Performance study of variational quantum linear solver with an improved ansatz for reservoir flow equations

Abstract

This paper studies the performance of the variational quantum linear solver (VQLS) with an improved ansatz for discretized reservoir flow equations for the first time. First, we introduce the two typical flow equations in reservoir simulation, namely, the diffusion equation for pressure and the convection-dominated Buckley–Leverett equation for water saturation, and their commonly used finite volume or finite difference-based discretized linear equations. Then, we propose an improved ansatz in VQLS to enhance the convergence and accuracy of VQLS and a strategy of adjusting grid order to reduce the complexity of the quantum circuit for preparing the quantum state corresponding to the coefficient vector of the discretized reservoir flow equations. Finally, we apply the modified VQLS to solve the discretized reservoir flow equations by employing the Xanadu's PennyLane open-source library. Four numerical examples are implemented, and the results show that VQLS can calculate reservoir flow equations with high accuracy, and the improved ansatz significantly outperforms the original one. Moreover, we study the effects of reservoir heterogeneity, the number of ansatz layers, the equation type, and the number of shots on the computational performance. Limited by the current computing capacity, the number of grids subject to the involved number of quantum bits in the implemented examples is small; we will further explore this quantum algorithm to practical examples that require a large number of quantum bits in the future.