# Finding spin-glass ground states using quantum walks

## TL;DR

This paper explores the use of continuous-time quantum walks to find spin glass ground states, revealing practical parameter settings and potential for real-world quantum optimization applications.

## Contribution

It demonstrates that quantum walks can effectively find spin glass ground states without precise parameter tuning, unlike in search problems.

## Key findings

- Quantum walks outperform classical methods in finding spin glass ground states.
- Parameter tuning is less critical for spin glass problems compared to search problems.
- Quantum walks achieve better than square-root scaling in this context.

## Abstract

Quantum computation using continuous-time evolution under a natural hardware Hamiltonian is a promising near- and mid-term direction toward powerful quantum computing hardware. We investigate the performance of continuous-time quantum walks as a tool for finding spin glass ground states, a problem that serves as a useful model for realistic optimization problems. By performing detailed numerics, we uncover significant ways in which solving spin glass problems differs from applying quantum walks to the search problem. Importantly, unlike for the search problem, parameters such as the hopping rate of the quantum walk do not need to be set precisely for the spin glass ground state problem. Heuristic values of the hopping rate determined from the energy scales in the problem Hamiltonian are sufficient for obtaining a better than square-root scaling. This makes it practical to use quantum walks for solving such problems, and opens the door for a range of applications on suitable quantum hardware.