Quantum combinatorial optimization beyond the variational paradigm: simple schedules for hard problems

TL;DR

This paper introduces a novel quantum annealing protocol using spin coherent-state path integrals that significantly improves the probability of finding optimal solutions in hard combinatorial problems, surpassing traditional linear schedules.

Contribution

The authors develop a new method to shape quantum adiabatic evolution geometry, enabling polynomial overhead annealing protocols that outperform linear schedules on complex problem instances.

Findings

Order-of-magnitude improvement in solution success probability.

Effective on large, randomly generated hard instances.

Robust and applicable to real quantum devices.

Abstract

Advances in quantum algorithms suggest a tentative scaling advantage on certain combinatorial optimization problems. Recent work, however, has also reinforced the idea that barren plateaus render variational algorithms ineffective on large Hilbert spaces. Hence, finding annealing protocols by variation ultimately appears to be difficult. Similarly, the adiabatic theorem fails on hard problem instances with first-order quantum phase transitions. Here, we show how to use the spin coherent-state path integral to shape the geometry of quantum adiabatic evolution, leading to annealing protocols at polynomial overhead that provide orders-of-magnitude improvements in the probability to measure optimal solutions, relative to linear protocols. These improvements are not obtained on a controllable toy problem but on randomly generated hard instances (Sherrington-Kirkpatrick and Maximum 2-Satisfiability), making them generic and robust. Our method works for large systems and may thus be used to improve the performance of state-of-the-art quantum devices.