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arXiv 2024年

作者： Arkhipov, Ievgen I. Minganti, Fabrizio Miranowicz, Adam Özdemir, Şahin K. Nori, Franco Joint Laboratory of Optics Palacký University Institute of Physics of CAS Faculty of Science Palacký University 17. listopadu 12 Olomouc771 46 Czech Republic LausanneCH-1015 Switzerland LausanneCH-1015 Switzerland Theoretical Quantum Physics Laboratory Cluster for Pioneering Research RIKEN Wako-shi Saitama351-0198 Japan Quantum Information Physics Theory Research Team Quantum Computing Center RIKEN Wakoshi Saitama351-0198 Japan Institute of Spintronics and Quantum Information Faculty of Physics Adam Mickiewicz University Poznań61-614 Poland The Pennsylvania State University University ParkPA16802 United States Physics Department The University of Michigan Ann ArborMI48109-1040 United States

Non-Hermitian systems have attracted much interest in recent decades, driven partly by the existence of exotic spectral singularities, known as exceptional points (EPs), where the dimensionality of the system evolution operator is reduced. Among various intriguing applications, the discovery of EPs has suggested the potential for implementing a symmetric mode switch, when encircling them in a system parameter space. However, subsequent theoretical and experimental works have revealed that dynamical encirclement of EPs invariably results in asymmetric mode conversion;namely, the mode switching depends only on the winding direction but not on the initial state. This chirality arises from the failure of adiabaticity due to the complex spectrum of non-Hermitian systems. Although the chirality revealed has undoubtedly made a significant impact in the field, a realization of the originally sought symmetric adiabatic passage in non-Hermitian systems with EPs has since been elusive. In this work, we bridge this gap and theoretically demonstrate that adiabaticity, and therefore a symmetric state transfer, is achievable when dynamically winding around an EP. This becomes feasible by specifically choosing a trajectory in the system parameter space along which the corresponding evolution operator attains a real spectrum. Our findings, thus, offer a promise for advancing various wave manipulation protocols in both quantum and classical domains. Copyright © 2024, The Authors. All rights reserved.

关键词： Chirality

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Distributed Deutsch-Jozsa Algorithm

SSRN

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SSRN 2024年

作者： Li, Hao Qiu, Daowen Luo, Le Institute of Quantum Computing and Software School of Computer Science and Engineering Sun Yat-sen University Guangzhou510006 China School of Physics and Astronomy Sun Yat-sen University Zhuhai519082 China The Guangdong Key Laboratory of Information Security Technology Sun Yat-sen University Guangzhou510006 China QUDOOR Technologies Inc. Zhuhai China

Deutsch-Jozsa (DJ) problem is one of the most important problems demonstrating the power of quantum algorithm, which can be described as a Boolean function $f: \{0,1\}^n\rightarrow \{0,1\}$ with promising it is either constant or balanced, and the purpose is to determine which type it is. DJ algorithm can compute it exactly with one query. However, classical deterministic algorithm requires $2^{n-1} + 1$ queries to compute it in the worse case. Therefore, DJ algorithm is essentially faster than any possible classical deterministic algorithm for computing DJ problem. In this paper, we discover the intrinsic structure of DJ problem in distributed scenario by giving a number of equivalence characterizations between $f$ being constant (balanced) and some properties of $f$'s subfunctions. We propose three distributed DJ algorithms, which have essential acceleration compared to distributed classical deterministic DJ algorithm. In comparison to DJ algorithm, our algorithms can reduce the number of qubits for a single computing node. Furthermore, compared to distributed DJ algorithm with errors, our algorithms possess accuracy and improved scalability. © 2024, The Authors. All rights reserved.

关键词： Boolean functions

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Parameterized complexity of reconfiguration of atoms

arXiv

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arXiv 2021年

作者： Cooper, Alexandre Maaz, Stephanie Mouawad, Amer E. Nishimura, Naomi Institute of Quantum Computing University of Waterloo Canada Department of Computer Science American University of Beirut Lebanon David R. Cheriton School of Computer Science Univeristy of Waterloo Canada

Our work is motivated by the challenges presented in preparing arrays of atoms for use in quantum simulation. The recently-developed process of loading atoms into traps results in approximately half of the traps being filled. To consolidate the atoms so that they form a dense and regular arrangement, such as all locations in a grid, atoms are rearranged using moving optical tweezers. Time is of the essence, as the longer that the process takes and the more that atoms are moved, the higher the chance that atoms will be lost in the process. Viewed as a problem on graphs, we wish to solve the problem of reconfiguring one arrangement of tokens (representing atoms) to another using as few moves as possible. Because the problem is NP-complete on general graphs as well as on grids [2], we focus on the parameterized complexity for various parameters, considering both undirected and directed graphs, and tokens with and without labels. For unlabelled tokens, the problem is in FPT when parameterizing by the number of tokens, the number of moves, or the number of moves plus the number of vertices without tokens in either the source or target configuration, but intractable when parameterizing by the difference between the number of moves and the number of differences in the placement of tokens in the source and target configurations. When labels are added to tokens, however, most of the tractability results are replaced by hardness results. Copyright © 2021, The Authors. All rights reserved.

关键词： Directed graphs

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Designing quantum annealing schedules using Bayesian optimization

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Physical Review Research 2024年第2期6卷 023063-023063页

作者： Jernej Rudi Finžgar Martin J. A. Schuetz J. Kyle Brubaker Hidetoshi Nishimori Helmut G. Katzgraber BMW AG 80809 Munich Germany Technical University Munich School of CIT Department of Computer Science 85748 Garching Germany Amazon Quantum Solutions Lab Seattle Washington 98170 USA AWS Center for Quantum Computing Pasadena California 91125 USA International Research Frontiers Initiative Tokyo Institute of Technology Shibaura Minato-ku Tokyo 108-0023 Japan Graduate School of Information Sciences Tohoku University Sendai 980-8579 Japan RIKEN Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS) Wako Saitama 351-0198 Japan

We propose and analyze the use of Bayesian optimization techniques to design quantum annealing schedules with minimal user and resource requirements. We showcase our scheme with results for two paradigmatic spin models. We find that Bayesian optimization is able to identify schedules resulting in fidelities several orders of magnitude better than standard protocols for both quantum and reverse annealing, as applied to the p-spin model. We also show that our scheme can help improve the design of hybrid quantum algorithms for hard combinatorial optimization problems, such as the maximum independent set problem, and illustrate these results via experiments on a neutral-atom quantum processor available on Amazon Braket.

关键词： Adiabatic quantum optimization quantum information with hybrid systems

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Towards practical and massively parallel quantum computing emulation for quantum chemistry

arXiv

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arXiv 2023年

作者： Shang, Honghui Fan, Yi Shen, Li Guo, Chu Liu, Jie Duan, Xiaohui Li, Fang Li, Zhenyu Institute of Computing Technology Chinese Academy of Sciences Beijing China Hefei National Laboratory University of Science and Technology of China Hefei230088 China Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education Department of Physics Synergetic Innovation Center for Quantum Effects and Applications Hunan Normal University Changsha410081 China School of Software Shandong University Jinan China National Research Center of Parallel Computer Engineering and Technology Beijing China

quantum computing is moving beyond its early stage and seeking for commercial applications in chemical and biomedical sciences. In the current noisy intermediate-scale quantum computing era, quantum resource is too scarce to support these explorations. Therefore, it is valuable to emulate quantum computing on classical computers for developing quantum algorithms and validating quantum hardware. However, existing simulators mostly suffer from the memory bottleneck so developing the approaches for large-scale quantum chemistry calculations remains challenging. Here we demonstrate a high-performance and massively parallel variational quantum eigensolver (VQE) simulator based on matrix product states, combined with embedding theory for solving large-scale quantum computing emulation for quantum chemistry on HPC platforms. We apply this method to study the torsional barrier of ethane and the quantification of the protein-ligand interactions. Our largest simulation reaches 1000 qubits, and a performance of 216.9 PFLOPS is achieved on a new Sunway supercomputer, which sets the state-of-the-art for quantum computing emulation for quantum chemistry. © 2023, CC BY.

关键词： Computational chemistry

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Algorithmic cooling for resolving state preparation and measurement errors in quantum computing

引用

Physical Review A 2022年第1期106卷 012439-012439页

作者： Raymond Laflamme Junan Lin Tal Mor Institute for Quantum Computing and Department of Physics and Astronomy University of Waterloo Waterloo Ontario Canada N2L 3G1 Perimeter Institute for Theoretical Physics Waterloo Ontario Canada N2L 2Y5 Computer Science Department Technion - Israel Institute of Technology Technion City Haifa 3200003 Israel

State preparation and measurement errors are commonly regarded as indistinguishable. The problem of distinguishing state preparation errors from measurement errors is important to the field of characterizing quantum processors. In this work, we propose a method to separately characterize state preparation and measurement errors using a different type of algorithmic cooling protocol called measurement-based algorithmic cooling (MBAC). MBAC assumes the ability to perform (potentially imperfect) projective measurements on individual qubits, which is available on many modern quantum processors. We demonstrate that MBAC can significantly reduce state preparation error under realistic assumptions, with a small overhead that can be upper bounded by measurable quantities. Thus, MBAC can be a valuable tool not only for benchmarking near-term quantum processors but also for improving the performance of quantum processors in an algorithmic manner.

关键词： quantum algorithms quantum benchmarking quantum tomography quantum verification

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Microwave interference from a spin ensemble and its mirror image in waveguide magnonics

arXiv

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arXiv 2024年

作者： Wu, B.-Y. Cheng, Y.-T. Lin, K.-T. Aziz, F. Liu, J.-C. Rangdhol, K.-V. Yeung, Y.-Y. Yang, Sen Shao, Qiming Wang, Xin Lin, G.-D. Nori, Franco Hoi, I.-C. Department of Physics City University of Hong Kong Kowloon Hong Kong Department of Physics Center for Quantum Science and Engineering National Taiwan University Taipei10617 Taiwan Department of Physics National Tsing Hua University Hsinchu30013 Taiwan Department of Electronic and Computer Engineering The Hong Kong University of Science and Technology Clear Water Bay Kowloon Hong Kong Department of Physics IAS Center of Quantum Technologies The Hong Kong University of Science and Technology Clear Water Bay Kowloon Hong Kong Physics Division National Center for Theoretical Sciences Taipei10617 Taiwan Trapped-Ion Quantum Computing Laboratory Hon Hai Research Institute Taipei11492 Taiwan Center for Quantum Computing Cluster for Pioneering Research RIKEN Wakoshi Saitama351-0198 Japan Physics Department The University of Michigan Ann ArborMI48109-1040 United States

We investigate microwave interference from a spin ensemble and its mirror image in a one-dimensional waveguide. Away from the mirror, the resonance frequencies of the Kittel mode (KM) inside a ferrimagnetic spin ensemble have sinusoidal shifts as the normalized distance between the spin ensemble and the mirror increases compared to the setup without the mirror. These shifts are a consequence of the KM’s interaction with its own image. Furthermore, the variation of the magnon radiative decay into the waveguide shows a cosine squared oscillation and is enhanced twofold when the KM sits at the magnetic antinode of the corresponding eigenmode. We can finely tune the KM to achieve the maximum adsorption of the input photons at the critical coupling point. Moreover, by placing the KM in proximity to the node of the resonance field, its lifetime is extended to more than eight times compared to its positioning near the antinode. Copyright © 2024, The Authors. All rights reserved.

关键词： Mirrors

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Upper Bounds on the Distillable Randomness of Bipartite quantum States

Upper Bounds on the Distillable Randomness of Bipartite Quan...

引用

IEEE (first ITW conference of the year) Information theory Workshop (ITW)

作者： Ludovico Lami Bartosz Regula Xin Wang Mark M. Wilde Institute for Theoretical Physics Korteweg–de Vries Institute for Mathematics and QuSoft University of Amsterdam The Netherlands Institute for Theoretical Physics and IQST University of Ulm Ulm Germany Department of Physics Graduate School of Science The University of Tokyo Bunkyo-ku Tokyo Japan Baidu Research Institute for Quantum Computing Beijing China School of Electrical and Computer Engineering Cornell University Ithaca New York USA

The distillable randomness of a bipartite quantum state is an information-theoretic quantity equal to the largest net rate at which shared randomness can be distilled from the state by means of local operations and classical communication. This quantity has been widely used as a measure of classical correlations, and one version of it is equal to the regularized Holevo information of the ensemble that results from measuring one share of the state. However, due to the regularization, the distillable randomness is difficult to compute in general. To address this problem, we define measures of classical correlations and prove a number of their properties, most importantly that they serve as upper bounds on the distillable randomness of an arbitrary bipartite state. We then further bound these measures from above by some that are efficiently computable by means of semi-definite programming, we evaluate one of them for the example of an isotropic state, and we remark on the relation to quantities previously proposed in the *** version at https://***/***

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quantum Simulation of Real-Space Dynamics

arXiv

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arXiv 2022年

作者： Childs, Andrew M. Leng, Jiaqi Li, Tongyang Liu, Jin-Peng Zhang, Chenyi Joint Center for Quantum Information and Computer Science University of Maryland United States Department of Computer Science University of Maryland United States Department of Mathematics University of Maryland United States Center on Frontiers of Computing Studies Peking University China School of Computer Science Peking University China Center for Theoretical Physics Massachusetts Institute of Technology United States Institute for Interdisciplinary Information Sciences Tsinghua University China

quantum simulation is a prominent application of quantum computers. While there is extensive previous work on simulating finite-dimensional systems, less is known about quantum algorithms for real-space dynamics. We conduct a systematic study of such algorithms. In particular, we show that the dynamics of a ddimensional Schrödinger equation with η particles can be simulated with gate complexity Õ(ηdF poly(log(g'/∊))), where ∊ is the discretization error, g' controls the higher-order derivatives of the wave function, and F measures the time-integrated strength of the potential. Compared to the best previous results, this exponentially improves the dependence on ∊ and g' from poly(g'/∊) to poly(log(g'/∊)) and polynomially improves the dependence on T and d, while maintaining best known performance with respect to η. For the case of Coulomb interactions, we give an algorithm using η3(d + η)T poly(log(ηdTg'/(∆∊)))/∆ one- and two-qubit gates, and another using η3(4d)d/2T poly(log(ηdTg'/(∆∊)))/∆ one- and two-qubit gates and QRAM operations, where T is the evolution time and the parameter ∆ regulates the unbounded Coulomb interaction. We give applications to several computational problems, including faster real-space simulation of quantum chemistry, rigorous analysis of discretization error for simulation of a uniform electron gas, and a quadratic improvement to a quantum algorithm for escaping saddle points in nonconvex optimization. © 2022, CC BY.

关键词： quantum chemistry

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Proxy Convexity: A Unified Framework for the Analysis of Neural Networks Trained by Gradient Descent

arXiv

引用

arXiv 2021年

作者： Frei, Spencer Gu, Quanquan Simons Institute for the Theory of Computing University of California Berkeley United States Department of Computer Science University of California Los Angeles United States

Although the optimization objectives for learning neural networks are highly non-convex, gradient-based methods have been wildly successful at learning neural networks in practice. This juxtaposition has led to a number of recent studies on provable guarantees for neural networks trained by gradient descent. Unfortunately, the techniques in these works are often highly specific to the particular setup in each problem, making it difficult to generalize across different settings. To address this drawback in the literature, we propose a unified non-convex optimization framework for the analysis of neural network training. We introduce the notions of proxy convexity and proxy Polyak-Lojasiewicz (PL) inequalities, which are satisfied if the original objective function induces a proxy objective function that is implicitly minimized when using gradient methods. We show that gradient descent on objectives satisfying proxy convexity or the proxy PL inequality leads to efficient guarantees for proxy objective functions. We further show that many existing guarantees for neural networks trained by gradient descent can be unified through proxy convexity and proxy PL inequalities. Copyright © 2021, The Authors. All rights reserved.

关键词： Gradient methods

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