01707nas a2200133 4500008004100000245007300041210006900114260001500183520128600198100001401484700001501498700002301513856003701536 2023 eng d00aClifford operations and homological codes for rotors and oscillators0 aClifford operations and homological codes for rotors and oscilla c11/13/20233 a

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].

1 aXu, Yijia1 aWang, Yixu1 aAlbert, Victor, V. uhttps://arxiv.org/abs/2311.0767901081nas a2200157 4500008004100000245004200041210004200083260001300125520065300138100001600791700001400807700002400821700002000845700002100865856003700886 2022 eng d00aBoson Sampling for Generalized Bosons0 aBoson Sampling for Generalized Bosons c5/2/20223 a

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.

1 aKuo, En-Jui1 aXu, Yijia1 aHangleiter, Dominik1 aGrankin, Andrey1 aHafezi, Mohammad uhttps://arxiv.org/abs/2204.0838901492nas a2200181 4500008004100000245008600041210006900127260001500196490000600211520094800217100001601165700002301181700002101204700001701225700001701242700001401259856003701273 2022 eng d00aEfficient Product Formulas for Commutators and Applications to Quantum Simulation0 aEfficient Product Formulas for Commutators and Applications to Q c03/10/20220 v43 a

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.

1 aChen, Yu-An1 aChilds, Andrew, M.1 aHafezi, Mohammad1 aJiang, Zhang1 aKim, Hwanmun1 aXu, Yijia uhttps://arxiv.org/abs/2111.12177