Universal Resources for QAOA and Quantum Annealing

TL;DR

This paper establishes a formal and empirical connection between QAOA and Quantum Annealing, showing they follow universal trajectories and act as cooling protocols with scalable properties related to resource investment.

Contribution

It formalizes the link between QAOA and QA, demonstrating universal trajectories and their interpretation as cooling processes with tunable target temperatures.

Findings

QAOA angles converge to QA trajectories

Both methods act as cooling protocols with scalable temperature reduction

Errors behave as thermal excitations in pseudo-Boltzmann distributions

Abstract

The Quantum Approximate Optimization Algorithm (QAOA) is a variational ansatz that resembles the Trotterized dynamics of a Quantum Annealing (QA) protocol. This work formalizes this connection formally and empirically, showing the angles of a multilayer QAOA circuit converge to universal QA trajectories. Furthermore, the errors in both QAOA circuits and QA paths act as thermal excitations in pseudo-Boltzmann probability distributions whose temperature decreases with the invested resource -- i.e. integrated angles or total time -- and which in QAOA also contain a higher temperature arising from the Trotterization. This also means QAOA and QA are cooling protocols and simulators of partition functions whose target temperature can be tuned by rescaling the universal trajectory. The average cooling power of both methods exhibits favorable algebraic scalings with respect to the target temperature and problem size, whereby in QAOA the coldest temperature is inversely proportional to the number of layers, $T\sim 1/p$, and to the integrated angles -- or integrated interactions in QA.