Variational quantum-neural hybrid imaginary time evolution

Abstract: Numerous methodologies have been proposed for performing imaginary time evolution (ITE) using quantum computers. Among these, variational ITE (VITE) for noisy intermediate-scale quantum (NISQ) computers has attracted much attention, which uses parametrized quantum circuits to mimic non-unitary dynamics. However, conventional variational quantum algorithms including VITE face challenges in achieving high accuracy due to their strong dependence on the choice of ansatz quantum circuits. Recently, the variational quantum-neural eigensolver (VQNHE), which combines the neural network (NN) with the variational quantum eigensolver, has been proposed. This approach enhances performance of estimating the expectation values of the state given by the parametrized quantum circuit and NN. In this study, we propose a variational quantum-neural hybrid ITE method (VQNHITE). Our proposal accurately estimates ITE by combining the NN and parameterized quantum circuit. We tested our approach with numerical simulations to evaluate the performance of VQNHITE relative to VITE.