Solving the subset sum problem by the quantum Ising model with variational quantum optimization based on conditional values at risk  

作　　者：Qilin Zheng Miaomiao Yu Pingyu Zhu Yan Wang Weihong Luo Ping Xu 

机构地区：[1]Institute for Quantum Information and State Key Laboratory of High Performance Computing,College of Computer Science and Technology,National University of Defense Technology,Changsha 410073,China [2]Hefei National Laboratory,Hefei 230088,China

出　　处：《Science China(Physics,Mechanics & Astronomy)》2024年第8期43-55,共13页中国科学：物理学、力学、天文学（英文版）

基　　金：supported by the National Key R&D Program of China(Grant No.2019YFA0308700);the Innovation Program for Quantum Science and Technology(Grant No.2021ZD0301500)。

摘　　要：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 2ndimensional 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.

关 键 词：subset sum problem quantum Ising model conditional values at risk variational quantum optimization 

分 类 号：O224[理学—运筹学与控制论]