Abstract
Geometric phase gates are promising tools toward robust quantum computing owing to their robustness against certain control errors and decoherence. Here, we propose a multiqubit architecture with a nonadiabatic geometric phase gate scheme that is feasible in widely used superconducting qubit designs such as transmon and fluxonium. Through segmented microwave drive on multiple qubits coupled off-resonantly to a common resonator, the geometric phase gate is obtained from the qubit-state-dependent displacement of the resonator without fine-tuning the qubit frequencies. Fidelity above 99.99% is achieved in simulation under the available experimental parameters. Our scheme uses all-microwave control and only exploits the lowest qubit levels with long coherence time; thus it is desirable for experiments. Together with the single-qubit holonomic gates demonstrated in earlier experiments, our scheme can realize universal all-geometric quantum computing, and it also finds applications in quantum simulation with many-body interactions.
Highlights
When a quantum system undergoes a cyclic evolution, it acquires a geometric phase, or more generally is subjected to a unitary operator known as a holonomy, which solely depends on the path geometry but not on how fast it is traversed [1,2,3,4]
Owing to the intrinsic robustness against certain types of control errors [8,9,10,11] and decoherence [10,12,13], geometric gates make a preferable approach toward fault-tolerant quantum computing, namely, the idea of geometric or holonomic quantum computing [14,15,16,17]
Geometric single-qubit and two-qubit gates have been demonstrated in experiments in various systems such as nuclear magnetic resonance (NMR) [18,19,20], nitrogen vacancy (NV) centers [21,22,23,24,25], trapped ions [26,27], and superconducting circuits [28,29,30,31,32,33,34]
Summary
When a quantum system undergoes a cyclic evolution, it acquires a geometric phase, or more generally is subjected to a unitary operator known as a holonomy, which solely depends on the path geometry but not on how fast it is traversed [1,2,3,4]. Proposals using only the low qubit levels exist based on the unconventional geometric phase through the coupling to a resonator [46,47]; they require specially designed superconducting qubits as well as time-dependent flux control for the gate operation and have not been realized yet. Compared with earlier schemes of geometric gates for superconducting qubits [29,32,33,34,51,54,55], our scheme uses only the lowest qubit levels and the cavity mode without touching higher-energy states, and provides relatively long coherence time; the single-tone microwave strategy on fixed-frequency qubits further reduces the circuit complexity to prevent extra decoherence.
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