Spin models and boson sampling

TL;DR

This paper establishes a theoretical equivalence between boson sampling and short-time evolution in XY spin models, enabling new quantum simulation approaches and highlighting the complexity of spin dynamics.

Contribution

It introduces an efficient mapping from boson sampling to XY spin models, facilitating quantum simulation and analysis of complex spin dynamics.

Findings

Mapping is efficient when boson bunching probability is low

Errors can be efficiently postselected in the simulation

Highlights complexity of spin model evolution even at short times

Abstract

In this work we proof that boson sampling with $N$ particles in $M$ modes is equivalent to short-time evolution with $N$ excitations in an XY model of $2N$ spins. This mapping is efficient whenever the boson bunching probability is small, and errors can be efficiently postselected. This mapping opens the door to boson sampling with quantum simulators or general purpose quantum computers, and highlights the complexity of time-evolution with critical spin models, even for very short times.