Variational Quantum Subspace Construction via Symmetry-Preserving Cost Functions

TL;DR

This paper introduces a symmetry-preserving variational method for constructing low-energy subspaces in quantum systems, improving efficiency and hardware compatibility for quantum chemistry calculations.

Contribution

It presents a novel variational approach that iteratively builds a reduced subspace using symmetry-preserving cost functions, aligning with Lanczos-like tridiagonal representations.

Findings

Effective in constructing low-energy states with reduced circuit depth

Demonstrated on H4 chain and ring systems

Achieves accurate ground-state energies and charge gaps

Abstract

Determining low-energy eigenstates in electronic many-body quantum systems is a key challenge in computational chemistry and condensed-matter physics. Hybrid quantum-classical approaches, such as the Variational Quantum Eigensolver and Quantum Subspace Methods, offer practical solutions but face limitations in circuit depth and measurement overhead. In this article, we propose a variational strategy based on symmetry-preserving cost functions to iteratively construct a reduced subspace for the extraction of low-lying energy states. We show that, under certain conditions, our approach leads to a tridiagonal representation similar to that obtained with the Lanczos algorithm. The iterative process allows control over the trade-off between circuit depth, the number of variational parameters, and the number of measurements required to achieve the desired accuracy, making it suitable for current quantum hardware. As a proof of concept, we test the proposed algorithms on H4 chain and ring, targeting both the ground-state energy and the charge gap.