Quantum approximate optimization algorithm in non-Markovian quantum systems

Although quantum approximate optimization algorithm (QAOA) has demonstrated its quantum supremacy, its performance on Noisy Intermediate-Scale Quantum (NISQ) devices would be influenced by complicated noises, e.g. quantum colored noises. To evaluate the performance of QAOA under these noises, this paper presents a framework for running QAOA on non-Markovian quantum systems which are represented by an augmented system model. In this model, a non-Markovian environment carrying quantum colored noises is modelled as an ancillary system driven by quantum white noises which is directly coupled to the corresponding principal system; i.e. the computational unit for the algorithm. With this model, we mathematically formulate QAOA as piecewise Hamiltonian control of the augmented system, where we also optimize the control depth to fit into the circuit depth of current quantum devices. For efficient simulation of QAOA in non-Markovian quantum systems, a boosted algorithm using quantum trajectory is further presented. Finally, we show that non-Markovianity can be utilized as a quantum resource to achieve a relatively good performance of QAOA, which is characterized by our proposed exploration rate.