Quantum Approximate Optimization Algorithm Parameter Prediction Using a Convolutional Neural Network

• URL: http://arxiv.org/abs/2211.09513v1
• Date: Thu, 17 Nov 2022 13:20:58 GMT
• Title: Quantum Approximate Optimization Algorithm Parameter Prediction Using a Convolutional Neural Network
• Authors: Ningyi Xie, Xinwei Lee, Dongsheng Cai, Yoshiyuki Saito, Nobuyoshi Asai
• Abstract summary: We build a convolutional neural network to predict parameters of depth $p+1$ QAOA by the parameters from the depth $p$ QAOA counterpart. An average approximation ratio of 92735$ for Max-Cut over $800$ ErdHos-R'enyi is obtained.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The Quantum approximate optimization algorithm (QAOA) is a quantum-classical hybrid algorithm aiming to produce approximate solutions for combinatorial optimization problems. In the QAOA, the quantum part prepares a quantum parameterized state that encodes the solution, where the parameters are optimized by a classical optimizer. However, it is difficult to find optimal parameters when the quantum circuit becomes deeper. Hence, there is numerous active research on the performance and the optimization cost of QAOA. In this work, we build a convolutional neural network to predict parameters of depth $p+1$ QAOA instance by the parameters from the depth $p$ QAOA counterpart. We propose two strategies based on this model. First, we recurrently apply the model to generate a set of initial values for a certain depth QAOA. It successfully initiates depth $10$ QAOA instances, whereas each model is only trained with the parameters from depths less than $6$. Second, the model is applied repetitively until the maximum expected value is reached. An average approximation ratio of $0.9735$ for Max-Cut over $800$ Erd\H{o}s-R\'{e}nyi graphs is obtained, while the optimizer is only adopted for generating the first input of the model.

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