An efficient adaptive variational quantum solver of the Schrodinger equation based on reduced density matrices

TL;DR

This paper introduces an improved adaptive variational quantum algorithm for solving the Schrödinger equation that significantly reduces measurement complexity, making it more practical for near-term quantum hardware, and extends it to excited states.

Contribution

The authors develop a measurement-efficient adaptive variational quantum solver based on reduced density matrices, reducing measurement scaling from O(N^8) to O(N^4) and enabling accurate simulations of ground and excited states.

Findings

Reduces measurement complexity from O(N^8) to O(N^4)

Accurately describes ground-state potential energy curves

Extends to excited states with comparable accuracy

Abstract

Recently, an adaptive variational algorithm termed Adaptive Derivative-Assembled Pseudo-Trotter ansatz Variational Quantum Eigensolver (ADAPT-VQE) has been proposed by Grimsley et al. (Nat. Commun. 10, 3007) while the number of measurements required to perform this algorithm scales O(N^8). In this work, we present an efficient adaptive variational quantum solver of the Schrodinger equation based on ADAPT-VQE together with the reduced density matrix reconstruction approach, which reduces the number of measurements from O(N^8) to O(N^4). This new algorithm is quite suitable for quantum simulations of chemical systems on near-term noisy intermediate-scale hardware due to low circuit complexity and reduced measurement. Numerical benchmark calculations for small molecules demonstrate that this new algorithm provides an accurate description of the ground-state potential energy curves. In addition, we generalize this new algorithm for excited states with the variational quantum deflation approach and achieve the same accuracy as ground-state simulations.