Two-Gate Extensions of Free Axis and Free Quaternion Selection for Sequential Optimization of Parameterized Quantum Circuits

TL;DR

This paper introduces two-gate extensions of existing quantum circuit optimizers, improving accuracy in various quantum tasks by optimizing two gates simultaneously, with a trade-off in measurement overhead.

Contribution

It proposes Two-Gate Fraxis and Two-Gate FQS methods that enhance local optimization by simultaneously updating two gates, outperforming single-gate methods in multiple quantum applications.

Findings

TGF and TGFQS often achieve lower energy errors or infidelity than single-gate methods.

Random and half-shifted gate pairing strategies perform best in many settings.

Best strategies maintain advantage across different shot counts in shallow circuits.

Abstract

We propose two-gate extensions of the sequential single-qubit optimizers, Free Axis Selection (Fraxis) and Free Quaternion Selection (FQS), termed Two-Gate Fraxis (TGF) and Two-Gate FQS (TGFQS), respectively. In contrast to Fraxis and FQS, which update one single-qubit gate at a time via quadratic local cost function and matrix diagonalization, TGF and TGFQS optimize two parameterized single-qubit gates simultaneously by constructing an exact quartic local cost function and optimizing it using classical optimizers. We further investigate how different gate pairing strategies affect optimization performance. Using numerical experiments on spin Hamiltonians, molecular Hamiltonians, and quantum state preparation tasks, we find that TGF and TGFQS frequently achieve a lower final relative error to the ground state energy or infidelity than their single gate counterparts. We observe that the random and half-shifted gate pairing strategies for TGF and TGFQS perform best in many of the tested settings. In the additional finite-shot experiments on Fermi-Hubbard and transverse-field Ising model Hamiltonians, the best gate pairing strategies retain their advantage across the tested shot counts in shallow circuits. These improvements come at the cost of increased circuit evaluations per gate update, highlighting a trade-off between the power of local optimization and measurement overhead.