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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/2403.08725">arXiv:2403.08725</a> <span> [<a href="https://arxiv.org/pdf/2403.08725">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="Mesoscale and Nanoscale Physics">cond-mat.mes-hall</span> </div> </div> <p class="title is-5 mathjax"> Driving non-trivial quantum phases in conventional semiconductors with intense excitonic fields </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Pareek%2C+V">Vivek Pareek</a>, <a href="/search/cond-mat?searchtype=author&query=Bacon%2C+D+R">David R. Bacon</a>, <a href="/search/cond-mat?searchtype=author&query=Zhu%2C+X">Xing Zhu</a>, <a href="/search/cond-mat?searchtype=author&query=Chan%2C+Y">Yang-Hao Chan</a>, <a href="/search/cond-mat?searchtype=author&query=Bussolotti%2C+F">Fabio Bussolotti</a>, <a href="/search/cond-mat?searchtype=author&query=Chan%2C+N+S">Nicholas S. Chan</a>, <a href="/search/cond-mat?searchtype=author&query=Urquizo%2C+J+P">Joel P茅rez Urquizo</a>, <a href="/search/cond-mat?searchtype=author&query=Watanabe%2C+K">Kenji Watanabe</a>, <a href="/search/cond-mat?searchtype=author&query=Taniguchi%2C+T">Takashi Taniguchi</a>, <a href="/search/cond-mat?searchtype=author&query=Man%2C+M+K+L">Michael K. L. Man</a>, <a href="/search/cond-mat?searchtype=author&query=Mad%C3%A9o%2C+J">Julien Mad茅o</a>, <a href="/search/cond-mat?searchtype=author&query=Qiu%2C+D+Y">Diana Y. Qiu</a>, <a href="/search/cond-mat?searchtype=author&query=Goh%2C+K+E+J">Kuan Eng Johnson Goh</a>, <a href="/search/cond-mat?searchtype=author&query=da+Jornada%2C+F+H">Felipe H. da Jornada</a>, <a href="/search/cond-mat?searchtype=author&query=Dani%2C+K+M">Keshav M. Dani</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2403.08725v1-abstract-short" style="display: inline;"> Inducing novel quantum phases and topologies in materials using intense light fields is a key objective of modern condensed matter physics, but nonetheless faces significant experimental challenges. Alternately, theory predicts that in the dense limit, excitons - collective excitations composed of Coulomb-bound electron-hole pairs - could also drive exotic quantum phenomena. However, the direct ob… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2403.08725v1-abstract-full').style.display = 'inline'; document.getElementById('2403.08725v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2403.08725v1-abstract-full" style="display: none;"> Inducing novel quantum phases and topologies in materials using intense light fields is a key objective of modern condensed matter physics, but nonetheless faces significant experimental challenges. Alternately, theory predicts that in the dense limit, excitons - collective excitations composed of Coulomb-bound electron-hole pairs - could also drive exotic quantum phenomena. However, the direct observation of these phenomena requires the resolution of electronic structure in momentum space in the presence of excitons, which became possible only recently. Here, using time- and angle-resolved photoemission spectroscopy of an atomically thin semiconductor in the presence of a high-density of resonantly and coherently photoexcited excitons, we observe the Bardeen-Cooper-Schrieffer (BCS) excitonic state - analogous to the Cooper pairs of superconductivity. We see the valence band transform from a conventional paraboloid into a Mexican-hat like Bogoliubov dispersion - a hallmark of the excitonic insulator phase; and we observe the recently predicted giant exciton-driven Floquet effects. Our work realizes the promise that intense bosonic fields, other than photons, can also drive novel quantum phenomena and phases in materials. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2403.08725v1-abstract-full').style.display = 'none'; document.getElementById('2403.08725v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 13 March, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 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/2108.01933">arXiv:2108.01933</a> <span> [<a href="https://arxiv.org/pdf/2108.01933">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> <span class="tag is-small is-grey 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="Applied Physics">physics.app-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Chemical Physics">physics.chem-ph</span> </div> </div> <p class="title is-5 mathjax"> Moir茅-localized interlayer exciton wavefunctions captured by imaging its electron and hole constituents </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Karni%2C+O">Ouri Karni</a>, <a href="/search/cond-mat?searchtype=author&query=Barr%C3%A9%2C+E">Elyse Barr茅</a>, <a href="/search/cond-mat?searchtype=author&query=Pareek%2C+V">Vivek Pareek</a>, <a href="/search/cond-mat?searchtype=author&query=Georgaras%2C+J+D">Johnathan D. Georgaras</a>, <a href="/search/cond-mat?searchtype=author&query=Man%2C+M+K+L">Michael K. L. Man</a>, <a href="/search/cond-mat?searchtype=author&query=Sahoo%2C+C">Chakradhar Sahoo</a>, <a href="/search/cond-mat?searchtype=author&query=Bacon%2C+D+R">David R. Bacon</a>, <a href="/search/cond-mat?searchtype=author&query=Zhu%2C+X">Xing Zhu</a>, <a href="/search/cond-mat?searchtype=author&query=Ribeiro%2C+H+B">Henrique B. Ribeiro</a>, <a href="/search/cond-mat?searchtype=author&query=O%27Beirne%2C+A+L">Aidan L. O'Beirne</a>, <a href="/search/cond-mat?searchtype=author&query=Hu%2C+J">Jenny Hu</a>, <a href="/search/cond-mat?searchtype=author&query=Al-Mahboob%2C+A">Abdullah Al-Mahboob</a>, <a href="/search/cond-mat?searchtype=author&query=Abdelrasoul%2C+M+M+M">Mohamed M. M. Abdelrasoul</a>, <a href="/search/cond-mat?searchtype=author&query=Chan%2C+N+S">Nicholas S. Chan</a>, <a href="/search/cond-mat?searchtype=author&query=Karmakar%2C+A">Arka Karmakar</a>, <a href="/search/cond-mat?searchtype=author&query=Winchester%2C+A+J">Andrew J. Winchester</a>, <a href="/search/cond-mat?searchtype=author&query=Kim%2C+B">Bumho Kim</a>, <a href="/search/cond-mat?searchtype=author&query=Watanabe%2C+K">Kenji Watanabe</a>, <a href="/search/cond-mat?searchtype=author&query=Taniguchi%2C+T">Takashi Taniguchi</a>, <a href="/search/cond-mat?searchtype=author&query=Barmak%2C+K">Katayun Barmak</a>, <a href="/search/cond-mat?searchtype=author&query=Mad%C3%A9o%2C+J">Julien Mad茅o</a>, <a href="/search/cond-mat?searchtype=author&query=da+Jornada%2C+F+H">Felipe H. da Jornada</a>, <a href="/search/cond-mat?searchtype=author&query=Heinz%2C+T+F">Tony F. Heinz</a>, <a href="/search/cond-mat?searchtype=author&query=Dani%2C+K+M">Keshav M. Dani</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="2108.01933v1-abstract-short" style="display: inline;"> Interlayer excitons (ILXs) - electron-hole pairs bound across two atomically thin layered semiconductors - have emerged as attractive platforms to study exciton condensation, single-photon emission and other quantum-information applications. Yet, despite extensive optical spectroscopic investigations, critical information about their size, valley configuration and the influence of the moir茅 potent… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2108.01933v1-abstract-full').style.display = 'inline'; document.getElementById('2108.01933v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2108.01933v1-abstract-full" style="display: none;"> Interlayer excitons (ILXs) - electron-hole pairs bound across two atomically thin layered semiconductors - have emerged as attractive platforms to study exciton condensation, single-photon emission and other quantum-information applications. Yet, despite extensive optical spectroscopic investigations, critical information about their size, valley configuration and the influence of the moir茅 potential remains unknown. Here, we captured images of the time- and momentum-resolved distribution of both the electron and the hole that bind to form the ILX in a WSe2/MoS2 heterostructure. We thereby obtain a direct measurement of the interlayer exciton diameter of ~5.4 nm, comparable to the moir茅 unit-cell length of 6.1 nm. Surprisingly, this large ILX is well localized within the moir茅 cell to a region of only 1.8 nm - smaller than the size of the exciton itself. This high degree of localization of the interlayer exciton is backed by Bethe-Salpeter equation calculations and demonstrates that the ILX can be localized within small moir茅 unit cells. Unlike large moir茅 cells, these are uniform over large regions, thus allowing the formation of extended arrays of localized excitations for quantum technology. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2108.01933v1-abstract-full').style.display = 'none'; document.getElementById('2108.01933v1-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 August, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 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">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/2011.13104">arXiv:2011.13104</a> <span> [<a href="https://arxiv.org/pdf/2011.13104">pdf</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> </div> </div> <p class="title is-5 mathjax"> Experimental measurement of the intrinsic excitonic wavefunction </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Man%2C+M+K+L">Michael K. L. Man</a>, <a href="/search/cond-mat?searchtype=author&query=Mad%C3%A9o%2C+J">Julien Mad茅o</a>, <a href="/search/cond-mat?searchtype=author&query=Sahoo%2C+C">Chakradhar Sahoo</a>, <a href="/search/cond-mat?searchtype=author&query=Xie%2C+K">Kaichen Xie</a>, <a href="/search/cond-mat?searchtype=author&query=Campbell%2C+M">Marshall Campbell</a>, <a href="/search/cond-mat?searchtype=author&query=Pareek%2C+V">Vivek Pareek</a>, <a href="/search/cond-mat?searchtype=author&query=Karmakar%2C+A">Arka Karmakar</a>, <a href="/search/cond-mat?searchtype=author&query=Wong%2C+E+L">E Laine Wong</a>, <a href="/search/cond-mat?searchtype=author&query=Al-Mahboob%2C+A">Abdullah Al-Mahboob</a>, <a href="/search/cond-mat?searchtype=author&query=Chan%2C+N+S">Nicholas S. Chan</a>, <a href="/search/cond-mat?searchtype=author&query=Bacon%2C+D+R">David R. Bacon</a>, <a href="/search/cond-mat?searchtype=author&query=Zhu%2C+X">Xing Zhu</a>, <a href="/search/cond-mat?searchtype=author&query=Abdelrasoul%2C+M">Mohamed Abdelrasoul</a>, <a href="/search/cond-mat?searchtype=author&query=Li%2C+X">Xiaoquin Li</a>, <a href="/search/cond-mat?searchtype=author&query=Heinz%2C+T+F">Tony F. Heinz</a>, <a href="/search/cond-mat?searchtype=author&query=da+Jornada%2C+F+H">Felipe H. da Jornada</a>, <a href="/search/cond-mat?searchtype=author&query=Cao%2C+T">Ting Cao</a>, <a href="/search/cond-mat?searchtype=author&query=Dani%2C+K+M">Keshav M. Dani</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="2011.13104v1-abstract-short" style="display: inline;"> An exciton, a two-body composite quasiparticle formed of an electron and hole, is a fundamental optical excitation in condensed-matter systems. Since its discovery nearly a century ago, a measurement of the excitonic wavefunction has remained beyond experimental reach. Here, we directly image the excitonic wavefunction in reciprocal space by measuring the momentum distribution of electrons photoem… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2011.13104v1-abstract-full').style.display = 'inline'; document.getElementById('2011.13104v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2011.13104v1-abstract-full" style="display: none;"> An exciton, a two-body composite quasiparticle formed of an electron and hole, is a fundamental optical excitation in condensed-matter systems. Since its discovery nearly a century ago, a measurement of the excitonic wavefunction has remained beyond experimental reach. Here, we directly image the excitonic wavefunction in reciprocal space by measuring the momentum distribution of electrons photoemitted from excitons in monolayer WSe2. By transforming to real space, we obtain a visual of the distribution of the electron around the hole in an exciton. Further, by also resolving the energy coordinate, we confirm the elusive theoretical prediction that the photoemitted electron exhibits an inverted energy-momentum dispersion relationship reflecting the valence band where the partner hole remains, rather than that of conduction-band states of the electron. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2011.13104v1-abstract-full').style.display = 'none'; document.getElementById('2011.13104v1-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 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">Comments:</span> <span class="has-text-grey-dark mathjax">27 pages</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2003.02989">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/1912.07577">arXiv:1912.07577</a> <span> [<a href="https://arxiv.org/pdf/1912.07577">pdf</a>, <a href="https://arxiv.org/format/1912.07577">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> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Nuclear Theory">nucl-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/10.1103/PRXQuantum.2.017001">10.1103/PRXQuantum.2.017001 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Quantum Computer Systems for Scientific Discovery </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Alexeev%2C+Y">Yuri Alexeev</a>, <a href="/search/cond-mat?searchtype=author&query=Bacon%2C+D">Dave Bacon</a>, <a href="/search/cond-mat?searchtype=author&query=Brown%2C+K+R">Kenneth R. Brown</a>, <a href="/search/cond-mat?searchtype=author&query=Calderbank%2C+R">Robert Calderbank</a>, <a href="/search/cond-mat?searchtype=author&query=Carr%2C+L+D">Lincoln D. Carr</a>, <a href="/search/cond-mat?searchtype=author&query=Chong%2C+F+T">Frederic T. Chong</a>, <a href="/search/cond-mat?searchtype=author&query=DeMarco%2C+B">Brian DeMarco</a>, <a href="/search/cond-mat?searchtype=author&query=Englund%2C+D">Dirk Englund</a>, <a href="/search/cond-mat?searchtype=author&query=Farhi%2C+E">Edward Farhi</a>, <a href="/search/cond-mat?searchtype=author&query=Fefferman%2C+B">Bill Fefferman</a>, <a href="/search/cond-mat?searchtype=author&query=Gorshkov%2C+A+V">Alexey V. Gorshkov</a>, <a href="/search/cond-mat?searchtype=author&query=Houck%2C+A">Andrew Houck</a>, <a href="/search/cond-mat?searchtype=author&query=Kim%2C+J">Jungsang Kim</a>, <a href="/search/cond-mat?searchtype=author&query=Kimmel%2C+S">Shelby Kimmel</a>, <a href="/search/cond-mat?searchtype=author&query=Lange%2C+M">Michael Lange</a>, <a href="/search/cond-mat?searchtype=author&query=Lloyd%2C+S">Seth Lloyd</a>, <a href="/search/cond-mat?searchtype=author&query=Lukin%2C+M+D">Mikhail D. Lukin</a>, <a href="/search/cond-mat?searchtype=author&query=Maslov%2C+D">Dmitri Maslov</a>, <a href="/search/cond-mat?searchtype=author&query=Maunz%2C+P">Peter Maunz</a>, <a href="/search/cond-mat?searchtype=author&query=Monroe%2C+C">Christopher Monroe</a>, <a href="/search/cond-mat?searchtype=author&query=Preskill%2C+J">John Preskill</a>, <a href="/search/cond-mat?searchtype=author&query=Roetteler%2C+M">Martin Roetteler</a>, <a href="/search/cond-mat?searchtype=author&query=Savage%2C+M">Martin Savage</a>, <a href="/search/cond-mat?searchtype=author&query=Thompson%2C+J">Jeff Thompson</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="1912.07577v3-abstract-short" style="display: inline;"> The great promise of quantum computers comes with the dual challenges of building them and finding their useful applications. We argue that these two challenges should be considered together, by co-designing full-stack quantum computer systems along with their applications in order to hasten their development and potential for scientific discovery. In this context, we identify scientific and commu… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1912.07577v3-abstract-full').style.display = 'inline'; document.getElementById('1912.07577v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1912.07577v3-abstract-full" style="display: none;"> The great promise of quantum computers comes with the dual challenges of building them and finding their useful applications. We argue that these two challenges should be considered together, by co-designing full-stack quantum computer systems along with their applications in order to hasten their development and potential for scientific discovery. In this context, we identify scientific and community needs, opportunities, a sampling of a few use case studies, and significant challenges for the development of quantum computers for science over the next 2--10 years. This document is written by a community of university, national laboratory, and industrial researchers in the field of Quantum Information Science and Technology, and is based on a summary from a U.S. National Science Foundation workshop on Quantum Computing held on October 21--22, 2019 in Alexandria, VA. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1912.07577v3-abstract-full').style.display = 'none'; document.getElementById('1912.07577v3-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, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 16 December, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> PRX Quantum 2, 017001 (2021) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1910.06024">arXiv:1910.06024</a> <span> [<a href="https://arxiv.org/pdf/1910.06024">pdf</a>, <a href="https://arxiv.org/format/1910.06024">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link 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> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> </div> <p class="title is-5 mathjax"> Direct measurement of non-local interactions in the many-body localized phase </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Chiaro%2C+B">B. Chiaro</a>, <a href="/search/cond-mat?searchtype=author&query=Neill%2C+C">C. Neill</a>, <a href="/search/cond-mat?searchtype=author&query=Bohrdt%2C+A">A. Bohrdt</a>, <a href="/search/cond-mat?searchtype=author&query=Filippone%2C+M">M. Filippone</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=Babbush%2C+R">R. Babbush</a>, <a href="/search/cond-mat?searchtype=author&query=Bacon%2C+D">D. Bacon</a>, <a href="/search/cond-mat?searchtype=author&query=Bardin%2C+J">J. Bardin</a>, <a href="/search/cond-mat?searchtype=author&query=Barends%2C+R">R. Barends</a>, <a href="/search/cond-mat?searchtype=author&query=Boixo%2C+S">S. Boixo</a>, <a href="/search/cond-mat?searchtype=author&query=Buell%2C+D">D. Buell</a>, <a href="/search/cond-mat?searchtype=author&query=Burkett%2C+B">B. Burkett</a>, <a href="/search/cond-mat?searchtype=author&query=Chen%2C+Y">Y. Chen</a>, <a href="/search/cond-mat?searchtype=author&query=Chen%2C+Z">Z. Chen</a>, <a href="/search/cond-mat?searchtype=author&query=Collins%2C+R">R. Collins</a>, <a href="/search/cond-mat?searchtype=author&query=Dunsworth%2C+A">A. Dunsworth</a>, <a href="/search/cond-mat?searchtype=author&query=Farhi%2C+E">E. Farhi</a>, <a href="/search/cond-mat?searchtype=author&query=Fowler%2C+A">A. Fowler</a>, <a href="/search/cond-mat?searchtype=author&query=Foxen%2C+B">B. Foxen</a>, <a href="/search/cond-mat?searchtype=author&query=Gidney%2C+C">C. Gidney</a>, <a href="/search/cond-mat?searchtype=author&query=Giustina%2C+M">M. Giustina</a>, <a href="/search/cond-mat?searchtype=author&query=Harrigan%2C+M">M. Harrigan</a>, <a href="/search/cond-mat?searchtype=author&query=Huang%2C+T">T. Huang</a>, <a href="/search/cond-mat?searchtype=author&query=Isakov%2C+S">S. Isakov</a> , et al. (36 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="1910.06024v2-abstract-short" style="display: inline;"> The interplay of interactions and strong disorder can lead to an exotic quantum many-body localized (MBL) phase. Beyond the absence of transport, the MBL phase has distinctive signatures, such as slow dephasing and logarithmic entanglement growth; they commonly result in slow and subtle modification of the dynamics, making their measurement challenging. Here, we experimentally characterize these p… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1910.06024v2-abstract-full').style.display = 'inline'; document.getElementById('1910.06024v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1910.06024v2-abstract-full" style="display: none;"> The interplay of interactions and strong disorder can lead to an exotic quantum many-body localized (MBL) phase. Beyond the absence of transport, the MBL phase has distinctive signatures, such as slow dephasing and logarithmic entanglement growth; they commonly result in slow and subtle modification of the dynamics, making their measurement challenging. Here, we experimentally characterize these properties of the MBL phase in a system of coupled superconducting qubits. By implementing phase sensitive techniques, we map out the structure of local integrals of motion in the MBL phase. Tomographic reconstruction of single and two qubit density matrices allowed us to determine the spatial and temporal entanglement growth between the localized sites. In addition, we study the preservation of entanglement in the MBL phase. The interferometric protocols implemented here measure affirmative correlations and allow us to exclude artifacts due to the imperfect isolation of the system. By measuring elusive MBL quantities, our work highlights the advantages of phase sensitive measurements in studying novel phases of matter. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1910.06024v2-abstract-full').style.display = 'none'; document.getElementById('1910.06024v2-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, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 14 October, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">5+28 pages, 5+22 figures, updated version</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1006.4388">arXiv:1006.4388</a> <span> [<a href="https://arxiv.org/pdf/1006.4388">pdf</a>, <a href="https://arxiv.org/format/1006.4388">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link 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="Computational Complexity">cs.CC</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/PhysRevE.82.031106">10.1103/PhysRevE.82.031106 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Making Classical Ground State Spin Computing Fault-Tolerant </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Crosson%2C+E">Elizabeth Crosson</a>, <a href="/search/cond-mat?searchtype=author&query=Bacon%2C+D">Dave Bacon</a>, <a href="/search/cond-mat?searchtype=author&query=Brown%2C+K+R">Kenneth R. Brown</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="1006.4388v2-abstract-short" style="display: inline;"> We examine a model of classical deterministic computing in which the ground state of the classical system is a spatial history of the computation. This model is relevant to quantum dot cellular automata as well as to recent universal adiabatic quantum computing constructions. In its most primitive form, systems constructed in this model cannot compute in an error free manner when working at non-ze… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1006.4388v2-abstract-full').style.display = 'inline'; document.getElementById('1006.4388v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1006.4388v2-abstract-full" style="display: none;"> We examine a model of classical deterministic computing in which the ground state of the classical system is a spatial history of the computation. This model is relevant to quantum dot cellular automata as well as to recent universal adiabatic quantum computing constructions. In its most primitive form, systems constructed in this model cannot compute in an error free manner when working at non-zero temperature. However, by exploiting a mapping between the partition function for this model and probabilistic classical circuits we are able to show that it is possible to make this model effectively error free. We achieve this by using techniques in fault-tolerant classical computing and the result is that the system can compute effectively error free if the temperature is below a critical temperature. We further link this model to computational complexity and show that a certain problem concerning finite temperature classical spin systems is complete for the complexity class Merlin-Arthur. This provides an interesting connection between the physical behavior of certain many-body spin systems and computational complexity. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1006.4388v2-abstract-full').style.display = 'none'; document.getElementById('1006.4388v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 18 November, 2014; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 22 June, 2010; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 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">24 pages, 1 figure</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Physical Review E, 82(3), 031106 (2010) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/quant-ph/0506023">arXiv:quant-ph/0506023</a> <span> [<a href="https://arxiv.org/pdf/quant-ph/0506023">pdf</a>, <a href="https://arxiv.org/ps/quant-ph/0506023">ps</a>, <a href="https://arxiv.org/format/quant-ph/0506023">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/10.1103/PhysRevA.73.012340">10.1103/PhysRevA.73.012340 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Operator Quantum Error Correcting Subsystems for Self-Correcting Quantum Memories </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Bacon%2C+D">Dave Bacon</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="quant-ph/0506023v4-abstract-short" style="display: inline;"> The most general method for encoding quantum information is not to encode the information into a subspace of a Hilbert space, but to encode information into a subsystem of a Hilbert space. Recently this notion has led to a more general notion of quantum error correction known as operator quantum error correction. In standard quantum error correcting codes, one requires the ability to apply a pro… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('quant-ph/0506023v4-abstract-full').style.display = 'inline'; document.getElementById('quant-ph/0506023v4-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="quant-ph/0506023v4-abstract-full" style="display: none;"> The most general method for encoding quantum information is not to encode the information into a subspace of a Hilbert space, but to encode information into a subsystem of a Hilbert space. Recently this notion has led to a more general notion of quantum error correction known as operator quantum error correction. In standard quantum error correcting codes, one requires the ability to apply a procedure which exactly reverses on the error correcting subspace any correctable error. In contrast, for operator error correcting subsystems, the correction procedure need not undo the error which has occurred, but instead one must perform correction only modulo the subsystem structure. This does not lead to codes which differ from subspace codes, but does lead to recovery routines which explicitly make use of the subsystem structure. Here we present two examples of such operator error correcting subsystems. These examples are motivated by simple spatially local Hamiltonians on square and cubic lattices. In three dimensions we provide evidence, in the form a simple mean field theory, that our Hamiltonian gives rise to a system which is self-correcting. Such a system will be a natural high-temperature quantum memory, robust to noise without external intervening quantum error correction procedures. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('quant-ph/0506023v4-abstract-full').style.display = 'none'; document.getElementById('quant-ph/0506023v4-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, 2005; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 2 June, 2005; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2005. </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">17 pages, 3 figures, typos fixed, references added</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. A 73, 012340 (2006) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/quant-ph/9907096">arXiv:quant-ph/9907096</a> <span> [<a href="https://arxiv.org/pdf/quant-ph/9907096">pdf</a>, <a href="https://arxiv.org/ps/quant-ph/9907096">ps</a>, <a href="https://arxiv.org/format/quant-ph/9907096">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="Condensed Matter">cond-mat</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.61.052307">10.1103/PhysRevA.61.052307 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Protecting Quantum Information Encoded in Decoherence Free States Against Exchange Errors </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cond-mat?searchtype=author&query=Lidar%2C+D+A">Daniel A. Lidar</a>, <a href="/search/cond-mat?searchtype=author&query=Bacon%2C+D">David Bacon</a>, <a href="/search/cond-mat?searchtype=author&query=Kempe%2C+J">Julia Kempe</a>, <a href="/search/cond-mat?searchtype=author&query=Whaley%2C+K+B">K. Birgitta Whaley</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="quant-ph/9907096v3-abstract-short" style="display: inline;"> The exchange interaction between identical qubits in a quantum information processor gives rise to unitary two-qubit errors. It is shown here that decoherence free subspaces (DFSs) for collective decoherence undergo Pauli errors under exchange, which however do not take the decoherence free states outside of the DFS. In order to protect DFSs against these errors it is sufficient to employ a rece… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('quant-ph/9907096v3-abstract-full').style.display = 'inline'; document.getElementById('quant-ph/9907096v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="quant-ph/9907096v3-abstract-full" style="display: none;"> The exchange interaction between identical qubits in a quantum information processor gives rise to unitary two-qubit errors. It is shown here that decoherence free subspaces (DFSs) for collective decoherence undergo Pauli errors under exchange, which however do not take the decoherence free states outside of the DFS. In order to protect DFSs against these errors it is sufficient to employ a recently proposed concatenated DFS-quantum error correcting code scheme [D.A. Lidar, D. Bacon and K.B. Whaley, Phys. Rev. Lett. {\bf 82}, 4556 (1999)]. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('quant-ph/9907096v3-abstract-full').style.display = 'none'; document.getElementById('quant-ph/9907096v3-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 December, 1999; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 29 July, 1999; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 1999. </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, no figures. Discussion in section V.A. significantly expanded. Several small changes. Two authors added</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. A Vol. 61(5), p. 52307 (2000) </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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