Quantum Spin Glasses on the GPU

We propose to investigate, with unprecedented accuracy and abundant statistics, the critical phase of the quantum spin glass in two dimensions.

Quantum spin glasses are the prototype of disordered systems whose dynamics is affected strongly by quantum effects.

The dynamics of quantum circuits in quantum annealers (i.e. devices implementing the Quantum Annealing algorithm), for example, falls in the realm of quantum spin glasses.The proposed activity will have important implications for two different but intertwined reasons:

1. The first is the discrimination between two theories of the quantum spin glass transition which have been proposed in the past (one based on a strong disorder renormalization group and the second on a more traditional field theory approach of replicated fields).
2. The second, which has immediate technological implications in the exploding field of quantum computing, is the assessment of the theoretical bound to the performance of Quantum Annealers solving instances of hard optimisation problems (specifically spin glasses).

Indeed, finding the ground state of a spin glass is a prototypical NP-complete problem. Commercial prototypes of Quantum Annealers already exist with a new generation of hardware under development.