Noncyclic Geometric Quantum Gates with Smooth Paths via Invariant-based Shortcuts

Nonadiabatic geometric quantum computation is dedicated to the realization of high-fidelity and robust quantum gates, which are necessary for fault-tolerant quantum computation. However, it is limited by cyclic and mutative evolution path, which usually requires longer gate-time and abrupt pulse control, weakening the gate performance. Here, we propose a scheme to realize geometric quantum gates with noncyclic and nonadiabatic evolution via invariant-based shortcuts, where universal quantum gates can be induced in one step without path mutation and the gate time is also effectively shortened. Our numerical simulations show that, comparing with the conventional dynamical gates, the constructed geometric gates have stronger resistance not only to systematic errors, induced by both qubit-frequency drift and the deviation of the amplitude of the driving fields, but also to environment-induced decoherence effect. In addition, our scheme can also be implemented on a superconducting circuit platform, with the fidelities of single-qubit and two-qubit gates are higher than 99.97$\%$ and 99.84$\%$, respectively. Therefore, our scheme provides a promising way to realize high-fidelity fault-tolerant quantum gates for scalable quantum computation.

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