Improving stabilizer approximation with quantum strategy

TL;DR

This work addresses the challenge of stabilizer-based ground-state approximations when competing Pauli terms hinder traditional stabilizer choices. It introduces a CHSH-game–inspired quantum strategy that induces a qubit-wise gauging of Pauli operators, using discrete rotations (π/4) and continuous rotations via $R_y(\theta)$ to redefine stabilizers as $X'$ and $Z'$ and improve ground-state energies. The authors demonstrate, through Ising and hydrogen molecule examples, that both discrete and continuous gauging can significantly lower the estimated energy toward the exact ground state, providing a natural initialization for quantum algorithms. The approach highlights a principled way to inject quantum resources into stabilizer methods and suggests broader connections to ZX-calculus and potential Heisenberg-picture universality.

Abstract

We introduce a quantum strategy from nonlocal games to improve the stabilizer approximation we proposed previously. The resulting approach turns out to be a qubit-by-qubit gauging procedure for standard stabilizers, which could involve discrete or continuous gauge parameters. We take examples from many-body physics and quantum chemistry to show such a procedure leads to an improvement of the performance.