Boson Sampling for Generalized Bosons

TL;DR

This paper introduces generalized bosons with exchange statistics similar to bosons but with modified local commutators, extending boson sampling to these particles and discussing potential implementations.

Contribution

It defines generalized bosons, analyzes their sampling complexity, and proposes experimental implementations in circuit-QED and ion-trap systems.

Findings

Output probabilities are given by permanents, maintaining sampling hardness.

Generalized bosons include boson pairs and spins.

Sampling complexity results extend to these particles.

Abstract

We introduce the notion of "generalized bosons" whose exchange statistics resemble those of bosons, but the local bosonic commutator $[a_i,a_i^\dagger]=1$ is replaced by an arbitrary single-mode operator that is diagonal in the generalized Fock basis. Examples of generalized bosons include boson pairs and spins. We consider the analogue of the boson sampling task for these particles and observe that its output probabilities are still given by permanents, so that the results regarding hardness of sampling directly carry over. Finally, we propose implementations of generalized boson sampling in circuit-QED and ion-trap platforms.