Correlation-Informed Permutation of Qubits for Reducing Ansatz Depth in VQE

TL;DR

This paper introduces PermVQE, a method that optimizes qubit permutations based on mutual information to reduce circuit depth in VQE, improving efficiency for molecular electronic structure calculations on near-term quantum computers.

Contribution

PermVQE is a novel approach that permutes qubits to minimize long-range correlations, thereby reducing circuit depth in VQE for molecular systems.

Findings

PermVQE reduces circuit depth for LiH, H2, and other molecules.

Proximity of entangled qubits leads to shallower circuits.

Method extends to various qubit connectivities and algorithms.

Abstract

The Variational Quantum Eigensolver (VQE) is a method of choice to solve the electronic structure problem for molecules on near-term gate-based quantum computers. However, the circuit depth is expected to grow significantly with problem size. Increased depth can both degrade the accuracy of the results and reduce trainability. In this work, we propose a novel approach to reduce ansatz circuit depth. Our approach, called PermVQE, adds an additional optimization loop to VQE that permutes qubits in order to solve for the qubit Hamiltonian that minimizes long-range correlations in the ground state. The choice of permutations is based on mutual information, which is a measure of interaction between electrons in spin-orbitals. Encoding strongly interacting spin-orbitals into proximal qubits on a quantum chip naturally reduces the circuit depth needed to prepare the ground state. For representative molecular systems, LiH, H$_2$, (H$_2$)$_2$, H$_4$, and H$_3^+$, we demonstrate for linear qubit connectivity that placing entangled qubits in close proximity leads to shallower depth circuits required to reach a given eigenvalue-eigenvector accuracy. This approach can be extended to any qubit connectivity and can significantly reduce the depth required to reach a desired accuracy in VQE. Moreover, our approach can be applied to other variational quantum algorithms beyond VQE.