A Bottom-up Approach to Constructing Symmetric Variational Quantum Circuits

TL;DR

This paper introduces a bottom-up method for constructing symmetric variational quantum circuits leveraging representation theory, specifically U(1) symmetry, to create more efficient and noise-robust quantum circuits for fermionic systems.

Contribution

It presents a novel approach to designing symmetric quantum circuits using representation theory, focusing on particle number conservation, which improves circuit efficiency and robustness.

Findings

Symmetric circuits are more compact and noise-resistant.

Derived particle-conserving exchange gates for fermionic systems.

Validated effectiveness using the Heisenberg XXZ model.

Abstract

In the age of noisy quantum processors, the exploitation of quantum symmetries can be quite beneficial in the efficient preparation of trial states, an important part of the variational quantum eigensolver algorithm. The benefits include building quantum circuits which are more compact, with lesser number of paramaters, and more robust to noise, than their non-symmetric counterparts. Leveraging on ideas from representation theory we show how to construct symmetric quantum circuits. Similar ideas have been previously used in the field of tensor networks to construct symmetric tensor networks. We focus on the specific case of particle number conservation, that is systems with U(1) symmetry. Based on the representation theory of U(1), we show how to derive the particle-conserving exchange gates, which are commonly used in constructing hardware-efficient quantum circuits for fermionic systems, like in quantum chemistry, material science, and condensed-matter physics. We tested the effectiveness of our circuits with the Heisenberg XXZ model.