%0 Journal Article %D 2023 %T Clifford operations and homological codes for rotors and oscillators %A Yijia Xu %A Yixu Wang %A Victor V. Albert %X

We develop quantum information processing primitives for the planar rotor, the state space of a particle on a circle. By interpreting rotor wavefunctions as periodically identified wavefunctions of a harmonic oscillator, we determine the group of bosonic Gaussian operations inherited by the rotor. This n-rotor Clifford group, U(1)n(n+1)/2⋊GLn(Z), is represented by continuous U(1) gates generated by polynomials quadratic in angular momenta, as well as discrete GLn(Z) momentum sign-flip and sum gates. We classify homological rotor error-correcting codes [arXiv:2303.13723] and various rotor states based on equivalence under Clifford operations.
Reversing direction, we map homological rotor codes and rotor Clifford operations back into oscillators by interpreting occupation-number states as rotor states of non-negative angular momentum. This yields new multimode homological bosonic codes protecting against dephasing and changes in occupation number, along with their corresponding encoding and decoding circuits. In particular, we show how to non-destructively measure the oscillator phase using conditional occupation-number addition and post selection. We also outline several rotor and oscillator varieties of the GKP-stabilizer codes [arXiv:1903.12615].

%8 11/13/2023 %G eng %U https://arxiv.org/abs/2311.07679 %0 Journal Article %D 2022 %T Boson Sampling for Generalized Bosons %A En-Jui Kuo %A Yijia Xu %A Dominik Hangleiter %A Andrey Grankin %A Mohammad Hafezi %X

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 %X

We 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