Compact fermionic quantum state preparation with a natural-orbitalizing variational quantum eigensolving scheme

TL;DR

This paper introduces a refined variational quantum eigensolver (VQE) method that uses natural-orbital updates to improve fermionic state preparation, reducing circuit depth and noise sensitivity in quantum simulations of strongly interacting systems.

Contribution

The authors propose a natural-orbitalizing VQE scheme that enhances state preparation efficiency and reduces circuit depth, especially when combined with adaptive circuit construction.

Findings

Improved state proximity to target with fixed circuit structure.

Reduced circuit depth requirements with orbital updates.

Enhanced robustness against noise in Hubbard model simulations.

Abstract

Assemblies of strongly interacting fermions, whether in a condensed-matter or a quantum chemistry context, range amongst the most promising candidate systems for which quantum computing platforms could provide an advantage. Near-term quantum state preparation is typically realized by means of the variational quantum eigensolver (VQE) algorithm. One of the main challenges to a successful implementation of VQE lies in the sensitivity to noise exhibited by deep variational circuits. On the other hand, sufficient depth must be allowed to be able to reach a good approximation to the target state. In this work, we present a refined VQE scheme that consists in topping VQE with state-informed updates of the elementary fermionic modes (spin-orbitals). These updates consist in moving to the natural-orbital basis of the current, converged variational state, a basis we argue eases the task of state preparation. We test the method on the Hubbard model in the presence of experimentally relevant noise levels. For a fixed circuit structure, the method is shown to enhance the capabilities of the circuit to reach a state close to the target state without incurring too much overhead from shot noise. Moreover, coupled with an adaptive VQE scheme that constructs the circuit on the fly, we evidence reduced requirements on the depth of the circuit as the orbitals get updated.