Variational Quantum Linear Solver with Dynamic Ansatz

TL;DR

This paper introduces a dynamic ansatz for the Variational Quantum Linear Solver, which adaptively adjusts the circuit depth to improve efficiency and resource usage in solving linear systems on quantum computers.

Contribution

The paper proposes a novel dynamic ansatz that evolves during the algorithm, reducing quantum resource requirements compared to static approaches.

Findings

Fewer quantum resources used with dynamic ansatz

Smaller quantum depth achieved on average

Effective under noise and increased system complexity

Abstract

Variational quantum algorithms have found success in the NISQ era owing to their hybrid quantum-classical approach which mitigate the problems of noise in quantum computers. In our study we introduce the dynamic ansatz in the Variational Quantum Linear Solver for a system of linear algebraic equations. In this improved algorithm, the number of layers in the hardware efficient ansatz circuit is evolved, starting from a small and gradually increasing until convergence of the solution is reached. We demonstrate the algorithm advantage in comparison to the standard, static ansatz by utilizing fewer quantum resources and with a smaller quantum depth on average, in presence and absence of quantum noise, and in cases when the number of qubits or condition number of the system matrix are increased. The numbers of iterations and layers can be altered by a switching parameter. The performance of the algorithm in using quantum resources is quantified by a newly defined metric.