter">cond-mat.other</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.5.L042043">10.1103/PhysRevResearch.5.L042043 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Dynamical phase transitions of information flow in random quantum circuits </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Zhuang%2C+J+-">J. -Z. Zhuang</a>, <a href="/search/quant-ph?searchtype=author&query=Wu%2C+Y+-">Y. -K. Wu</a>, <a href="/search/quant-ph?searchtype=author&query=Duan%2C+L+-">L. -M. Duan</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="2304.01256v2-abstract-short" style="display: inline;"> We study how the information flows in many-body dynamics governed by random quantum circuits and discover a rich set of dynamical phase transitions in this information flow. The phase transition points and their critical exponents are established across Clifford and Haar random circuits through finite-size scaling. The flow of both classical and quantum information, measured respectively by Holevo… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2304.01256v2-abstract-full').style.display = 'inline'; document.getElementById('2304.01256v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2304.01256v2-abstract-full" style="display: none;"> We study how the information flows in many-body dynamics governed by random quantum circuits and discover a rich set of dynamical phase transitions in this information flow. The phase transition points and their critical exponents are established across Clifford and Haar random circuits through finite-size scaling. The flow of both classical and quantum information, measured respectively by Holevo and coherent information, shows similar dynamical phase transition behaviors. We investigate how the phase transitions depend on the initial location of the information and the final probe region, and find ubiquitous behaviors in these transitions, revealing interesting properties about the information propagation and scrambling in this quantum many-body model. Our work underscores rich behaviors of the information flow in large systems with numerous phase transitions, thereby sheds new light on the understanding of quantum many-body dynamics. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2304.01256v2-abstract-full').style.display = 'none'; document.getElementById('2304.01256v2-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 November, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 3 April, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 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">11 pages, 12 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/2205.14169">arXiv:2205.14169</a> <span> [<a href="https://arxiv.org/pdf/2205.14169">pdf</a>, <a href="https://arxiv.org/format/2205.14169">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="Other Condensed Matter">cond-mat.other</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/PhysRevB.106.144308">10.1103/PhysRevB.106.144308 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Phase-transition-like behavior in information retrieval of a quantum scrambled random circuit system </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Zhuang%2C+J+-">J. -Z. Zhuang</a>, <a href="/search/quant-ph?searchtype=author&query=Wu%2C+Y+-">Y. -K. Wu</a>, <a href="/search/quant-ph?searchtype=author&query=Duan%2C+L+-">L. -M. Duan</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="2205.14169v3-abstract-short" style="display: inline;"> Information in a chaotic quantum system will scramble across the system, preventing any local measurement from reconstructing it. The scrambling dynamics is key to understanding a wide range of quantum many-body systems. Here we use Holevo information to quantify the scrambling dynamics, which shows a phase-transition-like behavior. When applying long random Clifford circuits to a large system, no… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2205.14169v3-abstract-full').style.display = 'inline'; document.getElementById('2205.14169v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2205.14169v3-abstract-full" style="display: none;"> Information in a chaotic quantum system will scramble across the system, preventing any local measurement from reconstructing it. The scrambling dynamics is key to understanding a wide range of quantum many-body systems. Here we use Holevo information to quantify the scrambling dynamics, which shows a phase-transition-like behavior. When applying long random Clifford circuits to a large system, no information can be recovered from a subsystem of less than half the system size. When exceeding half the system size, the amount of stored information grows by two bits of classical information per qubit until saturation through another sharp unanalytical change. We also study critical behavior near the transition points. Finally, we use coherent information to quantify the scrambling of quantum information in the system, which shows similar phase-transition-like behavior. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2205.14169v3-abstract-full').style.display = 'none'; document.getElementById('2205.14169v3-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 October, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 27 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">10 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/2111.11007">arXiv:2111.11007</a> <span> [<a href="https://arxiv.org/pdf/2111.11007">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Materials Science">cond-mat.mtrl-sci</span> <span class="tag is-small is-grey 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.17.064017">10.1103/PhysRevApplied.17.064017 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Facet Dependent Topological Phase Transition in Bi4Br4 </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Zhong%2C+J">Jingyuan Zhong</a>, <a href="/search/quant-ph?searchtype=author&query=Yang%2C+M">Ming Yang</a>, <a href="/search/quant-ph?searchtype=author&query=Ye%2C+F">Fei Ye</a>, <a href="/search/quant-ph?searchtype=author&query=Liu%2C+C">Chen Liu</a>, <a href="/search/quant-ph?searchtype=author&query=Wang%2C+J">Jiaou Wang</a>, <a href="/search/quant-ph?searchtype=author&query=Hao%2C+W">Weichang Hao</a>, <a href="/search/quant-ph?searchtype=author&query=Zhuang%2C+J">Jincheng Zhuang</a>, <a href="/search/quant-ph?searchtype=author&query=Du%2C+Y">Yi Du</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="2111.11007v1-abstract-short" style="display: inline;"> The realization of the coexistence of various topologically nontrivial surface states in one material is expected to lay a foundation for new electric applications with selective robust spin current. Here we apply the magnetoconductivity characteristic and angle-resolved photoemission spectroscopy (ARPES) to visualize the surface-selected electronic features evolution of quasi-one-dimensional mate… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2111.11007v1-abstract-full').style.display = 'inline'; document.getElementById('2111.11007v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2111.11007v1-abstract-full" style="display: none;"> The realization of the coexistence of various topologically nontrivial surface states in one material is expected to lay a foundation for new electric applications with selective robust spin current. Here we apply the magnetoconductivity characteristic and angle-resolved photoemission spectroscopy (ARPES) to visualize the surface-selected electronic features evolution of quasi-one-dimensional material Bi4Br4. The transport measurements indicate the quantum interference correction to conductivity possesses symbolic spin rotational characteristic correlated to the value of Berry phase with the effects of weak localization and weak antilocalization for (001) and (100) surfaces, respectively. The ARPES spectra provide the experimental evidence for quasi-one-dimensional massless Dirac surface state at the side (100) surface and anisotropic massive Dirac surface state at the top (001) surface, respectively, which is highly coincide with the angle-dependent scaling behavior of magnetoconductivity. Our results reveal the facet dependent topological phases in quasi-one-dimensional Bi4Br4, stimulating the further investigations of this dual topology classes and the applications of the feasible technologies of topological spintronics. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2111.11007v1-abstract-full').style.display = 'none'; document.getElementById('2111.11007v1-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> 22 November, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Physical Review Applied 17, 064017 (2022) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2106.06144">arXiv:2106.06144</a> <span> [<a href="https://arxiv.org/pdf/2106.06144">pdf</a>, <a href="https://arxiv.org/format/2106.06144">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Atomic Physics">physics.atom-ph</span> <span class="tag is-small is-grey 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/PhysRevLett.128.083202">10.1103/PhysRevLett.128.083202 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Defect-free arbitrary-geometry assembly of mixed-species atom arrays </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Sheng%2C+C">Cheng Sheng</a>, <a href="/search/quant-ph?searchtype=author&query=Hou%2C+J">Jiayi Hou</a>, <a href="/search/quant-ph?searchtype=author&query=He%2C+X">Xiaodong He</a>, <a href="/search/quant-ph?searchtype=author&query=Wang%2C+K">Kunpeng Wang</a>, <a href="/search/quant-ph?searchtype=author&query=Guo%2C+R">Ruijun Guo</a>, <a href="/search/quant-ph?searchtype=author&query=Zhuang%2C+J">Jun Zhuang</a>, <a href="/search/quant-ph?searchtype=author&query=Mamat%2C+B">Bahtiyar Mamat</a>, <a href="/search/quant-ph?searchtype=author&query=Xu%2C+P">Peng Xu</a>, <a href="/search/quant-ph?searchtype=author&query=Liu%2C+M">Min Liu</a>, <a href="/search/quant-ph?searchtype=author&query=Wang%2C+J">Jin Wang</a>, <a href="/search/quant-ph?searchtype=author&query=Zhan%2C+M">Mingsheng Zhan</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="2106.06144v1-abstract-short" style="display: inline;"> Optically trapped mixed-species single atom arrays with arbitrary geometries are an attractive and promising platform for various applications, because tunable quantum systems with multiple components provide extra degrees of freedom for experimental control. Here, we report the first demonstration of two-dimensional $6\times4$ dual-species atom assembly with a filling fraction of 0.88 (0.89) for… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2106.06144v1-abstract-full').style.display = 'inline'; document.getElementById('2106.06144v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2106.06144v1-abstract-full" style="display: none;"> Optically trapped mixed-species single atom arrays with arbitrary geometries are an attractive and promising platform for various applications, because tunable quantum systems with multiple components provide extra degrees of freedom for experimental control. Here, we report the first demonstration of two-dimensional $6\times4$ dual-species atom assembly with a filling fraction of 0.88 (0.89) for $^{85}$Rb ($^{87}$Rb) atoms. This mixed-species atomic synthetic is achieved via rearranging initially randomly distributed atoms using a sorting algorithm (heuristic heteronuclear algorithm) which is proposed for bottom-up atom assembly with both user-defined geometries and two-species atom number ratios. Our fully tunable hybrid-atom system of scalable advantages is a good starting point for high-fidelity quantum logic, many-body quantum simulation and forming defect-free single molecule arrays. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2106.06144v1-abstract-full').style.display = 'none'; document.getElementById('2106.06144v1-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 June, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. Lett. 128, 083202 (2022) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2011.10390">arXiv:2011.10390</a> <span> [<a href="https://arxiv.org/pdf/2011.10390">pdf</a>, <a href="https://arxiv.org/format/2011.10390">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="Atomic Physics">physics.atom-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.3.023008">10.1103/PhysRevResearch.3.023008 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Efficient preparation of 2D defect-free atom arrays with near-fewest sorting-atom moves </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Sheng%2C+C">Cheng Sheng</a>, <a href="/search/quant-ph?searchtype=author&query=Hou%2C+J">Jiayi Hou</a>, <a href="/search/quant-ph?searchtype=author&query=He%2C+X">Xiaodong He</a>, <a href="/search/quant-ph?searchtype=author&query=Xu%2C+P">Peng Xu</a>, <a href="/search/quant-ph?searchtype=author&query=Wang%2C+K">Kunpeng Wang</a>, <a href="/search/quant-ph?searchtype=author&query=Zhuang%2C+J">Jun Zhuang</a>, <a href="/search/quant-ph?searchtype=author&query=Li%2C+X">Xiao Li</a>, <a href="/search/quant-ph?searchtype=author&query=Liu%2C+M">Min Liu</a>, <a href="/search/quant-ph?searchtype=author&query=Wang%2C+J">Jin Wang</a>, <a href="/search/quant-ph?searchtype=author&query=Zhan%2C+M">Mingsheng Zhan</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="2011.10390v2-abstract-short" style="display: inline;"> Sorting atoms stochastically loaded in optical tweezer arrays via an auxiliary mobile tweezer is an efficient approach to preparing intermediate-scale defect-free atom arrays in arbitrary geometries. However, high filling fraction of atom-by-atom assemblers is impeded by redundant sorting moves with imperfect atom transport, especially for scaling the system size to larger atom numbers. Here, we p… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2011.10390v2-abstract-full').style.display = 'inline'; document.getElementById('2011.10390v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2011.10390v2-abstract-full" style="display: none;"> Sorting atoms stochastically loaded in optical tweezer arrays via an auxiliary mobile tweezer is an efficient approach to preparing intermediate-scale defect-free atom arrays in arbitrary geometries. However, high filling fraction of atom-by-atom assemblers is impeded by redundant sorting moves with imperfect atom transport, especially for scaling the system size to larger atom numbers. Here, we propose a new sorting algorithm (heuristic cluster algorithm, HCA) which provides near-fewest moves in our tailored atom assembler scheme and experimentally demonstrate a $5\times6$ defect-free atom array with 98.4(7)$\%$ filling fraction for one rearrangement cycle. The feature of HCA that the number of moves $N_{m}\approx N$ ($N$ is the number of defect sites to be filled) makes the filling fraction uniform as the size of atom assembler enlarged. Our method is essential to scale hundreds of assembled atoms for bottom-up quantum computation, quantum simulation and precision measurement. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2011.10390v2-abstract-full').style.display = 'none'; document.getElementById('2011.10390v2-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> 3 December, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 20 November, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. Research 3, 023008 (2021) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2001.01045">arXiv:2001.01045</a> <span> [<a href="https://arxiv.org/pdf/2001.01045">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Materials Science">cond-mat.mtrl-sci</span> <span class="tag is-small is-grey 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.nanolett.9b05316">10.1021/acs.nanolett.9b05316 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Experimental Realization of Two-Dimensional Buckled Lieb lattice </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Feng%2C+H">Haifeng Feng</a>, <a href="/search/quant-ph?searchtype=author&query=Liu%2C+C">Chen Liu</a>, <a href="/search/quant-ph?searchtype=author&query=Zhou%2C+S">Si Zhou</a>, <a href="/search/quant-ph?searchtype=author&query=Gao%2C+N">Nan Gao</a>, <a href="/search/quant-ph?searchtype=author&query=Gao%2C+Q">Qian Gao</a>, <a href="/search/quant-ph?searchtype=author&query=Zhuang%2C+J">Jincheng Zhuang</a>, <a href="/search/quant-ph?searchtype=author&query=Xu%2C+X">Xun Xu</a>, <a href="/search/quant-ph?searchtype=author&query=Hu%2C+Z">Zhenpeng Hu</a>, <a href="/search/quant-ph?searchtype=author&query=Wang%2C+J">Jiaou Wang</a>, <a href="/search/quant-ph?searchtype=author&query=Chen%2C+L">Lan Chen</a>, <a href="/search/quant-ph?searchtype=author&query=Zhao%2C+J">Jijun Zhao</a>, <a href="/search/quant-ph?searchtype=author&query=Du%2C+Y">Yi Du</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="2001.01045v1-abstract-short" style="display: inline;"> Two-dimensional (2D) materials with a Lieb lattice can host exotic electronic band structures. Such a system does not exist in nature, and it is also difficult to obtain in the laboratory due to its structural instability. Here, we experimentally realized a 2D system composed of a tin overlayer on an aluminum substrate by molecular beam epitaxy. The specific arrangement of Sn atoms on the Al(100)… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2001.01045v1-abstract-full').style.display = 'inline'; document.getElementById('2001.01045v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2001.01045v1-abstract-full" style="display: none;"> Two-dimensional (2D) materials with a Lieb lattice can host exotic electronic band structures. Such a system does not exist in nature, and it is also difficult to obtain in the laboratory due to its structural instability. Here, we experimentally realized a 2D system composed of a tin overlayer on an aluminum substrate by molecular beam epitaxy. The specific arrangement of Sn atoms on the Al(100) surface, which benefits from favorable interface interactions, forms a stabilized buckled Lieb lattice. Our theoretical calculations indicate a partially broken nodal line loop protected by its mirror reflection symmetry and a topologically nontrivial insulating state with a spin-orbital coupling (SOC) effect in the band structure of this Lieb lattice. The electronic structure of this system has also been experimentally characterized by scanning tunnelling spectroscopy and angle-resolved photoemmision spectroscopy. Our work provides an appealing method for constructing 2D quantum materials based on the Lieb lattice. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2001.01045v1-abstract-full').style.display = 'none'; document.getElementById('2001.01045v1-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> 4 January, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 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">14 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/1907.12722">arXiv:1907.12722</a> <span> [<a href="https://arxiv.org/pdf/1907.12722">pdf</a>, <a href="https://arxiv.org/ps/1907.12722">ps</a>, <a href="https://arxiv.org/format/1907.12722">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="Atomic Physics">physics.atom-ph</span> </div> </div> <p class="title is-5 mathjax"> Revealing Energy Dependence of Quantum Defects via Two Heteronuclear Atoms in an Optical Tweezer </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Wang%2C+K">Kunpeng Wang</a>, <a href="/search/quant-ph?searchtype=author&query=He%2C+X">Xiaodong He</a>, <a href="/search/quant-ph?searchtype=author&query=Gao%2C+X">Xiang Gao</a>, <a href="/search/quant-ph?searchtype=author&query=Guo%2C+R">Ruijun Guo</a>, <a href="/search/quant-ph?searchtype=author&query=Xu%2C+P">Peng Xu</a>, <a href="/search/quant-ph?searchtype=author&query=Zhuang%2C+J">Jun Zhuang</a>, <a href="/search/quant-ph?searchtype=author&query=Li%2C+R">Runbing Li</a>, <a href="/search/quant-ph?searchtype=author&query=Liu%2C+M">Min Liu</a>, <a href="/search/quant-ph?searchtype=author&query=Wang%2C+J">Jin Wang</a>, <a href="/search/quant-ph?searchtype=author&query=Li%2C+J">Jiaming Li</a>, <a href="/search/quant-ph?searchtype=author&query=Zhan%2C+M">Mingsheng Zhan</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="1907.12722v1-abstract-short" style="display: inline;"> As a physically motivated and computationally simple model for cold atomic and molecular collisions, the multichannel quantum defect theory (MQDT) with frame transformation (FT) formalism provides an analytical treatment of scattering resonances in an arbitrary partial wave between alkali-metal atoms, leading to the experimental observation of $p-$ and $d-$wave resonances. However, the inconsisten… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1907.12722v1-abstract-full').style.display = 'inline'; document.getElementById('1907.12722v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1907.12722v1-abstract-full" style="display: none;"> As a physically motivated and computationally simple model for cold atomic and molecular collisions, the multichannel quantum defect theory (MQDT) with frame transformation (FT) formalism provides an analytical treatment of scattering resonances in an arbitrary partial wave between alkali-metal atoms, leading to the experimental observation of $p-$ and $d-$wave resonances. However, the inconsistency of quantum defects for describing scattering resonances shows up when compared with experiments. Here, with two heteronuclear atoms in the ground state of an optical tweezer, the energy dependence of quantum defects is obviously revealed by comparing the measured s-wave scattering length with the prediction of MQDT-FT. By dividing the quantum defects into energy sensitive and insensitive categories, the inconsistency is ultimately removed while retaining the analytic structure of MQDT-FT. This study represents a significant improvement in the analytical MQDT-FT and demonstrates that a clean two-particle system is valuable to the test of collisional physics. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1907.12722v1-abstract-full').style.display = 'none'; document.getElementById('1907.12722v1-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 July, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 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,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/1902.04284">arXiv:1902.04284</a> <span> [<a href="https://arxiv.org/pdf/1902.04284">pdf</a>, <a href="https://arxiv.org/format/1902.04284">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Atomic Physics">physics.atom-ph</span> <span class="tag is-small is-grey 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/PhysRevA.100.063429">10.1103/PhysRevA.100.063429 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Preparation of a Heteronuclear Two-atom System in the 3D Motional Ground State in an Optical Tweezer </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Wang%2C+K">Kunpeng Wang</a>, <a href="/search/quant-ph?searchtype=author&query=He%2C+X">Xiaodong He</a>, <a href="/search/quant-ph?searchtype=author&query=Guo%2C+R">Ruijun Guo</a>, <a href="/search/quant-ph?searchtype=author&query=Xu%2C+P">Peng Xu</a>, <a href="/search/quant-ph?searchtype=author&query=Sheng%2C+C">Cheng Sheng</a>, <a href="/search/quant-ph?searchtype=author&query=Zhuang%2C+J">Jun Zhuang</a>, <a href="/search/quant-ph?searchtype=author&query=Xiong%2C+Z">Zongyuan Xiong</a>, <a href="/search/quant-ph?searchtype=author&query=Liu%2C+M">Min Liu</a>, <a href="/search/quant-ph?searchtype=author&query=Wang%2C+J">Jin Wang</a>, <a href="/search/quant-ph?searchtype=author&query=Zhan%2C+M">Mingsheng Zhan</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="1902.04284v2-abstract-short" style="display: inline;"> We report the realization of a heteronuclear two-atom of $^{87}$Rb-$^{85}$Rb in the ground state of an optical tweezer (OT). Starting by trapping two different isotopic single atoms, a $^{87}$Rb and a $^{85}$Rb in two strongly focused and linearly polarized OT with 4 $渭$m apart, we perform simultaneously three dimensional Raman sideband cooling for both atoms and the obtained 3D ground state proba… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1902.04284v2-abstract-full').style.display = 'inline'; document.getElementById('1902.04284v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1902.04284v2-abstract-full" style="display: none;"> We report the realization of a heteronuclear two-atom of $^{87}$Rb-$^{85}$Rb in the ground state of an optical tweezer (OT). Starting by trapping two different isotopic single atoms, a $^{87}$Rb and a $^{85}$Rb in two strongly focused and linearly polarized OT with 4 $渭$m apart, we perform simultaneously three dimensional Raman sideband cooling for both atoms and the obtained 3D ground state probabilities of $^{87}$Rb and $^{85}$Rb are 0.91(5) and 0.91(10) respectively. There is no obvious crosstalk observed during the cooling process. We then merge them into one tweezer via a species-dependent transport, where the species-dependent potentials are made by changing the polarization of the OTs for each species from linear polarization to the desired circular polarization. The measurable increment of vibrational quantum due to merging is $0.013(1)$ for the axial dimension. This two-atom system can be used to investigate cold collisional physics, to form quantum logic gates, and to build a single heteronuclear molecule. It can also be scaled up to few-atom regime and extended to other atomic species and molecules, and thus to ultracold chemistry. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1902.04284v2-abstract-full').style.display = 'none'; document.getElementById('1902.04284v2-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 December, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 12 February, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 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">10 pages, 11 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. A 100, 063429 (2019) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1201.1962">arXiv:1201.1962</a> <span> [<a href="https://arxiv.org/pdf/1201.1962">pdf</a>, <a href="https://arxiv.org/ps/1201.1962">ps</a>, <a href="https://arxiv.org/format/1201.1962">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/10.1088/1674-1056/22/9/090310">10.1088/1674-1056/22/9/090310 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Accelerating an adiabatic process by nonlinear sweeping </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Cao%2C+X">Xingxin Cao</a>, <a href="/search/quant-ph?searchtype=author&query=Zhuang%2C+J">Jun Zhuang</a>, <a href="/search/quant-ph?searchtype=author&query=Ning%2C+X+-">X. -J. Ning</a>, <a href="/search/quant-ph?searchtype=author&query=Zhang%2C+W">Wenxian Zhang</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="1201.1962v1-abstract-short" style="display: inline;"> We investigate the acceleration of an adiabatic process with the same survival probability of the ground state by sweeping a parameter nonlinearly, fast in the wide gap region and slow in the narrow gap region, as contrast to the usual linear sweeping. We find the expected acceleration in the Laudau-Zener tunneling model and in the adiabatic quantum computing model for factorizing the number N=21. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1201.1962v1-abstract-full" style="display: none;"> We investigate the acceleration of an adiabatic process with the same survival probability of the ground state by sweeping a parameter nonlinearly, fast in the wide gap region and slow in the narrow gap region, as contrast to the usual linear sweeping. We find the expected acceleration in the Laudau-Zener tunneling model and in the adiabatic quantum computing model for factorizing the number N=21. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1201.1962v1-abstract-full').style.display = 'none'; document.getElementById('1201.1962v1-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 January, 2012; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2012. </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">4 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/1201.1779">arXiv:1201.1779</a> <span> [<a href="https://arxiv.org/pdf/1201.1779">pdf</a>, <a href="https://arxiv.org/ps/1201.1779">ps</a>, <a href="https://arxiv.org/format/1201.1779">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Gases">cond-mat.quant-gas</span> <span class="tag is-small is-grey 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/PhysRevA.85.053646">10.1103/PhysRevA.85.053646 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Manipulating dipolar and spin-exchange interactions in spin-1 Bose-Einstein condensates </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Ning%2C+B">Bo-Yuan Ning</a>, <a href="/search/quant-ph?searchtype=author&query=Yi%2C+S">S. Yi</a>, <a href="/search/quant-ph?searchtype=author&query=Zhuang%2C+J">Jun Zhuang</a>, <a href="/search/quant-ph?searchtype=author&query=You%2C+J+Q">J. Q. You</a>, <a href="/search/quant-ph?searchtype=author&query=Zhang%2C+W">Wenxian Zhang</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="1201.1779v3-abstract-short" style="display: inline;"> It remains a challenge to independently manipulate the magnetic dipolar and the spin-exchange interactions, which are entangled in many spin systems, particularly in spin-1 Bose-Einstein condensates. For this purpose, we put forward a sequence of rf pulses and the periodic dynamical decoupling sequence of optical Feshbach resonance pulses to control the dipolar and the spin-exchange interactions,… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1201.1779v3-abstract-full').style.display = 'inline'; document.getElementById('1201.1779v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1201.1779v3-abstract-full" style="display: none;"> It remains a challenge to independently manipulate the magnetic dipolar and the spin-exchange interactions, which are entangled in many spin systems, particularly in spin-1 Bose-Einstein condensates. For this purpose, we put forward a sequence of rf pulses and the periodic dynamical decoupling sequence of optical Feshbach resonance pulses to control the dipolar and the spin-exchange interactions, respectively. Our analytic results and the numerical simulations demonstrate that either of the two interactions can be suppressed to make the other dominate the spin dynamics; furthermore, both of the interactions can be simultaneously suppressed to realize spinor-condensate-based magnetometers with a higher sensitivity. This manipulation method may find its wide applications in magnetic resonance and spintronics. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1201.1779v3-abstract-full').style.display = 'none'; document.getElementById('1201.1779v3-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 May, 2012; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 9 January, 2012; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2012. </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">To be published in PRA (5pages, 5 figures,)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. A 85, 053646 (2012) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1110.3396">arXiv:1110.3396</a> <span> [<a href="https://arxiv.org/pdf/1110.3396">pdf</a>, <a href="https://arxiv.org/ps/1110.3396">ps</a>, <a href="https://arxiv.org/format/1110.3396">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="Mesoscale and Nanoscale Physics">cond-mat.mes-hall</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/10.1016/j.physleta.2013.05.029">10.1016/j.physleta.2013.05.029 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Quantum Zeno and anti-Zeno effects induced by either frequent measurements, modulations, or a mix of them </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Zhang%2C+W">Wenxian Zhang</a>, <a href="/search/quant-ph?searchtype=author&query=Kofman%2C+A+G">A. G. Kofman</a>, <a href="/search/quant-ph?searchtype=author&query=Zhuang%2C+J">Jun Zhuang</a>, <a href="/search/quant-ph?searchtype=author&query=You%2C+J+Q">J. Q. You</a>, <a href="/search/quant-ph?searchtype=author&query=Nori%2C+F">Franco Nori</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="1110.3396v1-abstract-short" style="display: inline;"> Using numerical calculations, we compare the collective transition probabilities of many spins in random magnetic fields, subject to either frequent projective measurements, frequent phase modulations, or a mix of modulations and measurements. For three different distribution functions (Gaussian, Lorentzian, and exponential) we consider here, the transition probability under frequent modulations i… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1110.3396v1-abstract-full').style.display = 'inline'; document.getElementById('1110.3396v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1110.3396v1-abstract-full" style="display: none;"> Using numerical calculations, we compare the collective transition probabilities of many spins in random magnetic fields, subject to either frequent projective measurements, frequent phase modulations, or a mix of modulations and measurements. For three different distribution functions (Gaussian, Lorentzian, and exponential) we consider here, the transition probability under frequent modulations is suppressed most if the pulse delay is short and the evolution time is larger than a critical value. Furthermore, decoherence freezing (with a transition rate equals to zero) occurs when there are frequent phase modulations, while the transition rate only decreases when there are frequent measurements and a mix of them, as the pulse delay approaches zero. In the large pulse-delay region, however, the transition probabilities under frequent modulations are enhanced more than those under either frequent measurements or a mix of modulations and measurements. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1110.3396v1-abstract-full').style.display = 'none'; document.getElementById('1110.3396v1-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 October, 2011; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2011. </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, 4 eps figures, RevTex 4 format</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Lett. A 377, 1837-1843 (2013) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1105.3800">arXiv:1105.3800</a> <span> [<a href="https://arxiv.org/pdf/1105.3800">pdf</a>, <a href="https://arxiv.org/ps/1105.3800">ps</a>, <a href="https://arxiv.org/format/1105.3800">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="Atomic and Molecular Clusters">physics.atm-clus</span> </div> </div> <p class="title is-5 mathjax"> Crtierion of effective centre-of-mass method in Quantum Mechanics </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Ning%2C+B">Bo-Yuan Ning</a>, <a href="/search/quant-ph?searchtype=author&query=Zhuang%2C+J">Jun Zhuang</a>, <a href="/search/quant-ph?searchtype=author&query=Ning%2C+X">Xi-Jing Ning</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="1105.3800v1-abstract-short" style="display: inline;"> In describing the motion of atoms and clusters, we face with choosing quantum mechanics or classical mechanics under different conditions. In principle, there exist two criteria for this choice, but they do contradict in some cases though they are in agreement for other cases. Actually, this problem is closely related with the effective centre-of-mass method, the underlying application of quantum… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1105.3800v1-abstract-full').style.display = 'inline'; document.getElementById('1105.3800v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1105.3800v1-abstract-full" style="display: none;"> In describing the motion of atoms and clusters, we face with choosing quantum mechanics or classical mechanics under different conditions. In principle, there exist two criteria for this choice, but they do contradict in some cases though they are in agreement for other cases. Actually, this problem is closely related with the effective centre-of-mass method, the underlying application of quantum mechanics. It is shown that quantum mechanics must be selected for particle's motion when the de Broglie wave length of the mass centre is larger than the particle size, and in such case the effective centre-of-mass can be used in Quantum Mechanics. In order to test this conclusion, an easy-manufactured experiment is suggested. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1105.3800v1-abstract-full').style.display = 'none'; document.getElementById('1105.3800v1-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> 19 May, 2011; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2011. </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, 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/1003.4321">arXiv:1003.4321</a> <span> [<a href="https://arxiv.org/pdf/1003.4321">pdf</a>, <a href="https://arxiv.org/ps/1003.4321">ps</a>, <a href="https://arxiv.org/format/1003.4321">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Mesoscale and Nanoscale Physics">cond-mat.mes-hall</span> <span class="tag is-small is-grey 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/PhysRevB.82.045314.">10.1103/PhysRevB.82.045314. <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Protection of center-spin coherence by a dynamically polarized nuclear spin core </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Zhang%2C+W">Wenxian Zhang</a>, <a href="/search/quant-ph?searchtype=author&query=Hu%2C+J">Jian-Liang Hu</a>, <a href="/search/quant-ph?searchtype=author&query=Zhuang%2C+J">Jun Zhuang</a>, <a href="/search/quant-ph?searchtype=author&query=You%2C+J+Q">J. Q. You</a>, <a href="/search/quant-ph?searchtype=author&query=Liu%2C+R">Ren-Bao Liu</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="1003.4321v1-abstract-short" style="display: inline;"> Understanding fully the dynamics of coupled electron-nuclear spin systems, which are important for the development of long-lived qubits based on solid-state systems, remains a challenge. We show that in a singly charged semiconductor quantum dot with inhomogeneous hyperfine coupling, the nuclear spins relatively strongly coupled to the electron spin form a polarized core during the dynamical polar… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1003.4321v1-abstract-full').style.display = 'inline'; document.getElementById('1003.4321v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1003.4321v1-abstract-full" style="display: none;"> Understanding fully the dynamics of coupled electron-nuclear spin systems, which are important for the development of long-lived qubits based on solid-state systems, remains a challenge. We show that in a singly charged semiconductor quantum dot with inhomogeneous hyperfine coupling, the nuclear spins relatively strongly coupled to the electron spin form a polarized core during the dynamical polarization process. The polarized core provides a protection effect against the electron spin relaxation, reducing the decay rate by a factor of $N_1$, the number of the nuclear spins in the polarized core, at a relatively small total polarization. This protection effect may occur in quantum dots and solid-state spin systems defect centers, such as NV centers in diamonds, and could be harnessed to fabricate in a relatively simple way long-lived qubits and quantum memories. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1003.4321v1-abstract-full').style.display = 'none'; document.getElementById('1003.4321v1-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> 22 March, 2010; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2010. </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">5 pages, 3 color eps figures.</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. B 82, 045314 (2010) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1001.1041">arXiv:1001.1041</a> <span> [<a href="https://arxiv.org/pdf/1001.1041">pdf</a>, <a href="https://arxiv.org/ps/1001.1041">ps</a>, <a href="https://arxiv.org/format/1001.1041">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/PhysRevA.79.012310">10.1103/PhysRevA.79.012310 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Dynamical control of two-level system's decay and long time freezing </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Zhang%2C+W">Wenxian Zhang</a>, <a href="/search/quant-ph?searchtype=author&query=Zhuang%2C+J">Jun Zhuang</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="1001.1041v1-abstract-short" style="display: inline;"> We investigate with exact numerical calculation coherent control of a two-level quantum system's decay by subjecting the two-level system to many periodic ideal $2蟺$ phase modulation pulses. For three spectrum intensities (Gaussian, Lorentzian, and exponential), we find both suppression and acceleration of the decay of the two-level system, depending on difference between the spectrum peak posit… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1001.1041v1-abstract-full').style.display = 'inline'; document.getElementById('1001.1041v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1001.1041v1-abstract-full" style="display: none;"> We investigate with exact numerical calculation coherent control of a two-level quantum system's decay by subjecting the two-level system to many periodic ideal $2蟺$ phase modulation pulses. For three spectrum intensities (Gaussian, Lorentzian, and exponential), we find both suppression and acceleration of the decay of the two-level system, depending on difference between the spectrum peak position and the eigen frequency of the two-level system. Most interestingly, the decay of the two-level system freezes after many control pulses if the pulse delay is short. The decay freezing value is half of the decay in the first pulse delay. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1001.1041v1-abstract-full').style.display = 'none'; document.getElementById('1001.1041v1-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 January, 2010; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2010. </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, 6 figures, published in Phys. Rev. A</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. A 79, 012310 (2009) </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 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"/></svg> <a href="https://info.arxiv.org/help/contact.html"> Contact</a> </li> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>subscribe to arXiv mailings</title><desc>Click here to subscribe</desc><path d="M476 3.2L12.5 270.6c-18.1 10.4-15.8 35.6 2.2 43.2L121 358.4l287.3-253.2c5.5-4.9 13.3 2.6 8.6 8.3L176 407v80.5c0 23.6 28.5 32.9 42.5 15.8L282 426l124.6 52.2c14.2 6 30.4-2.9 33-18.2l72-432C515 7.8 493.3-6.8 476 3.2z"/></svg> <a href="https://info.arxiv.org/help/subscribe"> Subscribe</a> </li> </ul> </div> </div> </div>   <div class="column"> <div class="columns"> <div class="column"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/help/license/index.html">Copyright</a></li> <li><a href="https://info.arxiv.org/help/policies/privacy_policy.html">Privacy Policy</a></li> </ul> </div> <div class="column sorry-app-links"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/help/web_accessibility.html">Web Accessibility Assistance</a></li> <li> <p class="help"> <a class="a11y-main-link" href="https://status.arxiv.org" target="_blank">arXiv Operational Status <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 256 512" class="icon filter-dark_grey" role="presentation"><path d="M224.3 273l-136 136c-9.4 9.4-24.6 9.4-33.9 0l-22.6-22.6c-9.4-9.4-9.4-24.6 0-33.9l96.4-96.4-96.4-96.4c-9.4-9.4-9.4-24.6 0-33.9L54.3 103c9.4-9.4 24.6-9.4 33.9 0l136 136c9.5 9.4 9.5 24.6.1 34z"/></svg></a><br> Get status notifications via <a class="is-link" href="https://subscribe.sorryapp.com/24846f03/email/new" target="_blank"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><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 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"/></svg>email</a> or <a class="is-link" href="https://subscribe.sorryapp.com/24846f03/slack/new" target="_blank"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 448 512" class="icon filter-black" role="presentation"><path d="M94.12 315.1c0 25.9-21.16 47.06-47.06 47.06S0 341 0 315.1c0-25.9 21.16-47.06 47.06-47.06h47.06v47.06zm23.72 0c0-25.9 21.16-47.06 47.06-47.06s47.06 21.16 47.06 47.06v117.84c0 25.9-21.16 47.06-47.06 47.06s-47.06-21.16-47.06-47.06V315.1zm47.06-188.98c-25.9 0-47.06-21.16-47.06-47.06S139 32 164.9 32s47.06 21.16 47.06 47.06v47.06H164.9zm0 23.72c25.9 0 47.06 21.16 47.06 47.06s-21.16 47.06-47.06 47.06H47.06C21.16 243.96 0 222.8 0 196.9s21.16-47.06 47.06-47.06H164.9zm188.98 47.06c0-25.9 21.16-47.06 47.06-47.06 25.9 0 47.06 21.16 47.06 47.06s-21.16 47.06-47.06 47.06h-47.06V196.9zm-23.72 0c0 25.9-21.16 47.06-47.06 47.06-25.9 0-47.06-21.16-47.06-47.06V79.06c0-25.9 21.16-47.06 47.06-47.06 25.9 0 47.06 21.16 47.06 47.06V196.9zM283.1 385.88c25.9 0 47.06 21.16 47.06 47.06 0 25.9-21.16 47.06-47.06 47.06-25.9 0-47.06-21.16-47.06-47.06v-47.06h47.06zm0-23.72c-25.9 0-47.06-21.16-47.06-47.06 0-25.9 21.16-47.06 47.06-47.06h117.84c25.9 0 47.06 21.16 47.06 47.06 0 25.9-21.16 47.06-47.06 47.06H283.1z"/></svg>slack</a> </p> </li> </ul> </div> </div> </div>  </div> </footer> <script src="https://static.arxiv.org/static/base/1.0.0a5/js/member_acknowledgement.js"></script> </body> </html>

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