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A Hierarchy of Spectral Gap Certificates for Frustration-Free Spin Systems

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arXiv 2024年

作者： Rai, Kshiti Sneh Kull, Ilya Emonts, Patrick Tura, Jordi Schuch, Norbert Baccari, Flavio 〈aQaL〉 Applied Quantum Algorithms Universiteit Leiden Netherlands Instituut-Lorentz Universiteit Leiden Niels Bohrweg 2 CA Leiden2333 Netherlands University of Vienna Faculty of Physics Boltzmanngasse 5 ViennaA-1090 Austria University of Vienna Faculty of Mathematics Oskar-Morgenstern-Platz 1 ViennaA-1090 Austria Dipartimento di Fisica e Astronomia "G. Galilei" Università di Padova PadovaI-35131 Italy Padua Quantum Technologies Research Center Università degli Studi di Padova PadovaI-35131 Italy

Estimating spectral gaps of quantum many-body Hamiltonians is a highly challenging computational task, even under assumptions of locality and translation-invariance. Yet, the quest for rigorous gap certificates is motivated by their broad applicability, ranging from many-body physics to quantum computing and classical sampling techniques. Here we present a general method for obtaining lower bounds on the spectral gap of frustration-free quantum Hamiltonians in the thermodynamic limit. We formulate the gap certification problem as a hierarchy of optimization problems (semidefinite programs) in which the certificate—a proof of a lower bound on the gap—is improved with increasing levels. Our approach encompasses existing finite-size methods, such as Knabe’s bound and its subsequent improvements, as those appear as particular possible solutions in our optimization, which is thus guaranteed to either match or surpass them. We demonstrate the power of the method on one-dimensional spin-chain models where we observe an improvement by several orders of magnitude over existing finite size criteria in both the accuracy of the lower bound on the gap, as well as the range of parameters in which a gap is detected. Copyright © 2024, The Authors. All rights reserved.

关键词： Hamiltonians

Detecting Bell Correlations in Multipartite Non-Gaussian Spin States

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Physical Review Letters 2023年第7期131卷 070201-070201页

作者： Jiajie Guo Jordi Tura Qiongyi He Matteo Fadel State Key Laboratory for Mesoscopic Physics School of Physics Frontiers Science Center for Nano-optoelectronics & Collaborative Innovation Center of Quantum Matter Peking University Beijing 100871 China ⟨aQaL⟩ Applied Quantum Algorithms Leiden The Netherlands Instituut-Lorentz Universiteit Leiden P.O. Box 9506 2300 RA Leiden The Netherlands Collaborative Innovation Center of Extreme Optics Shanxi University Taiyuan Shanxi 030006 China Peking University Yangtze Delta Institute of Optoelectronics Nantong 226010 Jiangsu China Hefei National Laboratory Hefei 230088 China Department of Physics ETH Zürich 8093 Zürich Switzerland

We expand the toolbox for studying Bell correlations in multipartite systems by introducing permutationally invariant Bell inequalities (PIBIs) involving few-body correlators. First, we present around twenty families of PIBIs with up to three- or four-body correlators, that are valid for an arbitrary number of particles. Compared to known inequalities, these show higher noise robustness, or the capability to detect Bell correlations in highly non-Gaussian spin states. We then focus on finding PIBIs that are of practical experimental implementation, in the sense that the associated operators require collective spin measurements along only a few directions. To this end, we formulate this search problem as a semidefinite program that embeds the constraints required to look for PIBIs of the desired form.

关键词： Entanglement detection Entanglement in quantum gases Nonlocality quantum entanglement

Optimising entanglement distribution policies under classical communication constraints assisted by reinforcement learning

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arXiv 2024年

作者： Li, Jan Coopmans, Tim Emonts, Patrick Goodenough, Kenneth Tura, Jordi van Nieuwenburg, Evert aQaL Applied Quantum Algorithms Universiteit Leiden Netherlands Instituut-Lorentz Universiteit Leiden Niels Bohrweg 2 Leiden2333 CA Netherlands LIACS Universiteit Leiden Niels Bohrweg 1 Leiden2333 CA Netherlands QuTech Delft University of Technology Lorentzweg 1 Delft2628 CJ Netherlands EEMCS Delft University of Technology Mekelweg 4 Delft2628 CD Netherlands Manning College of Information and Computer Sciences University of Massachusetts Amherst 140 Governors Dr AmherstMA01002 United States

quantum repeaters play a crucial role in the effective distribution of entanglement over long distances. The nearest-future type of quantum repeater requires two operations: entanglement generation across neighbouring repeaters and entanglement swapping to promote short-range entanglement to long-range. For many hardware setups, these actions are probabilistic, leading to longer distribution times and incurred errors. Significant efforts have been vested in finding the optimal entanglement-distribution policy, i.e. the protocol specifying when a network node needs to generate or swap entanglement, such that the expected time to distribute long-distance entanglement is minimal. This problem is even more intricate in more realistic scenarios, especially when classical communication delays are taken into account. In this work, we formulate our problem as a Markov decision problem and use reinforcement learning (RL) to optimise over centralised strategies, where one designated node instructs other nodes which actions to perform. Contrary to most RL models, ours can be readily interpreted. Additionally, we introduce and evaluate a fixed local policy, the ‘predictive swap-asap’ policy, where nodes only coordinate with nearest neighbours. Compared to the straightforward generalization of the common swap-asap policy to the scenario with classical communication effects, the ‘wait-for-broadcast swap-asap’ policy, both of the aforementioned entanglement-delivery policies are faster at high success probabilities. Our work showcases the merit of considering policies acting with incomplete information in the realistic case when classical communication effects are significant. © 2024, CC BY.

关键词： Reinforcement learning

Efficient Qubit Calibration by Binary-Search Hamiltonian Tracking

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arXiv 2025年

作者： Berritta, Fabrizio Benestad, Jacob Pahl, Lukas Mathews, Melvin Krzywda, Jan A. Assouly, Réouven Sung, Youngkyu Kim, David K. Niedzielski, Bethany M. Serniak, Kyle Schwartz, Mollie E. Yoder, Jonilyn L. Chatterjee, Anasua Grover, Jeffrey A. Danon, Jeroen Oliver, William D. Kuemmeth, Ferdinand Research Laboratory of Electronics Massachusetts Institute of Technology CambridgeMA02139 United States Center for Quantum Devices Niels Bohr Institute University of Copenhagen Copenhagen2100 Denmark Center for Quantum Spintronics Department of Physics Norwegian University of Science and Technology TrondheimNO-7491 Norway Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology CambridgeMA02139 United States Department of Information Technology and Electrical Engineering ETH Zürich Zürich8093 Switzerland 〈aQaL〉 Applied Quantum Algorithms — Lorentz Insitute for Theoretical Physics & Leiden Institute of Advanced Computer Science Universiteit Leiden Netherlands Lincoln Laboratory Massachusetts Institute of Technology LexingtonMA02421 United States QuTech and Kavli Institute of Nanoscience Delft University of Technology Delft Netherlands Department of Physics Massachusetts Institute of Technology CambridgeMA02139 United States Institute of Experimental and Applied Physics University of Regensburg Regensburg93040 Germany QDevil Quantum Machines Ballerup2750 Denmark

We present a real-time method for calibrating the frequency of a resonantly driven qubit. The real-time processing capabilities of a classical controller dynamically generate adaptive probing sequences for qubit-frequency estimation. Each probing evolution time and drive frequency are calculated to divide the prior probability distribution into two branches, following a locally optimal strategy that mimics a conventional binary search. We show the algorithm’s efficacy by stabilizing a flux-tunable transmon qubit, leading to improved coherence and gate fidelity. By feeding forward the updated qubit frequency, the FPGA-powered control electronics partially mitigates non-Markovian noise in the system, which is detrimental to quantum error correction. Our protocol highlights the importance of feedback in improving the calibration and stability of qubits subject to drift and can be readily applied to other qubit platforms. © 2025, CC BY.

关键词： Hamiltonians

Necessary and Sufficient Condition for Randomness Certification from Incompatibility

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arXiv 2024年

作者： Li, Yi Xiang, Yu Tura, Jordi He, Qiongyi State Key Laboratory for Mesoscopic Physics School of Physics Frontiers Science Center for Nano-optoelectronics Collaborative Innovation Center of Quantum Matter Peking University Beijing100871 China Beijing Academy of Quantum Information Sciences Beijing100193 China Naturwissenschaftlich-Technische Fakultät Universität Siegen Walter-Flex-Straße 3 Siegen57068 Germany 〈aQaL〉 Applied Quantum Algorithms Leiden Netherlands Instituut-Lorentz Universiteit Leiden P.O. Box 9506 Leiden2300 RA Netherlands Collaborative Innovation Center of Extreme Optics Shanxi University Shanxi Taiyuan030006 China Peking University Yangtze Delta Institute of Optoelectronics Jiangsu Nantong226010 China Hefei National Laboratory Hefei230088 China

quantum randomness can be certified from probabilistic behaviors demonstrating Bell nonlocality or Einstein-Podolsky-Rosen steering, leveraging outcomes from uncharacterized devices. However, such nonlocal correlations are not always sufficient for this task, necessitating the identification of required minimum quantum resources. In this work, we provide the necessary and sufficient condition for nonzero certifiable randomness in terms of measurement incompatibility and develop approaches to detect them. Firstly, we show that the steering-based randomness can be certified if and only if the correlations arise from a measurement compatibility structure that is not isomorphic to a hypergraph containing a star subgraph. In such a structure, the central measurement is individually compatible with the measurements at branch sites, precluding certifiable randomness in the central measurement outcomes. Subsequently, we generalize this result to the Bell scenario, proving that the violation of any chain inequality involving m inputs and d outputs rules out such a compatibility structure, thereby validating all chain inequalities as credible witnesses for randomness certification. Our results point out the role of incompatibility structure in generating random numbers, offering a way to identify minimum quantum resources for the task. Copyright © 2024, The Authors. All rights reserved.

关键词： Statistical mechanics

Frustration graph formalism for qudit observables

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arXiv 2025年

作者： Makuta, Owidiusz Kuzaka, Blazej Augusiak, Remigiusz Instituut-Lorentz Universiteit Leiden P.O. Box 9506 Leiden2300 RA Netherlands 〈aQaL〉 Applied Quantum Algorithms Leiden Netherlands Center for Theoretical Physics Polish Academy of Sciences Aleja Lotników 32/46 Warsaw02-668 Poland

The incompatibility of measurements is the key feature of quantum theory that distinguishes it from the classical description of nature. Here, we consider groups of d-outcome quantum observables with prime d represented by non-Hermitian unitary operators whose eigenvalues are dth roots of unity. We additionally assume that these observables mutually commute up to a scalar factor being one of the d’th roots of unity. By representing commutation relations of these observables via a frustration graph, we show that for such a group, there exists a single unitary transforming them into a tensor product of generalized Pauli matrices and some ancillary mutually commuting operators. Building on this result, we derive upper bounds on the sum of the squares of the absolute values and the sum of the expected values of the observables forming a group. We finally utilize these bounds to compute the generalized geometric measure of entanglement for qudit stabilizer subspaces. © 2025, CC BY.

关键词： Mathematical operators

Learning interactions between Rydberg atoms

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arXiv 2024年

作者： Simard, Olivier Dawid, Anna Tindall, Joseph Ferrero, Michel Sengupta, Anirvan M. Georges, Antoine Collège de France PSL University 11 place Marcelin Berthelot Paris75005 France CPHT CNRS École Polytechnique IP Paris PalaiseauF-91128 France Center for Computational Quantum Physics Flatiron Institute 162 Fifth Avenue New YorkNY10010 United States 〈aQaL〉 Applied Quantum Algorithms – Leiden Institute of Advanced Computer Science Lorentz Insitute for Theoretical Physics Universiteit Leiden Netherlands Center for Computational Mathematics Flatiron Institute 162 5th Avenue New YorkNY10010 United States Department of Physics and Astronomy Rutgers University PiscatawayNJ08854 United States DQMP Université de Genève 24 quai Ernest Ansermet GenèveCH-1211 Switzerland

quantum simulators have the potential to solve quantum many-body problems that are beyond the reach of classical computers, especially when they feature long-range entanglement. To fulfill their prospects, quantum simulators must be fully controllable, allowing for precise tuning of the microscopic physical parameters that define their implementation. We consider Rydberg-atom arrays, a promising platform for quantum simulations. Experimental control of such arrays is limited by the imprecision on the optical tweezers positions when assembling the array, hence introducing uncertainties in the simulated Hamiltonian. In this work, we introduce a scalable approach to Hamiltonian learning using graph neural networks (GNNs). We employ the Density Matrix Renormalization Group (DMRG) to generate ground-state snapshots of the transverse field Ising model realized by the array, for many realizations of the Hamiltonian parameters. Correlation functions reconstructed from these snapshots serve as input data to carry out the training. We demonstrate that our GNN model has a remarkable capacity to extrapolate beyond its training domain, both regarding the size and the shape of the system, yielding an accurate determination of the Hamiltonian parameters with a minimal set of measurements. We prove a theorem establishing a bijective correspondence between the correlation functions and the interaction parameters in the Hamiltonian, which provides a theoretical foundation for our learning algorithm. Our work could open the road to feedback control of the positions of the optical tweezers, hence providing a decisive improvement of analog quantum simulators. Copyright © 2024, The Authors. All rights reserved.

关键词： Optical tweezers