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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

QCaMP: A 4-Week Summer Camp Introducing High School Students to quantum Information Science and Technology

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arXiv 2025年

作者： Ivory, Megan Balewski, Jan Bettale, Alisa Brewer, Jaden Boren, Rachel Camps, Daan Hackett, Lisa Juarez, Martin Kononov, Alina Lee, Kan-Heng Long, Maryanne Mounce, Andy Mniszewski, Susan Naik, Ravi K. Pakin, Scott Sanchez, Ernesto Sandia National Laboratories AlbuquerqueNM United States National Energy Research Scientific Computing Center Lawrence Berkeley National Laboratory BerkeleyCA United States Office of Government and Community Relations Lawrence Berkeley National Laboratory BerkeleyCA United States Quantum Photonics Lab Northern Arizona University FlagstaffAZ United States College of Health Education and Social Transformation New Mexico State University Las CrucesNM United States Bourns College of Engineering University of California Riverside RiversideCA United States Quantum Algorithms and Applications Collaboratory Sandia National Laboratories AlbuquerqueNM United States Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA United States Center for Integrated Nanotechnology Sandia National Laboratories AlbuquerqueNM United States Los Alamos National Laboratory Los AlamosNM United States Applied Computer Science Los Alamos National Laboratory Los AlamosNM United States

The 2024 quantum Computing, Math and Physics Camp (QCaMP) for Students was a 4-week long summer camp aimed at introducing high school students to quantum concepts and careers, including applications spanning quantum computing, sensing, and communication. The program ran for 7 hours/day, Monday–Friday, July 1–26, and included hands-on modules and activities, professional development, and project-based learning. Here we provide details on the camp curriculum and outcomes based on pre and post knowledge and attitudes assessments. © 2025, CC BY.

关键词： Qubits

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

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

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

High-dimensional monitoring and the emergence of realism via multiple observers

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arXiv 2023年

作者： Orthey, Alexandre C. Dieguez, Pedro R. Makuta, Owidiusz Augusiak, Remigiusz Center for Theoretical Physics Polish Academy of Sciences Al. Lotników 32/46 Warsaw02-668 Poland Institute of Fundamental Technological Research Polish Academy of Sciences Pawińskiego 5B Warsaw02-106 Poland International Centre for Theory of Quantum Technologies University of Gdańsk Jana Bazynskiego 8 Gdańsk80-309 Poland Instituut-Lorentz Universiteit Leiden P.O. Box 9506 Leiden2300 RA Netherlands Applied Quantum Algorithms Leiden Netherlands

Correlation is the basic mechanism of every measurement model, as one never accesses the measured system directly. Instead, correlations are created, codifying information about the measurable property into the environment. Here, we address the problem of the emergence of physical reality from the quantum world by introducing a model that interpolates between weak and strong non-selective measurements for qudits. By utilizing Heisenberg-Weyl operators, our model suggests that independently of the interaction intensity between the system and the environment, full information about the observable of interest can always be obtained by making the system interact with many environmental qudits, following a quantum Darwinism framework. © 2023, CC BY.

关键词：

A many-body approach to transport in quantum systems: From the transient regime to the stationary state

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arXiv 2022年

作者： Ridley, M. Talarico, N.W. Karlsson, D. Lo Gullo, N. Tuovinen, Riku School of Physics and Astronomy Tel-Aviv University Tel-Aviv69978 Israel Quantum Research Centre Technology Innovation Institute Abu Dhabi United Arab Emirates QTF Centre of Excellence Center for Quantum Engineering Department of Applied Physics Aalto University School of Science AaltoFIN-00076 Finland Algorithmiq Ltd. Kanavakatu 3c Helsinki00160 Finland Department of Physics Nanoscience Center University of Jyväskylä Jyväskylä40014 Finland CSC-IT Center for Science P.O. Box 405 Espoo02101 Finland Quantum Algorithms and Software VTT Technical Research Centre of Finland Ltd. Finland QTF Centre of Excellence Turku Centre for Quantum Physics Department of Physics and Astronomy University of Turku Turku20014 Finland QTF Centre of Excellence Department of Physics University of Helsinki P.O. Box 64 00014 Finland

We review one of the most versatile theoretical approaches to the study of time-dependent correlated quantum transport in nano-systems: the non-equilibrium Green’s function (NEGF) formalism. Within this formalism, one can treat, on the same footing, inter-particle interactions, external drives and/or perturbations, and coupling to baths with a (piece-wise) continuum set of degrees of freedom. After a historical overview on the theory of transport in quantum systems, we present a modern introduction of the NEGF approach to quantum transport. We discuss the inclusion of inter-particle interactions using diagrammatic techniques, and the use of the so-called embedding and inbedding techniques which take the bath couplings into account non-perturbatively. In various limits, such as the non-interacting limit and the steady-state limit, we then show how the NEGF formalism elegantly reduces to well-known formulae in quantum transport as special cases. We then discuss non-equilibrium transport in general, for both particle and energy currents. Under the presence of a time-dependent drive – encompassing pump–probe scenarios as well as driven quantum systems – we discuss the transient as well as asymptotic behavior, and also how to use NEGF to infer information on the out-of-equilibrium system. As illustrative examples, we consider model systems general enough to pave the way to realistic systems. These examples encompass one- and two-dimensional electronic systems, systems with electron–phonon couplings, topological superconductors, and optically responsive molecular junctions where electron–photon couplings are relevant. Copyright © 2022, The Authors. All rights reserved.

关键词： quantum optics

Mitigating shot noise in local overlapping quantum tomography with semidefinite programming

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Physical Review A 2025年第5期111卷 052444-052444页

作者： Zherui Jerry Wang David Dechant Yash J. Patel Jordi Tura 〈aQa〉 Applied Quantum Algorithms Universiteit Leiden The Netherlands Instituut-Lorentz Universiteit Leiden P.O. Box 9506 2300 RA Leiden The Netherlands QuTech Delft University of Technology P.O. Box 5046 Delft 2600 GA The Netherlands LIACS Universiteit Leiden Niels Bohrweg 1 2333 CA Leiden The Netherlands

Reduced density matrices (RDMs) are fundamental in quantum information processing, allowing the computation of local observables, such as energy and correlation functions, without the exponential complexity of fully characterizing quantum states. In the context of near-term quantum computing, RDMs provide sufficient information to effectively design variational quantum algorithms. However, their experimental estimation is challenging, as it involves preparing and measuring quantum states in multiple bases, a resource-intensive process susceptible to producing nonphysical RDMs due to shot noise from limited measurements. To address this, we propose a method to mitigate shot noise by reenforcing certain physicality constraints on RDMs. While verifying RDM compatibility with a global state is quantum Merlin-Arthur complete, we relax this condition by enforcing compatibility constraints up to a certain level using a polynomial-size semidefinite program to reconstruct overlapping RDMs from simulated data. Our approach yields, on average, tighter bounds for the same number of measurements compared to tomography without compatibility constraints. We demonstrate the versatility and efficacy of our method by integrating it into an algorithmic cooling procedure to prepare low-energy states of local Hamiltonians. Simulations on frustrated Hamiltonians reveal notable improvements in accuracy and resource efficiency, highlighting the potential of our approach for practical applications in near-term quantum computing.

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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