Non-adiabatic geometric quantum computation (NGQC) provides a promising way for implementing robust quantum gate operation. However, NGQC has no obvious advantage over the dynamical scheme in dealing with control errors. Here, we show a new geometric scheme, called Floquet geometric quantum computation (FGQC), in which error-resistant geometric gates based on periodically driven two-level systems can be constructed via a new non-Abelian geometric phase proposed in a recent work [V. Noviĉenko \emph{et al}, Phys. Rev. A 100, 012127 (2019) ]. Based on Rydberg atoms, the experimental feasibility of our proposal is demonstrated through numerical simulation using the recent experimental parameters. In addition, the numerical simulation of our geometric gates in the presence of global control error shows that the FGQC gates are more robust over NGQC and dynamical gate (DG). We further analytically prove the superiority of FGQC in terms of robustness against global control error. Consequently, our work makes an important step towards robust geometric quantum computation.
Non-adiabatic geometric quantum computation (NGQC) provides a promising way for implementing robust quantum gate operation. However, NGQC has no obvious advantage over the dynamical scheme in dealing with control errors. Here, we show a new geometric scheme, called Floquet geometric quantum computation (FGQC), in which error-resistant geometric gates based on periodically driven two-level systems can be constructed via a new non-Abelian geometric phase proposed in a recent work [V. Noviĉenko \emph{et al}, Phys. Rev. A 100, 012127 (2019) ]. Based on Rydberg atoms, the experimental feasibility of our proposal is demonstrated through numerical simulation using the recent experimental parameters. In addition, the numerical simulation of our geometric gates in the presence of global control error shows that the FGQC gates are more robust over NGQC and dynamical gate (DG). We further analytically prove the superiority of FGQC in terms of robustness against global control error. Consequently, our work makes an important step towards robust geometric quantum computation.
We propose a 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 non-Abelian geometric phase proposed in a recent study [V. Novi\ifmmode \check{c}\else \v{c}\fi{}enko and G. Juzeli\ifmmode \bar{u}\else \={u}\fi{}nas, Phys. Rev. A 100, 012127 (2019)]. Based on Rydberg atoms, we give possible implementations of universal FGQC single-qubit gates and a nontrivial FGQC two-qubit gate. By using numerical simulation, we evaluate the performance of the FGQC Z and X gates in the presence of both decoherence and a certain kind of systematic control error. For the currently available coherence time of the Rydberg state, ${T}_{2}\ensuremath{\approx}32\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{s}$, the numerical results show that the X and Z gate fidelities are about 0.900 and 0.899, respectively. In addition, we find that FGQC is robust against global control error; both analytical demonstration and numerical evidence are given. As the coherence time of various qubits grows, FGQC may provide a promising error-resilient quantum computation scheme in the future.
Non-adiabatic geometric quantum computation (NGQC) and non-adiabatic 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 of why non-adiabatic geometric gates are sensitive to the control errors, and further, we propose a new class of geometric property condition (GPC)-based non-adiabatic geometric gates, in which the global control condition can guarantee both high speed and robustness of geometric gate. To illustrate the working mechanism of GPC-based geometric gates, we give two simple examples of GPC-NGQC and GPC-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 comparing with the previous NGQC, NHQC and standard dynamical schemes. GPC-based 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.
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.
Quantum gates constructed by geometric phase are naturally robust to control errors due to the global nature of the geometric evolution path. Therefore, how to cope with the inevitable decoherence errors is worthy of serious attention for geometric quantum computation. Different from conventional nonadiabatic geometric quantum computation (NGQC), which needs the same evolution time for any geometric rotation angle, we have proposed and experimentally demonstrated nonadiabatic noncyclic geometric quantum computation (NNGQC) without the requirement of the cyclic evolution condition, which thus reduces decoherence errors due to shortened evolution time [J. W. Zhang et al., Phys. Rev. Lett. 127, 030502 (2021)]. In addition, the use of decoherence-free subspaces (DFS) is another effective strategy to protect quantum gates from dephasing error and has been studied in nonadiabatic holonomic quantum computation [G. F. Xu et al., Phys. Rev. Lett. 109, 170501 (2012)]. Motivated by previous studies, we propose a one-step scheme to implement single-qubit NNGQC operation in DFS constructed by two Rydberg atoms, and then generalize the scheme to the two-logical-qubit case in one step. The numerical results show that our scheme is robust against decoherence in contrast to the NGQC counterparts. The present scheme combines the features of NNGQC and DFS and can further reduce the impact of decoherence on gate infidelity, which may provide an option for the realization of Rydberg-atom-based quantum computation in the future.
Besides the intrinsic noise resilience property, nonadiabatic geometric phases are of the fast evolution nature, and thus can naturally be used in constructing quantum gates with excellent performance, i.e., the so-called nonadiabatic geometric quantum computation (NGQC). However, previous single-loop NGQC schemes are sensitive to the operational control error, i.e., the X error, due to the limitations of the implementation. Here, we propose a robust scheme for NGQC combining with the dynamical correction technique, which still uses only simplified pulses, and thus being experimental friendly. We numerically show that our scheme can greatly improve the gate robustness in previous protocols, retaining the intrinsic merit of geometric phases. Furthermore, to fight against the dephasing noise, due to the Z error, we can incorporate the decoherence-free subspace encoding strategy. In this way, our scheme can be robust against both types of errors. Finally, we also propose how to implement the scheme with encoding on superconducting quantum circuits with experimentally demonstrated technology. Therefore, due to the intrinsic robustness, our scheme provides a promising alternation for the future scalable fault-tolerant quantum computation.
Nonadiabatic geometric quantum computation (NGQC) has been developed to realize fast and robust geomet-ric gate. However, the conventiona NGQC is that all of the gates are performed with exactly the same amount of time, whether the geometric rotation angle is large or small, due to the limitation of cyclic condition. Here, we propose an unconventional scheme, called nonadiabatic noncyclic geometric quantum computation (NNGQC), that arbitrary single- and two-qubit geometric gate can be constructed via noncyclic non-Abelian geometric phase. Consequently, this scheme makes it possible to accelerate the implemented geometric gates against the effects from the environmental decoherence. Furthermore, this extensible scheme can be applied in various quantum platforms, such as superconducting qubit and Rydberg atoms. Specifically, for single-qubit gate, wemake simulations with practical parameters in neutral atom system to show the robustness of NNGQC and also compare with NGQC using the recent experimental parameters to show that the NNGQC can significantly suppress the decoherence error. In addition, we also demonstrate that nontrivial two-qubit geometric gate can berealized via unconventional Rydberg blockade regime within current experimental technologies. Therefore, our scheme provides a promising way for fast and robust neutral-atom-based quantum computation.