Abstract
We proposed a new geometric quantum computation (GQC) scheme, called Floquet GQC (FGQC), where error-resilient geometric gates based on periodically driven two-level systems can be constructed via a new non-Abelian geometric phase proposed in a recent study [V. Novi\^{c}enko \textit{et al}, Phys. Rev. A 100, 012127 (2019) ]. Based on Rydberg atoms, we gave possible implementations of universal single-qubit gates and a nontrivial two-qubit gate for FGQC. By using numerical simulation, we evaluated the performance of the FGQC Z and X gates in the presence of both decoherence and a certain kind of systematic control error. The gate fidelities of the Z and X gates are $F_{X,\text{gate}}\approx F_{Z,\text{gate}}\approx 0.9992$. The numerical results provide evidence that FGQC gates can achieve fairly high gate fidelities even in the presence of noise and control imperfection. In addition, we found FGQC is robust against global control error, both analytical demonstration and numerical evidence were given. Consequently, this study makes an important step towards robust geometric quantum computation.
Highlights
Quantum computations can solve certain problems much more effectively than classical computations, such as quantum simulations [1,2], prime factoring [3,4,5], searching unsorted data [6], and machine learning [7,8,9]
The numerical results show that, at present, the performance of Floquet GQC (FGQC) based on the Rydberg state is limited by the short coherence time of the latter
At present, the performance of FGQC based on the Rydberg state is limited by the short coherence time of the latter
Summary
Quantum computations can solve certain problems much more effectively than classical computations, such as quantum simulations [1,2], prime factoring [3,4,5], searching unsorted data [6], and machine learning [7,8,9]. We propose a geometric computation scheme, called Floquet GQC (FGQC), where universal error-resistant geometric gates can be constructed via a non-Abelian geometric phase This non-Abelian geometric phase emerges from a periodically driven quantum system and was found in a recent study [83].
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