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

%8 5/2/2022 %G eng %U https://arxiv.org/abs/2204.08389 %0 Journal Article %J Physical Review Research %D 2022 %T Efficient Product Formulas for Commutators and Applications to Quantum Simulation %A Yu-An Chen %A Andrew M. Childs %A Mohammad Hafezi %A Zhang Jiang %A Hwanmun Kim %A Yijia Xu %XWe construct product formulas for exponentials of commutators and explore their applications. First, we directly construct a third-order product formula with six exponentials by solving polynomial equations obtained using the operator differential method. We then derive higher-order product formulas recursively from the third-order formula. We improve over previous recursive constructions, reducing the number of gates required to achieve the same accuracy. In addition, we demonstrate that the constituent linear terms in the commutator can be included at no extra cost. As an application, we show how to use the product formulas in a digital protocol for counterdiabatic driving, which increases the fidelity for quantum state preparation. We also discuss applications to quantum simulation of one-dimensional fermion chains with nearest- and next-nearest-neighbor hopping terms, and two-dimensional fractional quantum Hall phases.

%B Physical Review Research %V 4 %8 03/10/2022 %G eng %U https://arxiv.org/abs/2111.12177 %& 013191 %R https://doi.org/10.1103/PhysRevResearch.4.013191