The Quantum Alternating Operator Ansatz (QAOA+) is one of the Variational Quantum Algorithm (VQA) specifically developed to tackle combinatorial optimization problems by exploring the feasible space in search of a target solution. For the Constrained Binary Optimization with Unconstrained Variables Problems (CBO‐UVPs), the mixed operators in the QAOA+ circuit are applied to the constrained variables, while the single‐qubit rotating gates operate on the unconstrained variables. The expressibility of this circuit is limited by the shortage of two‐qubit gates and the parameter sharing in the single‐qubit rotating gates, which consequently impacts the performance of QAOA+ for solving CBO‐UVPs. Therefore, it is crucial to develop a suitable ansatz for CBO‐UVPs. In this paper, the Variational Quantum Algorithm‐Preserving Feasible Space (VQA‐PFS) ansatz is proposed, exemplified by the Uncapacitated Facility Location Problem (UFLP), that applies mixed operators on constrained variables while employing Hardware‐Efficient Ansatz (HEA) on unconstrained variables. The numerical results demonstrate that VQA‐PFS significantly enhances the probability of success and exhibits faster convergence than QAOA+, Quantum Approximation Optimization Algorithm (QAOA), and HEA. Furthermore, VQA‐PFS reduces the circuit depth dramatically compared to QAOA+ and QAOA. The algorithm is general and instructive in tackling CBO‐UVPs.
{"title":"Variational Quantum Algorithm‐Preserving Feasible Space for Solving the Uncapacitated Facility Location Problem","authors":"Sha‐Sha Wang, Hai‐Ling Liu, Yong‐Mei Li, Fei Gao, Su‐Juan Qin, Qiao‐Yan Wen","doi":"10.1002/qute.202400201","DOIUrl":"https://doi.org/10.1002/qute.202400201","url":null,"abstract":"The Quantum Alternating Operator Ansatz (QAOA+) is one of the Variational Quantum Algorithm (VQA) specifically developed to tackle combinatorial optimization problems by exploring the feasible space in search of a target solution. For the Constrained Binary Optimization with Unconstrained Variables Problems (CBO‐UVPs), the mixed operators in the QAOA+ circuit are applied to the constrained variables, while the single‐qubit rotating gates operate on the unconstrained variables. The expressibility of this circuit is limited by the shortage of two‐qubit gates and the parameter sharing in the single‐qubit rotating gates, which consequently impacts the performance of QAOA+ for solving CBO‐UVPs. Therefore, it is crucial to develop a suitable ansatz for CBO‐UVPs. In this paper, the Variational Quantum Algorithm‐Preserving Feasible Space (VQA‐PFS) ansatz is proposed, exemplified by the Uncapacitated Facility Location Problem (UFLP), that applies mixed operators on constrained variables while employing Hardware‐Efficient Ansatz (HEA) on unconstrained variables. The numerical results demonstrate that VQA‐PFS significantly enhances the probability of success and exhibits faster convergence than QAOA+, Quantum Approximation Optimization Algorithm (QAOA), and HEA. Furthermore, VQA‐PFS reduces the circuit depth dramatically compared to QAOA+ and QAOA. The algorithm is general and instructive in tackling CBO‐UVPs.","PeriodicalId":501028,"journal":{"name":"Advanced Quantum Technologies","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142218910","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The coordination between distance and the secure key rate is one of the main challenges in the practical application of quantum key distribution (QKD). Mode‐pairing quantum key distribution is one of the schemes that can surpass the secret key capacity for repeaterless QKD. However, the protocol utilizes phase to encode the information, which leads to the problem of active stabilization in the interferometer. In this paper, a reference‐frame‐independent mode‐pairing quantum key distribution (RFI‐MP‐QKD) is proposed as an effective scheme to solve this problem. Moreover, the performance of the RFI‐MP‐QKD protocol is improved by applying the Advantage Distillation (AD) method in data post‐processing, which separates the highly correlated raw key bits from the weakly correlated information. The simulation results show that the secure key rate of RFI‐MP‐QKD has almost no degradation for reference frame deviation angles of . Compared to RFI‐MP‐QKD without AD method, the AD method decreases the quantum bit error rate from 0.04 to 0.012 and increases the maximum transmission distance from 406 to 450 km. The scheme proposed is expected to facilitate the practical implementation of RFI‐MP‐QKD, especially in cases of concerning reference frame alignment and high channel loss.
{"title":"Reference‐Frame‐Independent Mode‐Pairing Quantum Key Distribution with Advantage Distillation","authors":"Yuemei Li, Zhongqi Sun, Xinhe Liu, Zhenhua Li, Jiaao Li, Haoyang Wang, Kaiyi Shi, Chang Liu, Haiqiang Ma","doi":"10.1002/qute.202300387","DOIUrl":"https://doi.org/10.1002/qute.202300387","url":null,"abstract":"The coordination between distance and the secure key rate is one of the main challenges in the practical application of quantum key distribution (QKD). Mode‐pairing quantum key distribution is one of the schemes that can surpass the secret key capacity for repeaterless QKD. However, the protocol utilizes phase to encode the information, which leads to the problem of active stabilization in the interferometer. In this paper, a reference‐frame‐independent mode‐pairing quantum key distribution (RFI‐MP‐QKD) is proposed as an effective scheme to solve this problem. Moreover, the performance of the RFI‐MP‐QKD protocol is improved by applying the Advantage Distillation (AD) method in data post‐processing, which separates the highly correlated raw key bits from the weakly correlated information. The simulation results show that the secure key rate of RFI‐MP‐QKD has almost no degradation for reference frame deviation angles of . Compared to RFI‐MP‐QKD without AD method, the AD method decreases the quantum bit error rate from 0.04 to 0.012 and increases the maximum transmission distance from 406 to 450 km. The scheme proposed is expected to facilitate the practical implementation of RFI‐MP‐QKD, especially in cases of concerning reference frame alignment and high channel loss.","PeriodicalId":501028,"journal":{"name":"Advanced Quantum Technologies","volume":"44 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139866010","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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