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.
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.
Geometrical phases acquired in cyclic quantum evolutions can be utilized as
natural resources for constructing robust logic gates for quantum information
processing, which was originally proposed through adiabatic changes of the
driving Hamiltonian. Practically, much efforts have been made to shorten the
construction times of geometrical gates, known as non-adiabatic holonomic
quantum computation (NHQC). However, previous NHQC gates require the driving
Hamiltonian to satisfy a set of rather restrictive conditions, reducing the
robustness of the resulting geometric gates against control errors. Here we
show that non-adiabatic geometric gates can be constructed in an alternative
way where the driving Hamiltonian can exhibit a high degree of flexibility for
retaining the robustness of the geometric phases. Consequently, this approach
makes it possible to incorporate most of the existing optimal control methods,
such as dynamical decoupling, composite pulses, and shortcut to adiabaticity,
into the construction of geometrical gates, to further address different types
of errors. Furthermore, this extensible approach of geometric quantum
computation can be applied to various physical platform such as superconducting
qubits and nitrogen-vacancy (NV) centers. Specifically, we performed numerical
simulation to show how the noise robustness in the recent experimental
implementations [Phys. Rev. Lett. 119, 140503 (2017)] and [Nat. Photonics 11,
309 (2017)] of NHQC with NV centers can be significantly improved by our
optimized NHQC approach. These results cover a large class of new techniques
combing the noise robustness of both geometric phase and optimal control
theory.
Nonadiabatic holonomic quantum computation (NHQC) has been developed to shorten the construction times of geometric quantum gates. However, previous NHQC gates require the driving Hamiltonian to satisfy a set of rather restrictive conditions, reducing the robustness of the resulting geometric gates against control errors. Here we show that nonadiabatic geometric gates can be constructed in an extensible way, called NHQC+, for maintaining both flexibility and robustness against certain types of noises. Consequently, this approach makes it possible to incorporate most of the existing optimal control methods, such as dynamical decoupling, composite pulses, and a shortcut to adiabaticity, into the construction of single-looped geometric gates. Furthermore, this extensible approach of geometric quantum computation can be applied to various physical platforms such as superconducting qubits and nitrogen-vacancy centers. Specifically, we performed numerical simulation to show how the noise robustness in recent experimental implementations [Phys. Rev. Lett. 119, 140503 (2017)PRLTAO0031-900710.1103/PhysRevLett.119.140503; Nat. Photonics 11, 309 (2017)NPAHBY1749-488510.1038/nphoton.2017.40] can be significantly improved by our NHQC+.approach. These results cover a large class of new techniques combing the noise robustness of both geometric phase and optimal control theory.
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.
In quantum control, geometrical operations could provide an extra layer of robustness against control errors. However, the conventional non-adiabatic holonomic quantum computation (NHQC) is limited by the fact that all of the operations require exactly the same amount of evolution time, even for a small-angle rotation. Furthermore, NHQC confines the driving part of the Hamiltonian to strictly cover a fixed pulse area, making it sensitive to control errors. Here we present an unconventional approach of NHQC, termed brachistochronic NHQC, for bypassing these limitations. Specifically, with B-NHQC, non-Abelian geometric gates can be time-optimized by following the brachistochrone curve, minimizing the impact from the environmental decoherence. Additionally, we demonstrate that B-NHQC is compatible with composed pulses, which can further enhance the robustness against pulse errors. For benchmarking, we provide a thorough analysis on the performance of B-NHQC under experimental conditions; we found that the gate error can be reduced by as much as 64% compared with NHQC.
Geometric phases accompanying adiabatic quantum evolutions can be used to construct robust quantum control for quantum information processing due to their noise-resilient feature. A significant development along this line is to construct geometric gates using nonadiabatic quantum evolutions to reduce errors due to decoherence. However, it has been shown that nonadiabatic geometric gates are not necessarily more robust than dynamical ones, in contrast to an intuitive expectation. Here we experimentally investigate this issue for the case of nonadiabatic holonomic quantum computation~(NHQC) and show that conventional NHQC schemes cannot guarantee the expected robustness due to a cross coupling to the states outside the computational space. We implement a new set of constraints for gate construction in order to suppress such cross coupling to achieve an enhanced robustness. Using a superconducting quantum circuit, we demonstrate high-fidelity holonomic gates whose infidelity against quasi-static transverse errors can be suppressed up to the fourth order, instead of the second order in conventional NHQC and dynamical gates. In addition, we explicitly measure the accumulated dynamical phase due to the above mentioned cross coupling and verify that it is indeed much reduced in our NHQC scheme. We further demonstrate a protocol for constructing two-qubit NHQC gates also with an enhanced robustness.