Quantum annealing and condensed matter physics

TL;DR

The paper addresses how quantum annealing can be leveraged to tackle condensed-matter problems and how condensed-matter theory can inform the design and use of quantum annealing hardware. It provides a structured overview of related models—adiabatic quantum computing, continuous-time quantum walks, and quantum annealing—highlighting the governing Hamiltonians, schedules, and regime distinctions, including adiabatic, quasistatic, and diabatic dynamics. It then details problem-encoding strategies (hardware connectivity, unary vs binary, one-hot and domain-wall encodings) and surveys early quantum-annealing applications in quantum simulation and ground-state sampling within condensed-matter contexts, reporting on current capabilities and near-term potential. The outlook identifies key theoretical and practical gaps, such as understanding non-equilibrium diabatic dynamics and interference effects, and emphasizes ongoing collaboration between condensed-matter physicists and quantum-annealing researchers to realize meaningful scientific and computational advances.

Abstract

Quantum annealing leverages the properties of interacting quantum spin systems to solve computational problems, typically optimisation problems. Current hardware now has capabilities that can be used to solve condensed matter physics problems, too. In this topical review, we provide an overview of quantum annealing aimed at condensed matter physicists, to show the mutual benefits of working together to understand and improve how quantum annealers work, and to use them to advance condensed matter physics.

Figures (2)

• Figure 1: Illustration of changes in the average sign of spin values versus temperature and transverse field for 3x3 square spin glasses. This plot represents the places where spins change sign in all possible combinations of ferromagnetic and anti-ferromagnetic edges on this lattices. In some cases, spins react the same way to temperature and transverse field (blue), while in others (green and red) they illustrate complex behaviour. These categories can further be determined based on behaviour at low temperature and transverse field, as explained in chancellor2016DWaveKZ. Figure adapted from figure 5 of chancellor2016DWaveKZ, which also uses this system to analyse frozen-in fluctuations on a superconducting flux-qubit quantum annealer operating in the quasistatic regime.
• Figure 2: Illustration of the "shamrock" Hamiltonian used by Andriyash2017QMC to show an exponential separation between quantum Monte Carlo and physical, incoherent annealing. Black edges are ferromagnetic couplings of unit strength, while red are anti-ferromagnetic and of slightly weaker strength. The arrows show the configuration of the spins in one ground state. Ellipses (...) indicate there are many more "leaves".