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SSRN 2023年

作者： He, Zhimin Deng, Maijie Zheng, Shenggen Li, Lvzhou Situ, Haozhen School of Electronic and Information Engineering Foshan University Foshan528000 China School of Mechatronic Engineering and Automation Foshan University Foshan528000 China Peng Cheng Laboratory Shenzhen518055 China Institute of Quantum Computing and Computer Theory School of Computer Science and Engineering Sun Yat-Sen University Guangzhou510006 China College of Mathematics and Informatics South China Agricultural University Guangzhou510642 China

quantum Architecture Search (QAS) is a promising approach for designing quantum circuits specifically tailored for variational quantum algorithms (VQAs). However, existing QAS algorithms require calculating the ground-truth performances of a substantial number of quantum circuits during the search process, rendering them computationally demanding and limiting their applicability to large-scale quantum circuits. Recently, a predictor-based QAS has been proposed to address this challenge by estimating circuit performance directly based on their structures using a predictor trained on a set of labeled quantum circuits. However, the predictor is trained by purely supervised learning, which suffers from poor generalization ability when labeled training circuits are scarce. It is highly time-consuming to obtain a substantial number of labeled quantum circuits because the gate parameters of quantum circuits need to be optimized until convergence to obtain their ground-truth performances. To overcome these limitations, we propose GSQAS, a graph self-supervised QAS that trains a predictor by self-supervised learning. Specifically, we first pre-train a graph encoder using a well-designed pretext task on a large number of unlabeled quantum circuits, aiming to generate meaningful representations of quantum circuits. Subsequently, the downstream predictor is trained on a small set of quantum circuits' representations and their corresponding labels. Once the encoder is trained, it becomes applicable to various downstream tasks. To effectively encode spatial topology information and avoid huge dimensions of feature vectors for large-scale quantum circuits, we propose a graph-based encoding scheme for quantum circuits. Simulation results on QAS for variational quantum eigensolver and quantum state classification demonstrate that GSQAS outperforms the state-of-the-art predictor-based QAS, yielding superior performance with fewer labeled circuits. © 2023, The Authors. All rights rese

关键词： Timing circuits

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Intensity correlations in decoy-state BB84 quantum key distribution systems

arXiv

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arXiv 2024年

作者： Trefilov, Daniil Sixto, Xoel Zapatero, Víctor Huang, Anqi Curty, Marcos Makarov, Vadim Vigo Quantum Communication Center University of Vigo VigoE-36310 Spain School of Telecommunication Engineering Department of Signal Theory and Communications University of Vigo VigoE-36310 Spain atlanTTic Research Center University of Vigo VigoE-36310 Spain Russian Quantum Center Skolkovo Moscow121205 Russia National Research University Higher School of Economics Moscow101000 Russia Institute for Quantum Information State Key Laboratory of High Performance Computing College of Computer Science and Technology National University of Defense Technology Changsha410073 China NTI Center for Quantum Communications National University of Science and Technology MISiS Moscow119049 Russia

The decoy-state method is a prominent approach to enhance the performance of quantum key distribution (QKD) systems that operate with weak coherent laser sources. Due to the limited transmissivity of single photons in optical fiber, current experimental decoy-state QKD setups increase their secret key rate by raising the repetition rate of the transmitter. However, this usually leads to correlations between subsequent optical pulses. This phenomenon leaks information about the encoding settings, including the intensities of the generated signals, which invalidates a basic premise of decoy-state QKD. Here we characterize intensity correlations between the emitted optical pulses in two industrial prototypes of decoy-state BB84 QKD systems and show that they significantly reduce the asymptotic key rate. In contrast to what has been conjectured, we experimentally confirm that the impact of higher-order correlations on the intensity of the generated signals can be much higher than that of nearest-neighbour correlations. Copyright © 2024, The Authors. All rights reserved.

关键词： quantum cryptography

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Improved rate-distance trade-offs for quantum codes with restricted connectivity

arXiv

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arXiv 2023年

作者： Baspin, Nouédyn Guruswami, Venkatesan Krishna, Anirudh Li, Ray Centre for Engineered Quantum Systems School of Physics University of Sydney NSW2006 Australia Departments of EECS and Mathematics The Simons Institute for the Theory of Computing UC Berkeley BerkeleyCA94709 United States Department of Computer Science Stanford Institute for Theoretical Physics Stanford University StanfordCA94305 United States Department of EECS UC Berkeley BerkeleyCA94709 United States

For quantum error-correcting codes to be realizable, it is important that the qubits subject to the code constraints exhibit some form of limited connectivity. The works of Bravyi & Terhal [6] (BT) and Bravyi, Poulin & Terhal [5] (BPT) established that geometric locality constrains code properties—for instance Jn, k, dK quantum codes defined by local checks on the D-dimensional lattice must obey kd2/(D−1) ≤ O(n). Baspin and Krishna [3] studied the more general question of how the connectivity graph associated with a quantum code constrains the code parameters. These trade-offs apply to a richer class of codes compared to the BPT and BT bounds, which only capture geometrically-local codes. We extend and improve this work, establishing a tighter dimension-distance trade-off as a function of the size of separators in the connectivity graph. We also obtain a distance bound that covers all stabilizer codes with a particular separation profile, rather than only LDPC codes. Copyright © 2023, The Authors. All rights reserved.

关键词： Economic and social effects

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GSQAS: Graph Self-supervised quantum Architecture Search

arXiv

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arXiv 2023年

quantum Architecture Search (QAS) is a promising approach to designing quantum circuits for variational quantum algorithms (VQAs). However, existing QAS algorithms require to evaluate a large number of quantum circuits during the search process, which makes them computationally demanding and limits their applications to large-scale quantum circuits. Recently, predictor-based QAS has been proposed to alleviate this problem by directly estimating the performances of circuits according to their structures with a predictor trained on a set of labeled quantum circuits. However, the predictor is trained by purely supervised learning, which suffers from poor generalization ability when labeled training circuits are scarce. It is very time-consuming to obtain a large number of labeled quantum circuits because the gate parameters of quantum circuits need to be optimized until convergence to obtain their ground-truth performances. To overcome these limitations, we propose GSQAS, a graph self-supervised QAS, which trains a predictor based on self-supervised learning. Specifically, we first pre-train a graph encoder on a large number of unlabeled quantum circuits using a well-designed pretext task in order to generate meaningful representations of circuits. Then the downstream predictor is trained on a small number of quantum circuits’ representations and their labels. Once the encoder is trained, it can apply to different downstream tasks. In order to better encode the spatial topology information and avoid the huge dimension of feature vectors for large-scale quantum circuits, we design a scheme to encode quantum circuits as graphs. Simulation results on searching circuit structures for variational quantum eigensolver and quantum state classification show that GSQAS outperforms the state-of-the-art predictor-based QAS, achieving better performance with fewer labeled circuits. Copyright © 2023, The Authors. All rights reserved.

关键词： Encoding (symbols)

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Polynomial representation of general partial Boolean functions with a single quantum query

arXiv

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arXiv 2021年

作者： Guoliang, Xu Daowen, Qiu College of Information Technology Luoyang Normal University Luoyang471934 China Institute of Quantum Computing and Computer Theory School of Computer Science and Engineering Sun Yat-Sen University Guangzhou510006 China

Early in 1992, Deutsch-Jozsa algorithm computed a symmetric partial Boolean function with a single quantum query, and thus achieved the best separation between classical deterministic and exact quantum query complexity. Until recent years, it was clarified that all symmetric partial Boolean functions with a single quantum query can be computed exactly by Deutsch-Jozsa algorithm. For the general partial Boolean functions with a single quantum query, the latest characterizations is complex and not very satisfactory. Based on this, this paper proves and discovers three new results: (1) Establishing a new equivalence, each partial Boolean function with a single quantum query can be transformed to a simple partial Boolean function whose polynomial degree is just one;(2) For partial Boolean functions up to four bits, there are only 10 non-trivial partial Boolean functions with a single quantum query;(3) For each quantum 1-query algorithm with undefined measurement, there exists a constructive method for finding out all partial Boolean functions that can be computed exactly by the algorithm. Essentially, the first discovery represent a step forward for a fundamental conclusion that the polynomial degree of partial Boolean functions with a single quantum query is one or two, and the last two results contribute a way for searching more nontrival partial Boolean functions that have quantum advantages. Copyright © 2021, The Authors. All rights reserved.

关键词： quantum computers

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State Permutation Control in Non-Hermitian Multiqubit Systems with Suppressed Non-Adiabatic Transitions

arXiv

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arXiv 2025年

作者： Arkhipov, Ievgen I. Lewalle, Philippe Nori, Franco Özdemir, Şahin K. Whaley, K. Birgitta Joint Laboratory of Optics Palacký University Institute of Physics of CAS Faculty of Science Palacký University 17. listopadu 12 Olomouc771 46 Czech Republic Department of Chemistry University of California BerkeleyCA94720 United States Berkeley Center for Quantum Information and Computation BerkeleyCA94720 United States Theoretical Quantum Physics Laboratory Cluster for Pioneering Research RIKEN Saitama Wako-shi351-0198 Japan Quantum Information Physics Theory Research Team Quantum Computing Center RIKEN Wakoshi Saitama351-0198 Japan Physics Department The University of Michigan Ann ArborMI48109-1040 United States Department of Electrical and Computer Engineering Saint Louis University St. LouisMO63103 United States

Non-Hermitian systems have been at the focus of intense research for over a decade, partly due to their nontrivial energy topology formed by intersecting Riemann manifolds with branch points known as exceptional points (EPs). This spectral property can be exploited, e.g., to achieve controlled state permutations that are necessary for implementing a wide class of classical and quantum information protocols. However, the imaginary spectra of typical non-Hermitian systems lead to instabilities and breakdown of adiabaticity, which impedes the practical use of EP-induced energy topologies in quantum information protocols that explicitly rely on symmetric state flips. On the other hand, techniques that help to suppress non-adiabatic transitions in non-Hermitian systems have also been developed, but these advances have so far been limited to single qubits. In this work, we address this long-standing problem by introducing a model of interacting qubits governed by an effective non-Hermitian Hamiltonian that hosts EPs and possesses a completely real energy spectrum. We demonstrate that such non-Hermitian Hamiltonians enable realization of permutation groups in the multi-qubit eigenspace. Our findings indicate that, contrary to previous beliefs, non-Hermiticity can be utilized to achieve controlled state permutations in time-modulated multiqubit systems, thus paving the way for the advancement and development of novel quantum information protocols. Copyright © 2025, The Authors. All rights reserved.

关键词： Qubits

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Sample complexity of hidden subgroup problem

arXiv

引用

arXiv 2021年

作者： Ye, Zekun Li, Lvzhou Institute of Quantum Computing and Computer Science Theory School of Computer Science and Engineering Sun Yat-Sen University Guangzhou510006 China Ministry of Education Key Laboratory of Machine Intelligence and Advanced Computing Sun Yat-Sen University Guangzhou510006 China

The hidden subgroup problem (HSP) has been attracting much attention in quantum computing, since several well-known quantum algorithms including Shor algorithm can be described in a uniform framework as quantum methods to address different instances of it. One of the central issues about HSP is to characterize its quantum/classical complexity. For example, from the viewpoint of learning theory, sample complexity is a crucial concept. However, while the quantum sample complexity of the problem has been studied, a full characterization of the classical sample complexity of HSP seems to be absent, which will thus be the topic in this paper. HSP over a finite group is defined as follows: For a finite group G and a finite set V , given a function f : G → V and the promise that for any x, y ∈ G, f(x) = f(xy) iff y ∈ H for a subgroup H ∈ H, where H is a set of candidate subgroups of G, the goal is to identify H. Our contributions are as follows: i) For HSP, we show that the number of uniform examples necessary to learn the hidden subgroup with bounded error is at least Ω max (Hmin ∈H loglog |H|| | H G| |Hmin ∈Hr||HG|| loglog |H|| | H G| |)! , and on the other hand, O (Hmax ∈Hn sr(H), q||HG|| sr(H) o) uniform examples are sufficient, where sr(H) = max r(H) and r(H) is the rank of H. H∈H ii) By concretizing the parameters of HSP, we consider a class of restricted Abelian hidden subgroup problem (rAHSP) and obtain the upper and lower bounds for the sample complexity of rAHSP. iii) We continue to discuss a special case of rAHSP, generalized Simon’s problem (GSP), and show that the sample complexity of GSP is Θ (max n k, pk · pn-ko) . Thus we obtain a complete characterization of the sample complexity of GSP. © 2021, CC BY.

关键词： quantum computers

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Efficient quantum algorithm for nonlinear reaction-diffusion equations and energy estimation

arXiv

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arXiv 2022年

作者： Liu, Jin-Peng An, Dong Fang, Di Wang, Jiasu Low, Guang Hao Jordan, Stephen Joint Center for Quantum Information and Computer Science University of Maryland MD United States Simons Institute for the Theory of Computing BerkeleyCA United States Department of Mathematics University of California BerkeleyCA United States Center for Theoretical Physics Massachusetts Institute of Technology CambridgeMA United States Department of Mathematics and Duke Quantum Center Duke University DurhamNC United States Microsoft Quantum RedmondWA United States Google Quantum AI Santa BarbaraCA United States

Nonlinear differential equations exhibit rich phenomena in many fields but are notoriously challenging to solve. Recently, Liu et al. [1] demonstrated the first efficient quantum algorithm for dissipative quadratic differential equations under the condition R 2 norm. Here we develop an efficient quantum algorithm based on [1] for reaction-diffusion equations, a class of nonlinear partial differential equations (PDEs). To achieve this, we improve upon the Carleman linearization approach introduced in [1] to obtain a faster convergence rate under the condition RD D measures the ratio of nonlinearity to dissipation using the ∞ norm. Since RD is independent of the number of spatial grid points n while R increases with n, the criterion RD © 2022, CC BY.

关键词： Kinetic energy

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Entanglement area law for one-dimensional gauge theories and bosonic systems

引用

Physical Review A 2023年第4期108卷 042422-042422页

作者： Nilin Abrahamsen Yu Tong Ning Bao Yuan Su Nathan Wiebe Simons Institute for the Theory of Computing University of California Berkeley Berkeley California 94720-2190 USA Department of Mathematics University of California Berkeley Berkeley California 94720 USA Computational Science Initiative Brookhaven National Laboratory Upton New York 11973 USA Google Quantum AI Venice California 90291 USA Department of Computer Science University of Toronto Toronto Canada M5S 3E1 Pacific Northwest National Laboratory Richland Washington 99354 USA

We prove an entanglement area law for a class of one-dimensional quantum systems involving infinite-dimensional local Hilbert spaces. This class of quantum systems includes bosonic models and lattice gauge theories in one spatial dimension. Our proof relies on results concerning the robustness of the ground state and spectral gap to the truncation of Hilbert space, applied within the approximate-ground-state projector (AGSP) framework. Our result provides theoretical justification for using tensor networks to study the ground-state properties of quantum systems with infinite local degrees of freedom.

关键词： quantum entanglement

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Linear combination of Hamiltonian simulation for nonunitary dynamics with optimal state preparation cost

arXiv

引用

arXiv 2023年

作者： An, Dong Liu, Jin-Peng Lin, Lin Joint Center for Quantum Information and Computer Science University of Maryland MD20742 United States Department of Mathematics University of California BerkeleyCA94720 United States Simons Institute for the Theory of Computing University of California BerkeleyCA94720 United States Center for Theoretical Physics Massachusetts Institute of Technology CambridgeMA02139 United States Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Challenge Institute for Quantum Computation University of California BerkeleyCA94720 United States

We propose a simple method for simulating a general class of non-unitary dynamics as a linear combination of Hamiltonian simulation (LCHS) problems. LCHS does not rely on converting the problem into a dilated linear system problem, or on the spectral mapping theorem. The latter is the mathematical foundation of many quantum algorithms for solving a wide variety of tasks involving non-unitary processes, such as the quantum singular value transformation. The LCHS method can achieve optimal cost in terms of state preparation. We also demonstrate an application for open quantum dynamics simulation using the complex absorbing potential method with near-optimal dependence on all parameters. Copyright © 2023, The Authors. All rights reserved.

关键词： Hamiltonians

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