{"title":"用基于风险条件值的变分量子优化解决量子伊辛模型的子集和问题","authors":"Qilin Zheng, Miaomiao Yu, Pingyu Zhu, Yan Wang, Weihong Luo, Ping Xu","doi":"10.1007/s11433-024-2385-7","DOIUrl":null,"url":null,"abstract":"<div><p>The subset sum problem is a combinatorial optimization problem, and its complexity belongs to the nondeterministic polynomial time complete (NP-Complete) class. This problem is widely used in encryption, planning or scheduling, and integer partitions. An accurate search algorithm with polynomial time complexity has not been found, which makes it challenging to be solved on classical computers. To effectively solve this problem, we translate it into the quantum Ising model and solve it with a variational quantum optimization method based on conditional values at risk. The proposed model needs only <i>n</i> qubits to encode 2<sup><i>n</i></sup> dimensional search space, which can effectively save the encoding quantum resources. The model inherits the advantages of variational quantum algorithms and can obtain good performance at shallow circuit depths while being robust to noise, and it is convenient to be deployed in the Noisy Intermediate Scale Quantum era. We investigate the effects of the scalability, the variational ansatz type, the variational depth, and noise on the model. Moreover, we also discuss the performance of the model under different conditional values at risk. Through computer simulation, the scale can reach more than nine qubits. By selecting the noise type, we construct simulators with different QVs and study the performance of the model with them. In addition, we deploy the model on a superconducting quantum computer of the Origin Quantum Technology Company and successfully solve the subset sum problem. This model provides a new perspective for solving the subset sum problem.</p></div>","PeriodicalId":774,"journal":{"name":"Science China Physics, Mechanics & Astronomy","volume":null,"pages":null},"PeriodicalIF":6.4000,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Solving the subset sum problem by the quantum Ising model with variational quantum optimization based on conditional values at risk\",\"authors\":\"Qilin Zheng, Miaomiao Yu, Pingyu Zhu, Yan Wang, Weihong Luo, Ping Xu\",\"doi\":\"10.1007/s11433-024-2385-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The subset sum problem is a combinatorial optimization problem, and its complexity belongs to the nondeterministic polynomial time complete (NP-Complete) class. This problem is widely used in encryption, planning or scheduling, and integer partitions. An accurate search algorithm with polynomial time complexity has not been found, which makes it challenging to be solved on classical computers. To effectively solve this problem, we translate it into the quantum Ising model and solve it with a variational quantum optimization method based on conditional values at risk. The proposed model needs only <i>n</i> qubits to encode 2<sup><i>n</i></sup> dimensional search space, which can effectively save the encoding quantum resources. The model inherits the advantages of variational quantum algorithms and can obtain good performance at shallow circuit depths while being robust to noise, and it is convenient to be deployed in the Noisy Intermediate Scale Quantum era. We investigate the effects of the scalability, the variational ansatz type, the variational depth, and noise on the model. Moreover, we also discuss the performance of the model under different conditional values at risk. Through computer simulation, the scale can reach more than nine qubits. By selecting the noise type, we construct simulators with different QVs and study the performance of the model with them. In addition, we deploy the model on a superconducting quantum computer of the Origin Quantum Technology Company and successfully solve the subset sum problem. This model provides a new perspective for solving the subset sum problem.</p></div>\",\"PeriodicalId\":774,\"journal\":{\"name\":\"Science China Physics, Mechanics & Astronomy\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":6.4000,\"publicationDate\":\"2024-07-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Science China Physics, Mechanics & Astronomy\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s11433-024-2385-7\",\"RegionNum\":1,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Science China Physics, Mechanics & Astronomy","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s11433-024-2385-7","RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
摘要
子集和问题是一个组合优化问题,其复杂度属于非确定性多项式时间完全(NP-Complete)类。该问题广泛应用于加密、规划或调度以及整数分割等领域。目前尚未找到具有多项式时间复杂性的精确搜索算法,因此在经典计算机上解决该问题具有挑战性。为了有效解决这个问题,我们将其转化为量子伊辛模型,并采用基于风险条件值的变分量子优化方法来解决。所提出的模型只需要 n 个量子比特来编码 2n 维搜索空间,可以有效节省编码量子资源。该模型继承了变分量子算法的优点,可以在浅层电路深度获得良好的性能,同时对噪声具有鲁棒性,便于在噪声中尺度量子时代部署。我们研究了可扩展性、变分法类型、变分法深度和噪声对模型的影响。此外,我们还讨论了模型在不同风险条件值下的性能。通过计算机模拟,规模可以达到九比特以上。通过选择噪声类型,我们构建了不同 QV 的模拟器,并研究了模型在这些模拟器下的性能。此外,我们还在起源量子技术公司的超导量子计算机上部署了该模型,并成功解决了子集和问题。该模型为解决子集和问题提供了一个新的视角。
Solving the subset sum problem by the quantum Ising model with variational quantum optimization based on conditional values at risk
The subset sum problem is a combinatorial optimization problem, and its complexity belongs to the nondeterministic polynomial time complete (NP-Complete) class. This problem is widely used in encryption, planning or scheduling, and integer partitions. An accurate search algorithm with polynomial time complexity has not been found, which makes it challenging to be solved on classical computers. To effectively solve this problem, we translate it into the quantum Ising model and solve it with a variational quantum optimization method based on conditional values at risk. The proposed model needs only n qubits to encode 2n dimensional search space, which can effectively save the encoding quantum resources. The model inherits the advantages of variational quantum algorithms and can obtain good performance at shallow circuit depths while being robust to noise, and it is convenient to be deployed in the Noisy Intermediate Scale Quantum era. We investigate the effects of the scalability, the variational ansatz type, the variational depth, and noise on the model. Moreover, we also discuss the performance of the model under different conditional values at risk. Through computer simulation, the scale can reach more than nine qubits. By selecting the noise type, we construct simulators with different QVs and study the performance of the model with them. In addition, we deploy the model on a superconducting quantum computer of the Origin Quantum Technology Company and successfully solve the subset sum problem. This model provides a new perspective for solving the subset sum problem.
期刊介绍:
Science China Physics, Mechanics & Astronomy, an academic journal cosponsored by the Chinese Academy of Sciences and the National Natural Science Foundation of China, and published by Science China Press, is committed to publishing high-quality, original results in both basic and applied research.
Science China Physics, Mechanics & Astronomy, is published in both print and electronic forms. It is indexed by Science Citation Index.
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