Effects of Quantum Noise on Quantum Approximate Optimization AlgorithmSupported by the National Key Research and Development Program of China (Grant No. 2016YFA0301700), the National Natural Science Foundation of China (Grants No. 11625419), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB24030600), and the Anhui Initiative in Quantum Information Technologies (Grant No. AHY080000).

Abstract

The quantum-classical hybrid algorithm is a promising algorithm with respect to demonstrating the quantum advantage in noisy-intermediate-scale quantum (NISQ) devices. When running such algorithms, effects due to quantum noise are inevitable. In our work, we consider a well-known hybrid algorithm, the quantum approximate optimization algorithm (QAOA). We study the effects on QAOA from typical quantum noise channels, and produce several numerical results. Our research indicates that the output state fidelity, i.e., the cost function obtained from QAOA, decreases exponentially with respect to the number of gates and noise strength. Moreover, we find that when noise is not serious, the optimized parameters will not deviate from their ideal values. Our result provides evidence for the effectiveness of hybrid algorithms running on NISQ devices.