Instance Independence of Single Layer Quantum Approximate Optimization Algorithm on Mixed-Spin Models at Infinite Size

TL;DR

This paper demonstrates that for large mixed-spin models, the performance of depth-1 QAOA is instance-independent and concentrates around its expected value, with explicit formulas provided for expected energy and higher moments.

Contribution

It proves the instance independence and concentration of depth-1 QAOA performance on mixed-spin models at infinite size, with explicit performance formulas.

Findings

QAOA performance is independent of specific instances at infinite size.

Expected performance of QAOA concentrates around its mean.

Explicit formulas for expected energy and higher moments are derived.

Abstract

This paper studies the application of the Quantum Approximate Optimization Algorithm (QAOA) to spin-glass models with random multi-body couplings in the limit of a large number of spins. We show that for such mixed-spin models the performance of depth $1$ QAOA is independent of the specific instance in the limit of infinite sized systems and we give an explicit formula for the expected performance. We also give explicit expressions for the higher moments of the expected energy, thereby proving that the expected performance of QAOA concentrates.