Boson Sampling for Generalized Bosons

Abstract

We introduce the notion of "generalized bosons" whose exchange statistics resemble those of bosons, but the local bosonic commutator [a, a † ] = 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.

Quantum-inspired permanent identities

“…We use the formalism of linear optics with noninteracting bosons, but our approach can be applied more generally to linear optics with other types of particles. For instance, we expect our proof techniques to lead to determinant identities in the fermionic case [32], immanant identities in the case of partially distinguishable particles [33,34], and additional permanent identities in the case of generalized bosons [35]. Moreover, graphical languages are currently being developed for linear optical quantum computations [36,37], which could lead to graphical proofs of remarkable identities in combination with our approach.…”

Quantum-inspired permanent identities

“…We use the formalism of linear optics with noninteracting bosons, but our approach can be applied more generally to linear optics with other types of particles. For instance, we expect our proof techniques to lead to determinant identities in the fermionic case [31], immanant identities in the case of partially distinguishable particles [32,33], and additional permanent identities in the case of generalized bosons [34]. Moreover, graphical languages are currently being developed for linear optical quantum computations [35,36], which could lead to graphical proofs of remarkable identities in combination with our approach.…”