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Fermionic quantum approximate optimization algorithm

Physical Review Research 2023年第2期5卷 023071-023071页

作者： Takuya Yoshioka Keita Sasada Yuichiro Nakano Keisuke Fujii Strategic Technology Center TIS Inc. 2-2-1 Toyosu Koto-ku Tokyo 135-0061 Japan Graduate School of Engineering Science Osaka University 1-3 Machikaneyama Toyonaka Osaka 560-8531 Japan Center for Quantum Information and Quantum Biology Institute for Open and Transdisciplinary Research Initiatives Osaka Univrsity 1-2 Machikaneyama Toyonaka Osaka 560-0043 Japan Center for Quantum Computing RIKEN 2-1 Hirosawa Wako Saitama 351-0198 Japan

quantum computers are expected to accelerate solving combinatorial optimization problems, including algorithms such as Grover adaptive search and quantum approximate optimization algorithm (QAOA). However, many combinatorial optimization problems involve constraints which, when imposed as soft constraints in the cost function, can negatively impact the performance of the optimization algorithm. In this paper, we propose fermionic quantum approximate optimization algorithm (FQAOA) for solving combinatorial optimization problems with constraints. Specifically, FQAOA tackles the constrains issue by using fermion particle number preservation to intrinsically impose them throughout QAOA. We provide a systematic guideline for designing the driver Hamiltonian for a given problem Hamiltonian with constraints. The initial state can be chosen to be a superposition of states satisfying the constraint and the ground state of the driver Hamiltonian. This property is important since FQAOA reduced to quantum adiabatic computation in the large limit of circuit depth p and improved performance, even for shallow circuits with optimizing the parameters starting from the fixed-angle determined by Trotterized quantum adiabatic evolution. We perform an extensive numerical simulation and demonstrate that proposed FQAOA provides substantial performance advantages against existing approaches in portfolio optimization problems. Furthermore, the Hamiltonian design guideline is useful not only for QAOA but also Grover adaptive search and quantum phase estimation to solve combinatorial optimization problems with constraints. Since software tools for fermionic systems have been developed in quantum computational chemistry both for noisy intermediate-scale quantum computers and fault-tolerant quantum computers, FQAOA allows us to apply these tools for constrained combinatorial optimization problems.

关键词： quantum algorithms quantum computation quantum simulation quantum theory

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Variational learning of integrated quantum photonic circuits

arXiv

引用

arXiv 2024年

作者： Zhang, Hui Yang, Chengran Mok, Wai-Keong Wan, Lingxiao Cai, Hong Li, Qiang Gao, Feng Luo, Xianshu Lo, Guo-Qiang Chin, Lip Ket Shi, Yuzhi Thompson, Jayne Gu, Mile Liu, Ai Qun The Hong Kong Polytechnic University Hong Kong Nanyang Technological University Singapore Centre for Quantum Technologies National University of Singapore 3 Science Drive 2 117543 Singapore California Institute of Technology PasadenaCA91125 United States Singapore Advanced Micro Foundry 11 Science Park Rd Singapore Department of Electrical Engineering City University of Hong Kong Kowloon Tong Hong Kong Institute of Precision Optical Engineering School of Physics Science and Engineering Tongji University Shanghai200092 China Institute of High Performance Computing Agency for Science Technology and Research 138632 Singapore Complexity Institute Nanyang Technological University Singapore Nanyang Quantum Hub School of Physical and Mathematical Sciences Nanyang Technological University Singapore

Integrated photonic circuits play a crucial role in implementing quantum information processing in the noisy intermediate-scale quantum (NISQ) era. Variational learning is a promising avenue that leverages classical optimization techniques to enhance quantum advantages on NISQ devices. However, most variational algorithms are circuit-model-based and encounter challenges when implemented on integrated photonic circuits, because they involve explicit decomposition of large quantum circuits into sequences of basic entangled gates, leading to an exponential decay of success probability due to the non-deterministic nature of photonic entangling gates. Here, we present a variational learning approach for designing quantum photonic circuits, which directly incorporates post-selection and elementary photonic elements into the training process. The complicated circuit is treated as a single nonlinear logical operator, and a unified design is discovered for it through variational learning. engineering an integrated photonic chip with automated control, we adjust and optimize the internal parameters of the chip in real time for task-specific cost functions. We utilize a simple case of designing photonic circuits for a single ancilla CNOT gate with improved success rate to illustrate how our proposed approach works, and then apply the approach in the first demonstration of quantum stochastic simulation using integrated photonics. © 2024, CC BY.

关键词： Cost functions

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Model Checking quantum Continuous-Time Markov Chains 32

Model Checking Quantum Continuous-Time Markov Chains

引用

32nd International Conference on Concurrency Theory, CONCUR 2021

作者： Xu, Ming Mei, Jingyi Guan, Ji Yu, Nengkun MoE Engineering Research Center of Software/Hardware Co-design Technology and Application Shanghai Key Lab of Trustworthy Computing East China Normal University Shanghai China Shanghai Key Lab of Trustworthy Computing East China Normal University Shanghai China State Key Lab of Computer Science Institute of Software Chinese Academy of Sciences Beijing China Centre for Quantum Software and Information Faculty of Engineering and Information Technology University of Technology Sydney Australia

ISBN: (纸本)9783959772037

Verifying quantum systems has attracted a lot of interests in the last decades. In this paper, we initialise the model checking of quantum continuous-time Markov chain (QCTMC). As a real-time system, we specify the temporal properties on QCTMC by signal temporal logic (STL). To effectively check the atomic propositions in STL, we develop a state-of-the-art real root isolation algorithm under Schanuel's conjecture;further, we check the general STL formula by interval operations with a bottom-up fashion, whose query complexity turns out to be linear in the size of the input formula by calling the real root isolation algorithm. A running example of an open quantum walk is provided to demonstrate our method. © Ming Xu, Jingyi Mei, Ji Guan, and Nengkun Yu;.

关键词： Model checking

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Scalable Optical quantum State Synthesizer with Dual-Mode Cavity Memory

arXiv

引用

arXiv 2025年

作者： Hanamura, Fumiya Takase, Kan Hirota, Kazuki Nehra, Rajveer Lang, Florian Miki, Shigehito Terai, Hirotaka Yabuno, Masahiro Kashiwazaki, Takahiro Inoue, Asuka Umeki, Takeshi Asavanant, Warit Endo, Mamoru Yoshikawa, Jun-Ichi Furusawa, Akira Department of Applied Physics School of Engineering The University of Tokyo 7-3-1 Hongo Bunkyo-ku Tokyo113-8656 Japan Optical Quantum Computing Research Team RIKEN Center for Quantum Computing 2-1 Hirosawa Saitama Wako351-0198 Japan OptQC Corporation 1-16-15 Minami-Ikebukuro Toshima Tokyo Japan Department of Electrical and Computer Engineering University of Massachusetts-Amherst AmherstMA01003 United States Department of Physics University of Massachusetts-Amherst AmherstMA01003 United States Department of Information Technology and Electrical Engineering ETH Zurich Zurich8092 Switzerland Advanced ICT Research Institute National Institute of Information and Communications Technology 588-2 Iwaoka Nishi-ku Hyogo Kobe651-2492 Japan NTT Device Technology Labs NTT Corporation 3-1 Morinosato Wakamiya Kanagawa Atsugi243-0198 Japan

quantum computing with light is a promising approach to achieving large-scale quantum computation[1–3]. While Gaussian operations on optical states have been successfully scaled[4–6], the generation of highly non-Gaussian states remains a critical challenge for achieving universality and fault-tolerance[7, 8]. However, due to the inherently weak nonlinearity in optics, creating non-Gaussian states remains challenging. A promising solution is to "breed"[9–12] non-Gaussianity by combining multiple weakly non-Gaussian states using quantum memory systems. Here, we propose and demonstrate a scalable method for generating optical non-Gaussian states using a cavity-based quantum memory operating in continuous time. Our memory features dual-mode operation, enabling efficient switching between memory and entangling functionalities, allowing state generation and processing with minimal resources. By employing a time-domain-multiplexed breeding protocol, we successfully generated Wigner-negative states, a key requirement for quantum error correction. This work also marks the first full demonstration of continuous-time cavity-based quantum memory, encompassing the complete processes of writing, storage, and readout. These results represent a significant advancement in quantum information processing with light, providing a scalable method for generating complex non-Gaussian states essential for fault-tolerant quantum computing. Beyond advancing optical quantum computing, the techniques and insights from this work could impact a wide range of applications, from enhancing quantum communication networks to refining quantum sensing and metrology. Copyright © 2025, The Authors. All rights reserved.

关键词： Continuous time systems

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Demonstrating a long-coherence dual-rail erasure qubit using tunable transmons

arXiv

引用

arXiv 2023年

作者： Levine, H. Haim, A. Hung, J.S.C. Alidoust, N. Kalaee, M. DeLorenzo, L. Wollack, E.A. Arrangoiz-Arriola, P. Khalajhedayati, A. Sanil, R. Moradinejad, H. Vaknin, Y. Kubica, A. Hover, D. Aghaeimeibodi, S. Alcid, J.A. Baek, C. Barnett, J. Bawdekar, K. Bienias, P. Carson, H.A. Chen, C. Chen, L. Chinkezian, H. Chisholm, E.M. Clifford, A. Cosmic, R. Crisosto, N. Dalzell, A.M. Davis, E. D’Ewart, J.M. Diez, S. D’Souza, N. Dumitrescu, P.T. Elkhouly, E. Fang, M.T. Fang, Y. Flammia, S. Fling, M.J. Garcia, G. Gharzai, M.K. Gorshkov, A.V. Gray, M.J. Grimberg, S. Grimsmo, A.L. Hann, C.T. He, Y. Heidel, S. Howell, S. Hunt, M. Iverson, J. Jarrige, I. Jiang, L. Jones, W.M. Karabalin, R. Karalekas, P.J. Keller, A.J. Lasi, D. Lee, M. Ly, V. MacCabe, G. Mahuli, N. Marcaud, G. Matheny, M.H. McArdle, S. McCabe, G. Merton, G. Miles, C. Milsted, A. Mishra, A. Moncelsi, L. Naghiloo, M. Noh, K. Oblepias, E. Ortuno, G. Owens, J.C. Pagdilao, J. Panduro, A. Paquette, J.-P. Patel, R.N. Peairs, G. Perello, D.J. Peterson, E.C. Ponte, S. Putterman, H. Refael, G. Reinhold, P. Resnick, R. Reyna, O.A. Rodriguez, R. Rose, J. Rubin, A.H. Runyan, M. Ryan, C.A. Sahmoud, A. Scaffidi, T. Shah, B. Siavoshi, S. Sivarajah, P. Skogland, T. Su, C.-J. Swenson, L.J. Sylvia, J. Teo, S.M. Tomada, A. Torlai, G. Wistrom, M. Zhang, K. Zuk, I. Clerk, A.A. Brandão, F.G.S.L. Retzker, A. Painter, O. AWS Center for Quantum Computing PasadenaCA91125 United States Institute of Applied Physics The Hebrew University of Jerusalem Givat Ram Jerusalem91904 Israel Racah Institute of Physics The Hebrew University of Jerusalem Givat Ram Jerusalem91904 Israel Centre for Engineered Quantum Systems School of Physics The University of Sydney SydneyNSW2006 Australia Pritzker School of Molecular Engineering University of Chicago ChicagoIL60637 United States Institute for Quantum Information and Matter California Institute of Technology PasadenaCA91125 United States Department of Physics California Institute of Technology PasadenaCA91125 United States Laboratory of Applied Physics Kavli Nanoscience Institute California Institute of Technology PasadenaCA91125 United States

quantum error correction with erasure qubits promises significant advantages over standard error correction due to favorable thresholds for erasure errors. To realize this advantage in practice requires a qubit for which nearly all errors are such erasure errors, and the ability to check for erasure errors without dephasing the qubit. We demonstrate that a "dual-rail qubit" consisting of a pair of resonantly coupled transmons can form a highly coherent erasure qubit, where transmon T1 errors are converted into erasure errors and residual dephasing is strongly suppressed, leading to millisecond-scale coherence within the qubit subspace. We show that single-qubit gates are limited primarily by erasure errors, with erasure probability perasure = 2.19(2) × 10−3 per gate while the residual errors are ∼ 40 times lower. We further demonstrate mid-circuit detection of erasure errors while introducing Copyright © 2023, The Authors. All rights reserved.

关键词： Qubits

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Robust Qubit Mapping Algorithm via Double-Source Optimal Routing on Large quantum Circuits

arXiv

引用

arXiv 2022年

作者： Cheng, Chin-Yi Yang, Chien-Yi Kuo, Yi-Hsiang Wang, Ren-Chu Cheng, Hao-Chung Huang, Chung-Yang Department of Electrical Engineering National Taiwan University Taiwan Department of Computer Science and Engineering University of California San Diego United States Graduate Institute of Electronics Engineering National Taiwan University Taiwan College of Computing The Georgia Institute of Technology United States Department of Electrical Engineering Graduate Institute of Communication Engineering National Taiwan University Taiwan Center for Quantum Science and Engineering National Taiwan University Taiwan Physics Division and Mathematics Division National Center for Theoretical Sciences Taiwan Quantum Computing Center Taiwan Department of Electrical Engineering National Taiwan University Taiwan

Qubit Mapping is a critical aspect of implementing quantum circuits on real hardware devices. Currently, the existing algorithms for qubit mapping encounter difficulties when dealing with larger circuit sizes involving hundreds of qubits. In this paper, we introduce an innovative qubit mapping algorithm, Duostra, tailored to address the challenge of implementing large-scale quantum circuits on real hardware devices with limited connectivity. Duostra operates by efficiently determining optimal paths for double-qubit gates and inserting SWAP gates accordingly to implement the double-qubit operations on real devices. Together with two heuristic scheduling algorithms, the Limitedly-Exhausitive (LE) Search and the Shortest-Path (SP) Estimation, it yields results of good quality within a reasonable runtime, thereby striving toward achieving quantum advantage. Experimental results showcase our algorithm's superiority, especially for large circuits beyond the NISQ era. For example, on large circuits with more than 50 qubits, we can reduce the mapping cost on an average 21.75% over the virtual best results among QMAP, t|ket〉, Qiskit and SABRE. Besides, for mid-size circuits such as the SABRE-large benchmark, we improve the mapping costs by 4.5%, 5.2%, 16.3%, 20.7%, and 25.7%, when compared to QMAP, TOQM, t|ket〉, Qiskit, and SABRE, respectively. Copyright © 2022, The Authors. All rights reserved.

关键词： Qubits

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A quantum central path algorithm for linear optimization

arXiv

引用

arXiv 2023年

作者： Augustino, Brandon Leng, Jiaqi Nannicini, Giacomo Terlaky, Tamás Wu, Xiaodi Sloan School of Management Massachusetts Institute of Technology United States Simons Institute for the Theory of Computing Department of Mathematics University of California Berkeley United States Department of Industrial and Systems Engineering University of Southern California United States Department of Industrial and Systems Engineering Lehigh University United States Quantum Computing and Optimization Lab Lehigh University United States Department of Mathematics University of Maryland College Park United States Department of Computer Science University of Maryland College Park United States Joint Center for Quantum Information and Computer Science University of Maryland United States

We propose a novel quantum algorithm for solving linear optimization problems by quantum-mechanical simulation of the central path. While interior point methods follow the central path with an iterative algorithm that works with successive linearizations of the perturbed KKT conditions, we perform a single simulation working directly with the nonlinear complementarity equations. This approach yields an algorithm for solving linear optimization problems involving m constraints and n variables to Ε-optimality using O (√m + n · RΕ1) queries to an oracle that evaluates a potential function, where R1 is an 1-norm upper bound on the size of the optimal solution. In the standard gate model (i.e., without access to quantum RAM) our algorithm can obtain highly-precise solutions to LO problems using at most O (√m + n · nnz(A)RΕ1) elementary gates, where nnz(A) is the total number of non-zero elements found in the constraint matrix. © 2023, CC BY.

关键词： Optimization algorithms

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Small sets of genuinely nonlocal GHZ states in multipartite systems

arXiv

引用

arXiv 2023年

作者： Xiong, Zong-Xing Zhang, Yongli Li, Mao-Sheng Li, Lvzhou Institute of Quantum Computing and Software School of Computer Science and Engineering Sun Yat-Sen University Guangzhou510006 China School of Mathematics and Systems Science Guangdong Polytechnic Normal University Guangzhou510665 China School of Mathematics South China University of Technology Guangzhou510641 China

A set of orthogonal multipartite quantum states are called (distinguishability-based) genuinely nonlocal if they are locally indistinguishable across any bipartition of the subsystems. In this work, we consider the problem of constructing small genuinely nonlocal sets consisting of generalized GHZ states in multipartite systems. For system (C2) ⊗ N where N is large, using the language of group theory, we show that a tiny proportion Θ(1/√2N) of states among the N-qubit GHZ basis suffice to exhibit genuine nonlocality. Similar arguments also hold for the canonical generalized GHZ bases in systems (Cd) ⊗ N, wherever d is even and N is large. What is more, moving to the condition that any fixed N is given, we show that d + 1 genuinely nonlocal generalized GHZ states exist in (Cd) ⊗ N, provided the local dimension d is sufficiently large. As an additional merit, within and beyond an asymptotic sense, the latter result also indicates some evident limitations of the "trivial othogonality-preserving local measurements" (TOPLM) technique that has been utilized frequently for detecting genuine nonlocality. © 2023, CC BY.

关键词： Group theory

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Variational quantum eigensolver with linear depth problem-inspired ansatz for solving portfolio optimization in finance

arXiv

引用

arXiv 2024年

作者： Wang, Shengbin Wang, Peng Li, Guihui Zhao, Shubin Zhao, Dongyi Wang, Jing Fang, Yuan Dou, Menghan Gu, Yongjian Wu, Yu-Chun Guo, Guo-Ping Origin Quantum Computing Company Limited Anhui Hefei230026 China CAS Key Laboratory of Quantum Information University of Science and Technology of China Anhui Hefei230026 China Intelligent Information Sensing and Processing Lab College of Electronic Engineering Ocean University of China Shandong Qingdao266000 China College of Physics and Optoelectronic Engineering Ocean University of China Shandong Qingdao266100 China Institute of Artificial Intelligence Hefei Comprehensive National Science Center Anhui Hefei230088 China

Great efforts have been dedicated in recent years to explore practical applications for noisy intermediate-scale quantum (NISQ) computers, which is a fundamental and challenging problem in quantum computing. As one of the most promising methods, the variational quantum eigensolver (VQE) has been extensively studied. In this paper, VQE is applied to solve portfolio optimization problems in finance by designing two hardware-efficient Dicke state ansatze that reach a maximum of 2n two-qubit 2 gate depth and n2/4 parameters, with n being the number of qubits used. Both ansatze are partitioning-friendly, allowing for the proposal of a highly scalable quantum/classical hybrid distributed computing (HDC) scheme. Combining simultaneous sampling, problem-specific measurement error mitigation, and fragment reuse techniques, we successfully implement the HDC experiments on a superconducting quantum computer with up to 55 qubits. The simulation and experimental results illustrate that the restricted expressibility of the ansatze, induced by the small number of parameters and limited entanglement, is advantageous for solving classical optimization problems with the cost function of the conditional value-at-risk (CVaR) for the NISQ era and beyond. Furthermore, the HDC scheme shows great potential for achieving quantum advantage in the NISQ era. We hope that the heuristic idea presented in this paper can motivate fruitful investigations in current and future quantum computing paradigms. Copyright © 2024, The Authors. All rights reserved.

关键词： Optimization

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Distinguishing unitary gates on the IBM quantum processor

引用

Science China(Information Sciences) 2019年第7期62卷 210-216页

作者： Shusen LIU Yinan LI Runyao DUAN School of Data and Computer Science Sun Yat-sen University Centre for Quantum Software and Information Faculty of Engineering and Information TechnologyUniversity of Technology Sydney Centrum Wiskunde & Informatica and Research Center for Quantum Software Institute for Quantum Computing

An unknown unitary gate, which is secretly chosen from several known ones, can always be distinguished perfectly. In this paper, we implement such a task on IBM's quantum processor. More precisely,we experimentally demonstrate the discrimination of two qubit unitary gates, the identity gate and the 2/3π-phase shift gate, using two discrimination schemes — the parallel scheme and the sequential scheme. We program these two schemes on the ibmqx4, a 5-qubit superconducting quantum processor via IBM cloud,with the help of the QSI modules. We report that both discrimination schemes achieve success probabilities at least 85%.

关键词： quantum experiment IBM quantum computer software-aided quantum experiment sequential schemes for unitary discrimination parallel schemes for unitary discrimination

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