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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/2410.06557">arXiv:2410.06557</a> <span> [<a href="https://arxiv.org/pdf/2410.06557">pdf</a>, <a href="https://arxiv.org/format/2410.06557">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="Disordered Systems and Neural Networks">cond-mat.dis-nn</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="High Energy Physics - Lattice">hep-lat</span> </div> </div> <p class="title is-5 mathjax"> Observation of disorder-free localization and efficient disorder averaging on a quantum processor </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Gyawali%2C+G">Gaurav Gyawali</a>, <a href="/search/cond-mat?searchtype=author&query=Cochran%2C+T">Tyler Cochran</a>, <a href="/search/cond-mat?searchtype=author&query=Lensky%2C+Y">Yuri Lensky</a>, <a href="/search/cond-mat?searchtype=author&query=Rosenberg%2C+E">Eliott Rosenberg</a>, <a href="/search/cond-mat?searchtype=author&query=Karamlou%2C+A+H">Amir H. Karamlou</a>, <a href="/search/cond-mat?searchtype=author&query=Kechedzhi%2C+K">Kostyantyn Kechedzhi</a>, <a href="/search/cond-mat?searchtype=author&query=Berndtsson%2C+J">Julia Berndtsson</a>, <a href="/search/cond-mat?searchtype=author&query=Westerhout%2C+T">Tom Westerhout</a>, <a href="/search/cond-mat?searchtype=author&query=Asfaw%2C+A">Abraham Asfaw</a>, <a href="/search/cond-mat?searchtype=author&query=Abanin%2C+D">Dmitry Abanin</a>, <a href="/search/cond-mat?searchtype=author&query=Acharya%2C+R">Rajeev Acharya</a>, <a href="/search/cond-mat?searchtype=author&query=Beni%2C+L+A">Laleh Aghababaie Beni</a>, <a href="/search/cond-mat?searchtype=author&query=Andersen%2C+T+I">Trond I. Andersen</a>, <a href="/search/cond-mat?searchtype=author&query=Ansmann%2C+M">Markus Ansmann</a>, <a href="/search/cond-mat?searchtype=author&query=Arute%2C+F">Frank Arute</a>, <a href="/search/cond-mat?searchtype=author&query=Arya%2C+K">Kunal Arya</a>, <a href="/search/cond-mat?searchtype=author&query=Astrakhantsev%2C+N">Nikita Astrakhantsev</a>, <a href="/search/cond-mat?searchtype=author&query=Atalaya%2C+J">Juan Atalaya</a>, <a href="/search/cond-mat?searchtype=author&query=Babbush%2C+R">Ryan Babbush</a>, <a href="/search/cond-mat?searchtype=author&query=Ballard%2C+B">Brian Ballard</a>, <a href="/search/cond-mat?searchtype=author&query=Bardin%2C+J+C">Joseph C. Bardin</a>, <a href="/search/cond-mat?searchtype=author&query=Bengtsson%2C+A">Andreas Bengtsson</a>, <a href="/search/cond-mat?searchtype=author&query=Bilmes%2C+A">Alexander Bilmes</a>, <a href="/search/cond-mat?searchtype=author&query=Bortoli%2C+G">Gina Bortoli</a>, <a href="/search/cond-mat?searchtype=author&query=Bourassa%2C+A">Alexandre Bourassa</a> , et al. (195 additional authors not shown) </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="2410.06557v1-abstract-short" style="display: inline;"> One of the most challenging problems in the computational study of localization in quantum manybody systems is to capture the effects of rare events, which requires sampling over exponentially many disorder realizations. We implement an efficient procedure on a quantum processor, leveraging quantum parallelism, to efficiently sample over all disorder realizations. We observe localization without d… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2410.06557v1-abstract-full').style.display = 'inline'; document.getElementById('2410.06557v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2410.06557v1-abstract-full" style="display: none;"> One of the most challenging problems in the computational study of localization in quantum manybody systems is to capture the effects of rare events, which requires sampling over exponentially many disorder realizations. We implement an efficient procedure on a quantum processor, leveraging quantum parallelism, to efficiently sample over all disorder realizations. We observe localization without disorder in quantum many-body dynamics in one and two dimensions: perturbations do not diffuse even though both the generator of evolution and the initial states are fully translationally invariant. The disorder strength as well as its density can be readily tuned using the initial state. Furthermore, we demonstrate the versatility of our platform by measuring Renyi entropies. Our method could also be extended to higher moments of the physical observables and disorder learning. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2410.06557v1-abstract-full').style.display = 'none'; document.getElementById('2410.06557v1-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 October, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2409.17142">arXiv:2409.17142</a> <span> [<a href="https://arxiv.org/pdf/2409.17142">pdf</a>, <a href="https://arxiv.org/format/2409.17142">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="High Energy Physics - Lattice">hep-lat</span> </div> </div> <p class="title is-5 mathjax"> Visualizing Dynamics of Charges and Strings in (2+1)D Lattice Gauge Theories </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Cochran%2C+T+A">Tyler A. Cochran</a>, <a href="/search/cond-mat?searchtype=author&query=Jobst%2C+B">Bernhard Jobst</a>, <a href="/search/cond-mat?searchtype=author&query=Rosenberg%2C+E">Eliott Rosenberg</a>, <a href="/search/cond-mat?searchtype=author&query=Lensky%2C+Y+D">Yuri D. Lensky</a>, <a href="/search/cond-mat?searchtype=author&query=Gyawali%2C+G">Gaurav Gyawali</a>, <a href="/search/cond-mat?searchtype=author&query=Eassa%2C+N">Norhan Eassa</a>, <a href="/search/cond-mat?searchtype=author&query=Will%2C+M">Melissa Will</a>, <a href="/search/cond-mat?searchtype=author&query=Abanin%2C+D">Dmitry Abanin</a>, <a href="/search/cond-mat?searchtype=author&query=Acharya%2C+R">Rajeev Acharya</a>, <a href="/search/cond-mat?searchtype=author&query=Beni%2C+L+A">Laleh Aghababaie Beni</a>, <a href="/search/cond-mat?searchtype=author&query=Andersen%2C+T+I">Trond I. Andersen</a>, <a href="/search/cond-mat?searchtype=author&query=Ansmann%2C+M">Markus Ansmann</a>, <a href="/search/cond-mat?searchtype=author&query=Arute%2C+F">Frank Arute</a>, <a href="/search/cond-mat?searchtype=author&query=Arya%2C+K">Kunal Arya</a>, <a href="/search/cond-mat?searchtype=author&query=Asfaw%2C+A">Abraham Asfaw</a>, <a href="/search/cond-mat?searchtype=author&query=Atalaya%2C+J">Juan Atalaya</a>, <a href="/search/cond-mat?searchtype=author&query=Babbush%2C+R">Ryan Babbush</a>, <a href="/search/cond-mat?searchtype=author&query=Ballard%2C+B">Brian Ballard</a>, <a href="/search/cond-mat?searchtype=author&query=Bardin%2C+J+C">Joseph C. Bardin</a>, <a href="/search/cond-mat?searchtype=author&query=Bengtsson%2C+A">Andreas Bengtsson</a>, <a href="/search/cond-mat?searchtype=author&query=Bilmes%2C+A">Alexander Bilmes</a>, <a href="/search/cond-mat?searchtype=author&query=Bourassa%2C+A">Alexandre Bourassa</a>, <a href="/search/cond-mat?searchtype=author&query=Bovaird%2C+J">Jenna Bovaird</a>, <a href="/search/cond-mat?searchtype=author&query=Broughton%2C+M">Michael Broughton</a>, <a href="/search/cond-mat?searchtype=author&query=Browne%2C+D+A">David A. Browne</a> , et al. (167 additional authors not shown) </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="2409.17142v1-abstract-short" style="display: inline;"> Lattice gauge theories (LGTs) can be employed to understand a wide range of phenomena, from elementary particle scattering in high-energy physics to effective descriptions of many-body interactions in materials. Studying dynamical properties of emergent phases can be challenging as it requires solving many-body problems that are generally beyond perturbative limits. We investigate the dynamics of… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2409.17142v1-abstract-full').style.display = 'inline'; document.getElementById('2409.17142v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2409.17142v1-abstract-full" style="display: none;"> Lattice gauge theories (LGTs) can be employed to understand a wide range of phenomena, from elementary particle scattering in high-energy physics to effective descriptions of many-body interactions in materials. Studying dynamical properties of emergent phases can be challenging as it requires solving many-body problems that are generally beyond perturbative limits. We investigate the dynamics of local excitations in a $\mathbb{Z}_2$ LGT using a two-dimensional lattice of superconducting qubits. We first construct a simple variational circuit which prepares low-energy states that have a large overlap with the ground state; then we create particles with local gates and simulate their quantum dynamics via a discretized time evolution. As the effective magnetic field is increased, our measurements show signatures of transitioning from deconfined to confined dynamics. For confined excitations, the magnetic field induces a tension in the string connecting them. Our method allows us to experimentally image string dynamics in a (2+1)D LGT from which we uncover two distinct regimes inside the confining phase: for weak confinement the string fluctuates strongly in the transverse direction, while for strong confinement transverse fluctuations are effectively frozen. In addition, we demonstrate a resonance condition at which dynamical string breaking is facilitated. Our LGT implementation on a quantum processor presents a novel set of techniques for investigating emergent particle and string dynamics. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2409.17142v1-abstract-full').style.display = 'none'; document.getElementById('2409.17142v1-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> 25 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/2405.17385">arXiv:2405.17385</a> <span> [<a href="https://arxiv.org/pdf/2405.17385">pdf</a>, <a href="https://arxiv.org/format/2405.17385">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> <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"> Thermalization and Criticality on an Analog-Digital Quantum Simulator </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Andersen%2C+T+I">Trond I. Andersen</a>, <a href="/search/cond-mat?searchtype=author&query=Astrakhantsev%2C+N">Nikita Astrakhantsev</a>, <a href="/search/cond-mat?searchtype=author&query=Karamlou%2C+A+H">Amir H. Karamlou</a>, <a href="/search/cond-mat?searchtype=author&query=Berndtsson%2C+J">Julia Berndtsson</a>, <a href="/search/cond-mat?searchtype=author&query=Motruk%2C+J">Johannes Motruk</a>, <a href="/search/cond-mat?searchtype=author&query=Szasz%2C+A">Aaron Szasz</a>, <a href="/search/cond-mat?searchtype=author&query=Gross%2C+J+A">Jonathan A. Gross</a>, <a href="/search/cond-mat?searchtype=author&query=Schuckert%2C+A">Alexander Schuckert</a>, <a href="/search/cond-mat?searchtype=author&query=Westerhout%2C+T">Tom Westerhout</a>, <a href="/search/cond-mat?searchtype=author&query=Zhang%2C+Y">Yaxing Zhang</a>, <a href="/search/cond-mat?searchtype=author&query=Forati%2C+E">Ebrahim Forati</a>, <a href="/search/cond-mat?searchtype=author&query=Rossi%2C+D">Dario Rossi</a>, <a href="/search/cond-mat?searchtype=author&query=Kobrin%2C+B">Bryce Kobrin</a>, <a href="/search/cond-mat?searchtype=author&query=Di+Paolo%2C+A">Agustin Di Paolo</a>, <a href="/search/cond-mat?searchtype=author&query=Klots%2C+A+R">Andrey R. Klots</a>, <a href="/search/cond-mat?searchtype=author&query=Drozdov%2C+I">Ilya Drozdov</a>, <a href="/search/cond-mat?searchtype=author&query=Kurilovich%2C+V+D">Vladislav D. Kurilovich</a>, <a href="/search/cond-mat?searchtype=author&query=Petukhov%2C+A">Andre Petukhov</a>, <a href="/search/cond-mat?searchtype=author&query=Ioffe%2C+L+B">Lev B. Ioffe</a>, <a href="/search/cond-mat?searchtype=author&query=Elben%2C+A">Andreas Elben</a>, <a href="/search/cond-mat?searchtype=author&query=Rath%2C+A">Aniket Rath</a>, <a href="/search/cond-mat?searchtype=author&query=Vitale%2C+V">Vittorio Vitale</a>, <a href="/search/cond-mat?searchtype=author&query=Vermersch%2C+B">Benoit Vermersch</a>, <a href="/search/cond-mat?searchtype=author&query=Acharya%2C+R">Rajeev Acharya</a>, <a href="/search/cond-mat?searchtype=author&query=Beni%2C+L+A">Laleh Aghababaie Beni</a> , et al. (202 additional authors not shown) </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="2405.17385v2-abstract-short" style="display: inline;"> Understanding how interacting particles approach thermal equilibrium is a major challenge of quantum simulators. Unlocking the full potential of such systems toward this goal requires flexible initial state preparation, precise time evolution, and extensive probes for final state characterization. We present a quantum simulator comprising 69 superconducting qubits which supports both universal qua… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2405.17385v2-abstract-full').style.display = 'inline'; document.getElementById('2405.17385v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2405.17385v2-abstract-full" style="display: none;"> Understanding how interacting particles approach thermal equilibrium is a major challenge of quantum simulators. Unlocking the full potential of such systems toward this goal requires flexible initial state preparation, precise time evolution, and extensive probes for final state characterization. We present a quantum simulator comprising 69 superconducting qubits which supports both universal quantum gates and high-fidelity analog evolution, with performance beyond the reach of classical simulation in cross-entropy benchmarking experiments. Emulating a two-dimensional (2D) XY quantum magnet, we leverage a wide range of measurement techniques to study quantum states after ramps from an antiferromagnetic initial state. We observe signatures of the classical Kosterlitz-Thouless phase transition, as well as strong deviations from Kibble-Zurek scaling predictions attributed to the interplay between quantum and classical coarsening of the correlated domains. This interpretation is corroborated by injecting variable energy density into the initial state, which enables studying the effects of the eigenstate thermalization hypothesis (ETH) in targeted parts of the eigenspectrum. Finally, we digitally prepare the system in pairwise-entangled dimer states and image the transport of energy and vorticity during thermalization. These results establish the efficacy of superconducting analog-digital quantum processors for preparing states across many-body spectra and unveiling their thermalization dynamics. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2405.17385v2-abstract-full').style.display = 'none'; document.getElementById('2405.17385v2-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> 8 July, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 27 May, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2303.04792">arXiv:2303.04792</a> <span> [<a href="https://arxiv.org/pdf/2303.04792">pdf</a>, <a href="https://arxiv.org/format/2303.04792">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="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</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/s41586-023-06505-7">10.1038/s41586-023-06505-7 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Measurement-induced entanglement and teleportation on a noisy quantum processor </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Hoke%2C+J+C">Jesse C. Hoke</a>, <a href="/search/cond-mat?searchtype=author&query=Ippoliti%2C+M">Matteo Ippoliti</a>, <a href="/search/cond-mat?searchtype=author&query=Rosenberg%2C+E">Eliott Rosenberg</a>, <a href="/search/cond-mat?searchtype=author&query=Abanin%2C+D">Dmitry Abanin</a>, <a href="/search/cond-mat?searchtype=author&query=Acharya%2C+R">Rajeev Acharya</a>, <a href="/search/cond-mat?searchtype=author&query=Andersen%2C+T+I">Trond I. Andersen</a>, <a href="/search/cond-mat?searchtype=author&query=Ansmann%2C+M">Markus Ansmann</a>, <a href="/search/cond-mat?searchtype=author&query=Arute%2C+F">Frank Arute</a>, <a href="/search/cond-mat?searchtype=author&query=Arya%2C+K">Kunal Arya</a>, <a href="/search/cond-mat?searchtype=author&query=Asfaw%2C+A">Abraham Asfaw</a>, <a href="/search/cond-mat?searchtype=author&query=Atalaya%2C+J">Juan Atalaya</a>, <a href="/search/cond-mat?searchtype=author&query=Bardin%2C+J+C">Joseph C. Bardin</a>, <a href="/search/cond-mat?searchtype=author&query=Bengtsson%2C+A">Andreas Bengtsson</a>, <a href="/search/cond-mat?searchtype=author&query=Bortoli%2C+G">Gina Bortoli</a>, <a href="/search/cond-mat?searchtype=author&query=Bourassa%2C+A">Alexandre Bourassa</a>, <a href="/search/cond-mat?searchtype=author&query=Bovaird%2C+J">Jenna Bovaird</a>, <a href="/search/cond-mat?searchtype=author&query=Brill%2C+L">Leon Brill</a>, <a href="/search/cond-mat?searchtype=author&query=Broughton%2C+M">Michael Broughton</a>, <a href="/search/cond-mat?searchtype=author&query=Buckley%2C+B+B">Bob B. Buckley</a>, <a href="/search/cond-mat?searchtype=author&query=Buell%2C+D+A">David A. Buell</a>, <a href="/search/cond-mat?searchtype=author&query=Burger%2C+T">Tim Burger</a>, <a href="/search/cond-mat?searchtype=author&query=Burkett%2C+B">Brian Burkett</a>, <a href="/search/cond-mat?searchtype=author&query=Bushnell%2C+N">Nicholas Bushnell</a>, <a href="/search/cond-mat?searchtype=author&query=Chen%2C+Z">Zijun Chen</a>, <a href="/search/cond-mat?searchtype=author&query=Chiaro%2C+B">Ben Chiaro</a> , et al. (138 additional authors not shown) </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="2303.04792v2-abstract-short" style="display: inline;"> Measurement has a special role in quantum theory: by collapsing the wavefunction it can enable phenomena such as teleportation and thereby alter the "arrow of time" that constrains unitary evolution. When integrated in many-body dynamics, measurements can lead to emergent patterns of quantum information in space-time that go beyond established paradigms for characterizing phases, either in or out… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2303.04792v2-abstract-full').style.display = 'inline'; document.getElementById('2303.04792v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2303.04792v2-abstract-full" style="display: none;"> Measurement has a special role in quantum theory: by collapsing the wavefunction it can enable phenomena such as teleportation and thereby alter the "arrow of time" that constrains unitary evolution. When integrated in many-body dynamics, measurements can lead to emergent patterns of quantum information in space-time that go beyond established paradigms for characterizing phases, either in or out of equilibrium. On present-day NISQ processors, the experimental realization of this physics is challenging due to noise, hardware limitations, and the stochastic nature of quantum measurement. Here we address each of these experimental challenges and investigate measurement-induced quantum information phases on up to 70 superconducting qubits. By leveraging the interchangeability of space and time, we use a duality mapping, to avoid mid-circuit measurement and access different manifestations of the underlying phases -- from entanglement scaling to measurement-induced teleportation -- in a unified way. We obtain finite-size signatures of a phase transition with a decoding protocol that correlates the experimental measurement record with classical simulation data. The phases display sharply different sensitivity to noise, which we exploit to turn an inherent hardware limitation into a useful diagnostic. Our work demonstrates an approach to realize measurement-induced physics at scales that are at the limits of current NISQ processors. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2303.04792v2-abstract-full').style.display = 'none'; document.getElementById('2303.04792v2-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> 17 October, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 8 March, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Nature 622, 481-486 (2023) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2210.10255">arXiv:2210.10255</a> <span> [<a href="https://arxiv.org/pdf/2210.10255">pdf</a>, <a href="https://arxiv.org/format/2210.10255">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> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Other Condensed Matter">cond-mat.other</span> </div> </div> <p class="title is-5 mathjax"> Non-Abelian braiding of graph vertices in a superconducting processor </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Andersen%2C+T+I">Trond I. Andersen</a>, <a href="/search/cond-mat?searchtype=author&query=Lensky%2C+Y+D">Yuri D. Lensky</a>, <a href="/search/cond-mat?searchtype=author&query=Kechedzhi%2C+K">Kostyantyn Kechedzhi</a>, <a href="/search/cond-mat?searchtype=author&query=Drozdov%2C+I">Ilya Drozdov</a>, <a href="/search/cond-mat?searchtype=author&query=Bengtsson%2C+A">Andreas Bengtsson</a>, <a href="/search/cond-mat?searchtype=author&query=Hong%2C+S">Sabrina Hong</a>, <a href="/search/cond-mat?searchtype=author&query=Morvan%2C+A">Alexis Morvan</a>, <a href="/search/cond-mat?searchtype=author&query=Mi%2C+X">Xiao Mi</a>, <a href="/search/cond-mat?searchtype=author&query=Opremcak%2C+A">Alex Opremcak</a>, <a href="/search/cond-mat?searchtype=author&query=Acharya%2C+R">Rajeev Acharya</a>, <a href="/search/cond-mat?searchtype=author&query=Allen%2C+R">Richard Allen</a>, <a href="/search/cond-mat?searchtype=author&query=Ansmann%2C+M">Markus Ansmann</a>, <a href="/search/cond-mat?searchtype=author&query=Arute%2C+F">Frank Arute</a>, <a href="/search/cond-mat?searchtype=author&query=Arya%2C+K">Kunal Arya</a>, <a href="/search/cond-mat?searchtype=author&query=Asfaw%2C+A">Abraham Asfaw</a>, <a href="/search/cond-mat?searchtype=author&query=Atalaya%2C+J">Juan Atalaya</a>, <a href="/search/cond-mat?searchtype=author&query=Babbush%2C+R">Ryan Babbush</a>, <a href="/search/cond-mat?searchtype=author&query=Bacon%2C+D">Dave Bacon</a>, <a href="/search/cond-mat?searchtype=author&query=Bardin%2C+J+C">Joseph C. Bardin</a>, <a href="/search/cond-mat?searchtype=author&query=Bortoli%2C+G">Gina Bortoli</a>, <a href="/search/cond-mat?searchtype=author&query=Bourassa%2C+A">Alexandre Bourassa</a>, <a href="/search/cond-mat?searchtype=author&query=Bovaird%2C+J">Jenna Bovaird</a>, <a href="/search/cond-mat?searchtype=author&query=Brill%2C+L">Leon Brill</a>, <a href="/search/cond-mat?searchtype=author&query=Broughton%2C+M">Michael Broughton</a>, <a href="/search/cond-mat?searchtype=author&query=Buckley%2C+B+B">Bob B. Buckley</a> , et al. (144 additional authors not shown) </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="2210.10255v2-abstract-short" style="display: inline;"> Indistinguishability of particles is a fundamental principle of quantum mechanics. For all elementary and quasiparticles observed to date - including fermions, bosons, and Abelian anyons - this principle guarantees that the braiding of identical particles leaves the system unchanged. However, in two spatial dimensions, an intriguing possibility exists: braiding of non-Abelian anyons causes rotatio… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2210.10255v2-abstract-full').style.display = 'inline'; document.getElementById('2210.10255v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2210.10255v2-abstract-full" style="display: none;"> Indistinguishability of particles is a fundamental principle of quantum mechanics. For all elementary and quasiparticles observed to date - including fermions, bosons, and Abelian anyons - this principle guarantees that the braiding of identical particles leaves the system unchanged. However, in two spatial dimensions, an intriguing possibility exists: braiding of non-Abelian anyons causes rotations in a space of topologically degenerate wavefunctions. Hence, it can change the observables of the system without violating the principle of indistinguishability. Despite the well developed mathematical description of non-Abelian anyons and numerous theoretical proposals, the experimental observation of their exchange statistics has remained elusive for decades. Controllable many-body quantum states generated on quantum processors offer another path for exploring these fundamental phenomena. While efforts on conventional solid-state platforms typically involve Hamiltonian dynamics of quasi-particles, superconducting quantum processors allow for directly manipulating the many-body wavefunction via unitary gates. Building on predictions that stabilizer codes can host projective non-Abelian Ising anyons, we implement a generalized stabilizer code and unitary protocol to create and braid them. This allows us to experimentally verify the fusion rules of the anyons and braid them to realize their statistics. We then study the prospect of employing the anyons for quantum computation and utilize braiding to create an entangled state of anyons encoding three logical qubits. Our work provides new insights about non-Abelian braiding and - through the future inclusion of error correction to achieve topological protection - could open a path toward fault-tolerant quantum computing. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2210.10255v2-abstract-full').style.display = 'none'; document.getElementById('2210.10255v2-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> 31 May, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 18 October, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2022. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2206.05254">arXiv:2206.05254</a> <span> [<a href="https://arxiv.org/pdf/2206.05254">pdf</a>, <a href="https://arxiv.org/format/2206.05254">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> <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/10.1038/s41586-022-05348-y">10.1038/s41586-022-05348-y <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Formation of robust bound states of interacting microwave photons </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Morvan%2C+A">Alexis Morvan</a>, <a href="/search/cond-mat?searchtype=author&query=Andersen%2C+T+I">Trond I. Andersen</a>, <a href="/search/cond-mat?searchtype=author&query=Mi%2C+X">Xiao Mi</a>, <a href="/search/cond-mat?searchtype=author&query=Neill%2C+C">Charles Neill</a>, <a href="/search/cond-mat?searchtype=author&query=Petukhov%2C+A">Andre Petukhov</a>, <a href="/search/cond-mat?searchtype=author&query=Kechedzhi%2C+K">Kostyantyn Kechedzhi</a>, <a href="/search/cond-mat?searchtype=author&query=Abanin%2C+D">Dmitry Abanin</a>, <a href="/search/cond-mat?searchtype=author&query=Acharya%2C+R">Rajeev Acharya</a>, <a href="/search/cond-mat?searchtype=author&query=Arute%2C+F">Frank Arute</a>, <a href="/search/cond-mat?searchtype=author&query=Arya%2C+K">Kunal Arya</a>, <a href="/search/cond-mat?searchtype=author&query=Asfaw%2C+A">Abraham Asfaw</a>, <a href="/search/cond-mat?searchtype=author&query=Atalaya%2C+J">Juan Atalaya</a>, <a href="/search/cond-mat?searchtype=author&query=Babbush%2C+R">Ryan Babbush</a>, <a href="/search/cond-mat?searchtype=author&query=Bacon%2C+D">Dave Bacon</a>, <a href="/search/cond-mat?searchtype=author&query=Bardin%2C+J+C">Joseph C. Bardin</a>, <a href="/search/cond-mat?searchtype=author&query=Basso%2C+J">Joao Basso</a>, <a href="/search/cond-mat?searchtype=author&query=Bengtsson%2C+A">Andreas Bengtsson</a>, <a href="/search/cond-mat?searchtype=author&query=Bortoli%2C+G">Gina Bortoli</a>, <a href="/search/cond-mat?searchtype=author&query=Bourassa%2C+A">Alexandre Bourassa</a>, <a href="/search/cond-mat?searchtype=author&query=Bovaird%2C+J">Jenna Bovaird</a>, <a href="/search/cond-mat?searchtype=author&query=Brill%2C+L">Leon Brill</a>, <a href="/search/cond-mat?searchtype=author&query=Broughton%2C+M">Michael Broughton</a>, <a href="/search/cond-mat?searchtype=author&query=Buckley%2C+B+B">Bob B. Buckley</a>, <a href="/search/cond-mat?searchtype=author&query=Buell%2C+D+A">David A. Buell</a>, <a href="/search/cond-mat?searchtype=author&query=Burger%2C+T">Tim Burger</a> , et al. (125 additional authors not shown) </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="2206.05254v3-abstract-short" style="display: inline;"> Systems of correlated particles appear in many fields of science and represent some of the most intractable puzzles in nature. The computational challenge in these systems arises when interactions become comparable to other energy scales, which makes the state of each particle depend on all other particles. The lack of general solutions for the 3-body problem and acceptable theory for strongly cor… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2206.05254v3-abstract-full').style.display = 'inline'; document.getElementById('2206.05254v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2206.05254v3-abstract-full" style="display: none;"> Systems of correlated particles appear in many fields of science and represent some of the most intractable puzzles in nature. The computational challenge in these systems arises when interactions become comparable to other energy scales, which makes the state of each particle depend on all other particles. The lack of general solutions for the 3-body problem and acceptable theory for strongly correlated electrons shows that our understanding of correlated systems fades when the particle number or the interaction strength increases. One of the hallmarks of interacting systems is the formation of multi-particle bound states. In a ring of 24 superconducting qubits, we develop a high fidelity parameterizable fSim gate that we use to implement the periodic quantum circuit of the spin-1/2 XXZ model, an archetypal model of interaction. By placing microwave photons in adjacent qubit sites, we study the propagation of these excitations and observe their bound nature for up to 5 photons. We devise a phase sensitive method for constructing the few-body spectrum of the bound states and extract their pseudo-charge by introducing a synthetic flux. By introducing interactions between the ring and additional qubits, we observe an unexpected resilience of the bound states to integrability breaking. This finding goes against the common wisdom that bound states in non-integrable systems are unstable when their energies overlap with the continuum spectrum. Our work provides experimental evidence for bound states of interacting photons and discovers their stability beyond the integrability limit. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2206.05254v3-abstract-full').style.display = 'none'; document.getElementById('2206.05254v3-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 December, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 10 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">7 pages + 15 pages supplements</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Nature 612, 240-245 (2022) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2204.11372">arXiv:2204.11372</a> <span> [<a href="https://arxiv.org/pdf/2204.11372">pdf</a>, <a href="https://arxiv.org/format/2204.11372">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> <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/10.1126/science.abq5769">10.1126/science.abq5769 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Noise-resilient Edge Modes on a Chain of Superconducting Qubits </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Mi%2C+X">Xiao Mi</a>, <a href="/search/cond-mat?searchtype=author&query=Sonner%2C+M">Michael Sonner</a>, <a href="/search/cond-mat?searchtype=author&query=Niu%2C+M+Y">Murphy Yuezhen Niu</a>, <a href="/search/cond-mat?searchtype=author&query=Lee%2C+K+W">Kenneth W. Lee</a>, <a href="/search/cond-mat?searchtype=author&query=Foxen%2C+B">Brooks Foxen</a>, <a href="/search/cond-mat?searchtype=author&query=Acharya%2C+R">Rajeev Acharya</a>, <a href="/search/cond-mat?searchtype=author&query=Aleiner%2C+I">Igor Aleiner</a>, <a href="/search/cond-mat?searchtype=author&query=Andersen%2C+T+I">Trond I. Andersen</a>, <a href="/search/cond-mat?searchtype=author&query=Arute%2C+F">Frank Arute</a>, <a href="/search/cond-mat?searchtype=author&query=Arya%2C+K">Kunal Arya</a>, <a href="/search/cond-mat?searchtype=author&query=Asfaw%2C+A">Abraham Asfaw</a>, <a href="/search/cond-mat?searchtype=author&query=Atalaya%2C+J">Juan Atalaya</a>, <a href="/search/cond-mat?searchtype=author&query=Babbush%2C+R">Ryan Babbush</a>, <a href="/search/cond-mat?searchtype=author&query=Bacon%2C+D">Dave Bacon</a>, <a href="/search/cond-mat?searchtype=author&query=Bardin%2C+J+C">Joseph C. Bardin</a>, <a href="/search/cond-mat?searchtype=author&query=Basso%2C+J">Joao Basso</a>, <a href="/search/cond-mat?searchtype=author&query=Bengtsson%2C+A">Andreas Bengtsson</a>, <a href="/search/cond-mat?searchtype=author&query=Bortoli%2C+G">Gina Bortoli</a>, <a href="/search/cond-mat?searchtype=author&query=Bourassa%2C+A">Alexandre Bourassa</a>, <a href="/search/cond-mat?searchtype=author&query=Brill%2C+L">Leon Brill</a>, <a href="/search/cond-mat?searchtype=author&query=Broughton%2C+M">Michael Broughton</a>, <a href="/search/cond-mat?searchtype=author&query=Buckley%2C+B+B">Bob B. Buckley</a>, <a href="/search/cond-mat?searchtype=author&query=Buell%2C+D+A">David A. Buell</a>, <a href="/search/cond-mat?searchtype=author&query=Burkett%2C+B">Brian Burkett</a>, <a href="/search/cond-mat?searchtype=author&query=Bushnell%2C+N">Nicholas Bushnell</a> , et al. (103 additional authors not shown) </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="2204.11372v2-abstract-short" style="display: inline;"> Inherent symmetry of a quantum system may protect its otherwise fragile states. Leveraging such protection requires testing its robustness against uncontrolled environmental interactions. Using 47 superconducting qubits, we implement the one-dimensional kicked Ising model which exhibits non-local Majorana edge modes (MEMs) with $\mathbb{Z}_2$ parity symmetry. Remarkably, we find that any multi-qub… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2204.11372v2-abstract-full').style.display = 'inline'; document.getElementById('2204.11372v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2204.11372v2-abstract-full" style="display: none;"> Inherent symmetry of a quantum system may protect its otherwise fragile states. Leveraging such protection requires testing its robustness against uncontrolled environmental interactions. Using 47 superconducting qubits, we implement the one-dimensional kicked Ising model which exhibits non-local Majorana edge modes (MEMs) with $\mathbb{Z}_2$ parity symmetry. Remarkably, we find that any multi-qubit Pauli operator overlapping with the MEMs exhibits a uniform late-time decay rate comparable to single-qubit relaxation rates, irrespective of its size or composition. This characteristic allows us to accurately reconstruct the exponentially localized spatial profiles of the MEMs. Furthermore, the MEMs are found to be resilient against certain symmetry-breaking noise owing to a prethermalization mechanism. Our work elucidates the complex interplay between noise and symmetry-protected edge modes in a solid-state environment. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2204.11372v2-abstract-full').style.display = 'none'; document.getElementById('2204.11372v2-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> 8 December, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 24 April, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Science 378, 785 (2022) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2107.13571">arXiv:2107.13571</a> <span> [<a href="https://arxiv.org/pdf/2107.13571">pdf</a>, <a href="https://arxiv.org/format/2107.13571">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="Disordered Systems and Neural Networks">cond-mat.dis-nn</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Strongly Correlated Electrons">cond-mat.str-el</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/s41586-021-04257-w">10.1038/s41586-021-04257-w <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Observation of Time-Crystalline Eigenstate Order on a Quantum Processor </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Mi%2C+X">Xiao Mi</a>, <a href="/search/cond-mat?searchtype=author&query=Ippoliti%2C+M">Matteo Ippoliti</a>, <a href="/search/cond-mat?searchtype=author&query=Quintana%2C+C">Chris Quintana</a>, <a href="/search/cond-mat?searchtype=author&query=Greene%2C+A">Ami Greene</a>, <a href="/search/cond-mat?searchtype=author&query=Chen%2C+Z">Zijun Chen</a>, <a href="/search/cond-mat?searchtype=author&query=Gross%2C+J">Jonathan Gross</a>, <a href="/search/cond-mat?searchtype=author&query=Arute%2C+F">Frank Arute</a>, <a href="/search/cond-mat?searchtype=author&query=Arya%2C+K">Kunal Arya</a>, <a href="/search/cond-mat?searchtype=author&query=Atalaya%2C+J">Juan Atalaya</a>, <a href="/search/cond-mat?searchtype=author&query=Babbush%2C+R">Ryan Babbush</a>, <a href="/search/cond-mat?searchtype=author&query=Bardin%2C+J+C">Joseph C. Bardin</a>, <a href="/search/cond-mat?searchtype=author&query=Basso%2C+J">Joao Basso</a>, <a href="/search/cond-mat?searchtype=author&query=Bengtsson%2C+A">Andreas Bengtsson</a>, <a href="/search/cond-mat?searchtype=author&query=Bilmes%2C+A">Alexander Bilmes</a>, <a href="/search/cond-mat?searchtype=author&query=Bourassa%2C+A">Alexandre Bourassa</a>, <a href="/search/cond-mat?searchtype=author&query=Brill%2C+L">Leon Brill</a>, <a href="/search/cond-mat?searchtype=author&query=Broughton%2C+M">Michael Broughton</a>, <a href="/search/cond-mat?searchtype=author&query=Buckley%2C+B+B">Bob B. Buckley</a>, <a href="/search/cond-mat?searchtype=author&query=Buell%2C+D+A">David A. Buell</a>, <a href="/search/cond-mat?searchtype=author&query=Burkett%2C+B">Brian Burkett</a>, <a href="/search/cond-mat?searchtype=author&query=Bushnell%2C+N">Nicholas Bushnell</a>, <a href="/search/cond-mat?searchtype=author&query=Chiaro%2C+B">Benjamin Chiaro</a>, <a href="/search/cond-mat?searchtype=author&query=Collins%2C+R">Roberto Collins</a>, <a href="/search/cond-mat?searchtype=author&query=Courtney%2C+W">William Courtney</a>, <a href="/search/cond-mat?searchtype=author&query=Debroy%2C+D">Dripto Debroy</a> , et al. (80 additional authors not shown) </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="2107.13571v2-abstract-short" style="display: inline;"> Quantum many-body systems display rich phase structure in their low-temperature equilibrium states. However, much of nature is not in thermal equilibrium. Remarkably, it was recently predicted that out-of-equilibrium systems can exhibit novel dynamical phases that may otherwise be forbidden by equilibrium thermodynamics, a paradigmatic example being the discrete time crystal (DTC). Concretely, dyn… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2107.13571v2-abstract-full').style.display = 'inline'; document.getElementById('2107.13571v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2107.13571v2-abstract-full" style="display: none;"> Quantum many-body systems display rich phase structure in their low-temperature equilibrium states. However, much of nature is not in thermal equilibrium. Remarkably, it was recently predicted that out-of-equilibrium systems can exhibit novel dynamical phases that may otherwise be forbidden by equilibrium thermodynamics, a paradigmatic example being the discrete time crystal (DTC). Concretely, dynamical phases can be defined in periodically driven many-body localized systems via the concept of eigenstate order. In eigenstate-ordered phases, the entire many-body spectrum exhibits quantum correlations and long-range order, with characteristic signatures in late-time dynamics from all initial states. It is, however, challenging to experimentally distinguish such stable phases from transient phenomena, wherein few select states can mask typical behavior. Here we implement a continuous family of tunable CPHASE gates on an array of superconducting qubits to experimentally observe an eigenstate-ordered DTC. We demonstrate the characteristic spatiotemporal response of a DTC for generic initial states. Our work employs a time-reversal protocol that discriminates external decoherence from intrinsic thermalization, and leverages quantum typicality to circumvent the exponential cost of densely sampling the eigenspectrum. In addition, we locate the phase transition out of the DTC with an experimental finite-size analysis. These results establish a scalable approach to study non-equilibrium phases of matter on current quantum processors. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2107.13571v2-abstract-full').style.display = 'none'; document.getElementById('2107.13571v2-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 August, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 28 July, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Nature 601, 531 (2022) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2104.01180">arXiv:2104.01180</a> <span> [<a href="https://arxiv.org/pdf/2104.01180">pdf</a>, <a href="https://arxiv.org/format/2104.01180">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 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/10.1126/science.abi8378">10.1126/science.abi8378 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Realizing topologically ordered states on a quantum processor </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Satzinger%2C+K+J">K. J. Satzinger</a>, <a href="/search/cond-mat?searchtype=author&query=Liu%2C+Y">Y. Liu</a>, <a href="/search/cond-mat?searchtype=author&query=Smith%2C+A">A. Smith</a>, <a href="/search/cond-mat?searchtype=author&query=Knapp%2C+C">C. Knapp</a>, <a href="/search/cond-mat?searchtype=author&query=Newman%2C+M">M. Newman</a>, <a href="/search/cond-mat?searchtype=author&query=Jones%2C+C">C. Jones</a>, <a href="/search/cond-mat?searchtype=author&query=Chen%2C+Z">Z. Chen</a>, <a href="/search/cond-mat?searchtype=author&query=Quintana%2C+C">C. Quintana</a>, <a href="/search/cond-mat?searchtype=author&query=Mi%2C+X">X. Mi</a>, <a href="/search/cond-mat?searchtype=author&query=Dunsworth%2C+A">A. Dunsworth</a>, <a href="/search/cond-mat?searchtype=author&query=Gidney%2C+C">C. Gidney</a>, <a href="/search/cond-mat?searchtype=author&query=Aleiner%2C+I">I. Aleiner</a>, <a href="/search/cond-mat?searchtype=author&query=Arute%2C+F">F. Arute</a>, <a href="/search/cond-mat?searchtype=author&query=Arya%2C+K">K. Arya</a>, <a href="/search/cond-mat?searchtype=author&query=Atalaya%2C+J">J. Atalaya</a>, <a href="/search/cond-mat?searchtype=author&query=Babbush%2C+R">R. Babbush</a>, <a href="/search/cond-mat?searchtype=author&query=Bardin%2C+J+C">J. C. Bardin</a>, <a href="/search/cond-mat?searchtype=author&query=Barends%2C+R">R. Barends</a>, <a href="/search/cond-mat?searchtype=author&query=Basso%2C+J">J. Basso</a>, <a href="/search/cond-mat?searchtype=author&query=Bengtsson%2C+A">A. Bengtsson</a>, <a href="/search/cond-mat?searchtype=author&query=Bilmes%2C+A">A. Bilmes</a>, <a href="/search/cond-mat?searchtype=author&query=Broughton%2C+M">M. Broughton</a>, <a href="/search/cond-mat?searchtype=author&query=Buckley%2C+B+B">B. B. Buckley</a>, <a href="/search/cond-mat?searchtype=author&query=Buell%2C+D+A">D. A. Buell</a>, <a href="/search/cond-mat?searchtype=author&query=Burkett%2C+B">B. Burkett</a> , et al. (73 additional authors not shown) </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="2104.01180v1-abstract-short" style="display: inline;"> The discovery of topological order has revolutionized the understanding of quantum matter in modern physics and provided the theoretical foundation for many quantum error correcting codes. Realizing topologically ordered states has proven to be extremely challenging in both condensed matter and synthetic quantum systems. Here, we prepare the ground state of the toric code Hamiltonian using an effi… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2104.01180v1-abstract-full').style.display = 'inline'; document.getElementById('2104.01180v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2104.01180v1-abstract-full" style="display: none;"> The discovery of topological order has revolutionized the understanding of quantum matter in modern physics and provided the theoretical foundation for many quantum error correcting codes. Realizing topologically ordered states has proven to be extremely challenging in both condensed matter and synthetic quantum systems. Here, we prepare the ground state of the toric code Hamiltonian using an efficient quantum circuit on a superconducting quantum processor. We measure a topological entanglement entropy near the expected value of $\ln2$, and simulate anyon interferometry to extract the braiding statistics of the emergent excitations. Furthermore, we investigate key aspects of the surface code, including logical state injection and the decay of the non-local order parameter. Our results demonstrate the potential for quantum processors to provide key insights into topological quantum matter and quantum error correction. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2104.01180v1-abstract-full').style.display = 'none'; document.getElementById('2104.01180v1-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 April, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 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">6 pages 4 figures, plus supplementary materials</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Science 374, 1237-1241 (2021) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2101.08870">arXiv:2101.08870</a> <span> [<a href="https://arxiv.org/pdf/2101.08870">pdf</a>, <a href="https://arxiv.org/format/2101.08870">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="High Energy Physics - Theory">hep-th</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/10.1126/science.abg5029">10.1126/science.abg5029 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Information Scrambling in Computationally Complex Quantum Circuits </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Mi%2C+X">Xiao Mi</a>, <a href="/search/cond-mat?searchtype=author&query=Roushan%2C+P">Pedram Roushan</a>, <a href="/search/cond-mat?searchtype=author&query=Quintana%2C+C">Chris Quintana</a>, <a href="/search/cond-mat?searchtype=author&query=Mandra%2C+S">Salvatore Mandra</a>, <a href="/search/cond-mat?searchtype=author&query=Marshall%2C+J">Jeffrey Marshall</a>, <a href="/search/cond-mat?searchtype=author&query=Neill%2C+C">Charles Neill</a>, <a href="/search/cond-mat?searchtype=author&query=Arute%2C+F">Frank Arute</a>, <a href="/search/cond-mat?searchtype=author&query=Arya%2C+K">Kunal Arya</a>, <a href="/search/cond-mat?searchtype=author&query=Atalaya%2C+J">Juan Atalaya</a>, <a href="/search/cond-mat?searchtype=author&query=Babbush%2C+R">Ryan Babbush</a>, <a href="/search/cond-mat?searchtype=author&query=Bardin%2C+J+C">Joseph C. Bardin</a>, <a href="/search/cond-mat?searchtype=author&query=Barends%2C+R">Rami Barends</a>, <a href="/search/cond-mat?searchtype=author&query=Bengtsson%2C+A">Andreas Bengtsson</a>, <a href="/search/cond-mat?searchtype=author&query=Boixo%2C+S">Sergio Boixo</a>, <a href="/search/cond-mat?searchtype=author&query=Bourassa%2C+A">Alexandre Bourassa</a>, <a href="/search/cond-mat?searchtype=author&query=Broughton%2C+M">Michael Broughton</a>, <a href="/search/cond-mat?searchtype=author&query=Buckley%2C+B+B">Bob B. Buckley</a>, <a href="/search/cond-mat?searchtype=author&query=Buell%2C+D+A">David A. Buell</a>, <a href="/search/cond-mat?searchtype=author&query=Burkett%2C+B">Brian Burkett</a>, <a href="/search/cond-mat?searchtype=author&query=Bushnell%2C+N">Nicholas Bushnell</a>, <a href="/search/cond-mat?searchtype=author&query=Chen%2C+Z">Zijun Chen</a>, <a href="/search/cond-mat?searchtype=author&query=Chiaro%2C+B">Benjamin Chiaro</a>, <a href="/search/cond-mat?searchtype=author&query=Collins%2C+R">Roberto Collins</a>, <a href="/search/cond-mat?searchtype=author&query=Courtney%2C+W">William Courtney</a>, <a href="/search/cond-mat?searchtype=author&query=Demura%2C+S">Sean Demura</a> , et al. (68 additional authors not shown) </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="2101.08870v1-abstract-short" style="display: inline;"> Interaction in quantum systems can spread initially localized quantum information into the many degrees of freedom of the entire system. Understanding this process, known as quantum scrambling, is the key to resolving various conundrums in physics. Here, by measuring the time-dependent evolution and fluctuation of out-of-time-order correlators, we experimentally investigate the dynamics of quantum… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2101.08870v1-abstract-full').style.display = 'inline'; document.getElementById('2101.08870v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2101.08870v1-abstract-full" style="display: none;"> Interaction in quantum systems can spread initially localized quantum information into the many degrees of freedom of the entire system. Understanding this process, known as quantum scrambling, is the key to resolving various conundrums in physics. Here, by measuring the time-dependent evolution and fluctuation of out-of-time-order correlators, we experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor. We engineer quantum circuits that distinguish the two mechanisms associated with quantum scrambling, operator spreading and operator entanglement, and experimentally observe their respective signatures. We show that while operator spreading is captured by an efficient classical model, operator entanglement requires exponentially scaled computational resources to simulate. These results open the path to studying complex and practically relevant physical observables with near-term quantum processors. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2101.08870v1-abstract-full').style.display = 'none'; document.getElementById('2101.08870v1-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 January, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Science 374, 1479 (2021) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2003.02989">arXiv:2003.02989</a> <span> [<a href="https://arxiv.org/pdf/2003.02989">pdf</a>, <a href="https://arxiv.org/format/2003.02989">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="Disordered Systems and Neural Networks">cond-mat.dis-nn</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Machine Learning">cs.LG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Programming Languages">cs.PL</span> </div> </div> <p class="title is-5 mathjax"> TensorFlow Quantum: A Software Framework for Quantum Machine Learning </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Broughton%2C+M">Michael Broughton</a>, <a href="/search/cond-mat?searchtype=author&query=Verdon%2C+G">Guillaume Verdon</a>, <a href="/search/cond-mat?searchtype=author&query=McCourt%2C+T">Trevor McCourt</a>, <a href="/search/cond-mat?searchtype=author&query=Martinez%2C+A+J">Antonio J. Martinez</a>, <a href="/search/cond-mat?searchtype=author&query=Yoo%2C+J+H">Jae Hyeon Yoo</a>, <a href="/search/cond-mat?searchtype=author&query=Isakov%2C+S+V">Sergei V. Isakov</a>, <a href="/search/cond-mat?searchtype=author&query=Massey%2C+P">Philip Massey</a>, <a href="/search/cond-mat?searchtype=author&query=Halavati%2C+R">Ramin Halavati</a>, <a href="/search/cond-mat?searchtype=author&query=Niu%2C+M+Y">Murphy Yuezhen Niu</a>, <a href="/search/cond-mat?searchtype=author&query=Zlokapa%2C+A">Alexander Zlokapa</a>, <a href="/search/cond-mat?searchtype=author&query=Peters%2C+E">Evan Peters</a>, <a href="/search/cond-mat?searchtype=author&query=Lockwood%2C+O">Owen Lockwood</a>, <a href="/search/cond-mat?searchtype=author&query=Skolik%2C+A">Andrea Skolik</a>, <a href="/search/cond-mat?searchtype=author&query=Jerbi%2C+S">Sofiene Jerbi</a>, <a href="/search/cond-mat?searchtype=author&query=Dunjko%2C+V">Vedran Dunjko</a>, <a href="/search/cond-mat?searchtype=author&query=Leib%2C+M">Martin Leib</a>, <a href="/search/cond-mat?searchtype=author&query=Streif%2C+M">Michael Streif</a>, <a href="/search/cond-mat?searchtype=author&query=Von+Dollen%2C+D">David Von Dollen</a>, <a href="/search/cond-mat?searchtype=author&query=Chen%2C+H">Hongxiang Chen</a>, <a href="/search/cond-mat?searchtype=author&query=Cao%2C+S">Shuxiang Cao</a>, <a href="/search/cond-mat?searchtype=author&query=Wiersema%2C+R">Roeland Wiersema</a>, <a href="/search/cond-mat?searchtype=author&query=Huang%2C+H">Hsin-Yuan Huang</a>, <a href="/search/cond-mat?searchtype=author&query=McClean%2C+J+R">Jarrod R. McClean</a>, <a href="/search/cond-mat?searchtype=author&query=Babbush%2C+R">Ryan Babbush</a>, <a href="/search/cond-mat?searchtype=author&query=Boixo%2C+S">Sergio Boixo</a> , et al. (4 additional authors not shown) </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="2003.02989v2-abstract-short" style="display: inline;"> We introduce TensorFlow Quantum (TFQ), an open source library for the rapid prototyping of hybrid quantum-classical models for classical or quantum data. This framework offers high-level abstractions for the design and training of both discriminative and generative quantum models under TensorFlow and supports high-performance quantum circuit simulators. We provide an overview of the software archi… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2003.02989v2-abstract-full').style.display = 'inline'; document.getElementById('2003.02989v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2003.02989v2-abstract-full" style="display: none;"> We introduce TensorFlow Quantum (TFQ), an open source library for the rapid prototyping of hybrid quantum-classical models for classical or quantum data. This framework offers high-level abstractions for the design and training of both discriminative and generative quantum models under TensorFlow and supports high-performance quantum circuit simulators. We provide an overview of the software architecture and building blocks through several examples and review the theory of hybrid quantum-classical neural networks. We illustrate TFQ functionalities via several basic applications including supervised learning for quantum classification, quantum control, simulating noisy quantum circuits, and quantum approximate optimization. Moreover, we demonstrate how one can apply TFQ to tackle advanced quantum learning tasks including meta-learning, layerwise learning, Hamiltonian learning, sampling thermal states, variational quantum eigensolvers, classification of quantum phase transitions, generative adversarial networks, and reinforcement learning. We hope this framework provides the necessary tools for the quantum computing and machine learning research communities to explore models of both natural and artificial quantum systems, and ultimately discover new quantum algorithms which could potentially yield a quantum advantage. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2003.02989v2-abstract-full').style.display = 'none'; document.getElementById('2003.02989v2-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> 26 August, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 5 March, 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">Comments:</span> <span class="has-text-grey-dark mathjax">56 pages, 34 figures, many updates throughout the manuscript, several new sections are added</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1712.05304">arXiv:1712.05304</a> <span> [<a href="https://arxiv.org/pdf/1712.05304">pdf</a>, <a href="https://arxiv.org/format/1712.05304">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="Disordered Systems and Neural Networks">cond-mat.dis-nn</span> </div> </div> <p class="title is-5 mathjax"> A quantum algorithm to train neural networks using low-depth circuits </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Verdon%2C+G">Guillaume Verdon</a>, <a href="/search/cond-mat?searchtype=author&query=Broughton%2C+M">Michael Broughton</a>, <a href="/search/cond-mat?searchtype=author&query=Biamonte%2C+J">Jacob Biamonte</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="1712.05304v2-abstract-short" style="display: inline;"> Can near-term gate model based quantum processors offer quantum advantage for practical applications in the pre-fault tolerance noise regime? A class of algorithms which have shown some promise in this regard are the so-called classical-quantum hybrid variational algorithms. Here we develop a low-depth quantum algorithm to generative neural networks using variational quantum circuits. We introduce… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1712.05304v2-abstract-full').style.display = 'inline'; document.getElementById('1712.05304v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1712.05304v2-abstract-full" style="display: none;"> Can near-term gate model based quantum processors offer quantum advantage for practical applications in the pre-fault tolerance noise regime? A class of algorithms which have shown some promise in this regard are the so-called classical-quantum hybrid variational algorithms. Here we develop a low-depth quantum algorithm to generative neural networks using variational quantum circuits. We introduce a method which employs the quantum approximate optimization algorithm as a subroutine in order produce then sample low-energy distributions of Ising Hamiltonians. We sample these states to train neural networks and demonstrate training convergence for numerically simulated noisy circuits with depolarizing errors of rates of up to $4\%$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1712.05304v2-abstract-full').style.display = 'none'; document.getElementById('1712.05304v2-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 August, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 14 December, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2017. </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, submitted to review in a journal</span> </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 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