Machine learning assisted quantum adiabatic algorithm design

Lin Jian; Ye Meng; Zhu Jia-Wei; Li Xiao-Peng

doi:10.7498/aps.70.20210831

Abstract

Quantum computing has made dramatic progress in the last decade. The quantum platforms including superconducting qubits, photonic devices, and atomic ensembles, have all reached a new era, with unprecedented quantum control capability developed. Quantum computation advantage over classical computers has been reported on certain computation tasks. A promising computing protocol of using the computation power in these controllable quantum devices is implemented through quantum adiabatic computing, where quantum algorithm design plays an essential role in fully using the quantum advantage. Here in this paper, we review recent developments in using machine learning approach to design the quantum adiabatic algorithm. Its applications to 3-SAT problems, and also the Grover search problems are discussed.

Keywords:

Authors and contacts

Department of Physics, Fudan University, Shanghai 200433, China

Corresponding author: Li Xiao-Peng, xiaopeng_li@fudan.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11934002), the National Basic Research Program of China (Grant No. 2017YFA0304204), and the Shanghai Municipal Science and Technology Major Project, China (Grant No. 2019SHZDZX01)

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References

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Cited By

图 1 强化学习辅助绝热量子算法设计的示意图^[173]. 其中强化学习中的智能体(agent)根据绝热量子计算(AQC)输出的结果来获取奖励, 并根据深度神经网络近似表示的Q值表格来选择动作更新绝热量子算法

Figure 1. Schematic diagram of the reinforcement learning approach for quantum adiabatic algorithm design^[173]. The learning agent collects the reward according to the result obtained from adiabatic quantum computing (AQC) and produces an action to update the quantum adiabatic algorithm based on its Q table represented by a deep neural network.

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图 2 强化学习辅助设计的绝热量子算法在Grover搜索问题上的表现^[173]. 其中成功概率(success probability)是演化终态与目标态交叠的平方, 总的演化时间T与系统规模n的关系为$ T = \sqrt{2^n}$. 图中蓝色虚线表示的线性演化路径成功概率会随着系统尺寸增大不断降低. 红色实线和黑色虚线分别表示强化学习设计得到的演化路径和解析获得的非线性路径^[66]的表现. 在选择的演化时间下, 两者的成功概率都能接近于1, 说明两者都具有平方的量子加速

Figure 2. Performance of reinforcement learning designed quantum adiabatic algorithm in success probability for Grover search problem^[173]. The success probability is obtained by taking the square of wave-function overlap of the final evolved quantum state with the target state. The total adiabatic evolution time is chosen as $ T = \sqrt{2^n}$ where n is the system size. The blue dashed line denotes the success probability of linear path which decreases as increasing the system size. The red solid line and black dashed line denote the performance of the reinforcement learning designed path and the nonlinear path^[66], respectively. Given the choice of total evolution time, the success probability close to 1 by both implies that they both exhibit quadratic quantum speed up.

DownLoad: Full-Size Img PowerPoint

图 3 强化学习在Grover搜索问题的绝热量子算法设计中的拓展性^[173]. 其中绿线是线性路径的表现, 蓝线是将10 qubits系统中强化学习学到的路径推广到更大系统, 橘线是将在n qubits系统强化学习获得的路径推广到$ n+1$qubits系统

Figure 3. Transferability of reinforcement learning based quantum adiabatic algorithm design for Grover search problem^[173]. The green line denotes the infidelity of linear path. The blue line denotes the infidelity of the path obtained by training the 10 qubits system. The orange line denotes the performance of applying the path learned from the n qubits system to the $ n+1$ qubits system.

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