Abstract
Nonadiabatic geometric quantum computation (NGQC) and nonadiabatic holonomic quantum computation (NHQC) have been proposed to reduce the run time of geometric quantum gates. However, in terms of robustness against experimental control errors, the existing NGQC and NHQC scenarios have no advantage over standard dynamical gates in most cases. Here, we give the reasons why nonadiabatic geometric gates are sensitive to the control errors and, further, we propose a scheme of super-robust nonadiabatic geometric quantum control, in which the super-robust condition can guarantee both high speed and robustness of the geometric gate. To illustrate the working mechanism of super-robust geometric quantum gates, we give two simple examples of SR-NGQC and SR-NHQC for two- and three-level quantum systems, respectively. Theoretical and numerical results with the experimental parameters indicate that our scheme can significantly improve the gate performance compared to the previous NGQC, NHQC, and standard dynamical schemes. Super-robust geometric quantum computation can be applied to various physical platforms such as superconducting qubits, quantum dots, and trapped ions. All of these sufficiently show that our scheme provides a promising way towards robust geometric quantum computation.
Highlights
Realizing high-fidelity and fault-tolerant quantum gates is very essential for quantum information processing since control errors and environment-induced noises are ubiquitous in operating real quantum devices
We demonstrate a class of super-robust nonadiabatic geometric gates in which robustness against the control errors is ensured by a super-robust control condition
We have explained why the existing nonadiabatic geometric gates are so sensitive to the control errors, and proposed the scheme of super-robust nonadiabatic geometric gates
Summary
Realizing high-fidelity and fault-tolerant quantum gates is very essential for quantum information processing since control errors and environment-induced noises are ubiquitous in operating real quantum devices. Adiabatic quantum dynamics implies lengthy gate time and long exposure time to the environment-induced decoherence To overcome such a problem, nonadiabatic geometric quantum computation (NGQC) [17,18,19,20,21,22,23] and nonadiabatic holonomic quantum computation (NHQC) [24,25,26,27,28,29,30,31,32,33,34,35,36] based on a nonadiabatic Abelian and non-Abelian geometric phase [2,4], respectively, have been proposed to reduce the run times of geometric quantum gates. We implement our schemes in two- and three-level systems, respectively, to realize super-robust Abelian (non-Abelian) nonadiabatic geometric (holonomic) quantum gates, called
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