Improving Ground State Accuracy of Variational Quantum Eigensolvers with Soft-coded Orthogonal Subspace Representations

TL;DR

This paper introduces a novel soft-coded orthogonality approach in VQE algorithms, enabling shallower circuits and improved ground state accuracy by relaxing orthogonality constraints with penalty terms.

Contribution

It presents a new subspace representation with soft-coded orthogonality constraints, enhancing VQE performance over existing hard-coded methods.

Findings

Achieves high fidelity with shallower circuits.

Outperforms standard VQE, SSVQE, and MCVQE on benchmark models.

Maintains accuracy with reduced circuit depth.

Abstract

We propose a new approach to improve the accuracy of ground state estimates in Variational Quantum Eigensolver (VQE) algorithms by employing subspace representations with soft-coded orthogonality constraints. As in other subspace-based VQE methods, such as the Subspace-Search VQE (SSVQE) and Multistate Contracted VQE (MCVQE), once the parameters are optimized to maximize the subspace overlap with the low-energy sector of the Hamiltonian, one diagonalizes the Hamiltonian restricted to the subspace. Unlike these methods, where \emph{hard-coded} orthogonality constraints are enforced at the circuit level among the states spanning the subspace, we consider a subspace representation where orthogonality is \emph{soft-coded} via penalty terms in the cost function. We show that this representation allows for shallower quantum circuits while maintaining high fidelity when compared to single-state (standard VQE) and multi-state (SSVQE or MCVQE) representations, on two benchmark cases: a $3\times 3$ transverse-field Ising model and random realizations of the Edwards--Anderson spin-glass model on a $4\times 4$ lattice.