In this paper, we propose a protocol to realize non-adiabatic holonomic quantum computation (NHQC) of cavity modes via invariant-based reverse engineering. Coupling cavity modes with an auxiliary atom trapped in a cavity, we derive effective Hamiltonians with the help of laser pulses. Based on the derived Hamiltonians, invariant-based reverse engineering is used to find proper evolution paths for NHQC. Moreover, the systematic-error-sensitivity nullified optimal control method is considered in the parameter selections, making the protocol insensitive to the influence of systematic errors of pulses. We also estimate the imperfections induced by random noise and decoherence. Numerical results show that the protocol holds robustness against these imperfections. Therefore, the protocol may provide useful perspectives to quantum computation with optical qubits in cavity quantum electrodynamics systems. This article is part of the theme issue 'Shortcuts to adiabaticity: theoretical, experimental and interdisciplinary perspectives'.
In this paper, we propose a protocol to realize non-adiabatic holonomic quantum computation (NHQC) of cavity modes via invariant-based reverse engineering. Coupling cavity modes with an auxiliary atom trapped in a cavity, we derive effective Hamiltonians with the help of laser pulses. Based on the derived Hamiltonians, invariant-based reverse engineering is used to find proper evolution paths for NHQC. Moreover, the systematic-error-sensitivity nullified optimal control method is considered in the parameter selections, making the protocol insensitive to the influence of systematic errors of pulses. We also estimate the imperfections induced by random noise and decoherence. Numerical results show that the protocol holds robustness against these imperfections. Therefore, the protocol may provide useful perspectives to quantum computation with optical qubits in cavity quantum electrodynamics systems. This article is part of the theme issue 'Shortcuts to adiabaticity: theoretical, experimental and interdisciplinary perspectives'.
In this paper, we propose a one-step scheme for implementing the nonadiabatic holonomic swap gate with Rydberg atoms. By applying invariant-based reverse engineering to design the effective Hamiltonian of the system, a suitable evolution path for implementing nonadiabatic holonomic quantum computation is found. In addition, the systematic-error-sensitivity nullified optimal control method is considered in the parameter selections, so that the scheme is insensitive to the systematic error of pulses. We also estimate the effects of random noise, the random initial phase of the pulses, the Doppler shift, and decoherence on the scheme. The numerical results show that the scheme exhibits fairly good performance against these negative factors. Finally, we generalize the scheme to realize the non-Clifford swap gates. Therefore, this scheme can provide a feasible framework for implementing high-fidelity and robust swap gates and non-Clifford swap gates with Rydberg atoms.
In this paper, we propose a scheme for implementing the nonadiabatic holonomic quantum computation (NHQC+) of two Rydberg atoms by using invariant-based reverse engineering (IBRE). The scheme is based on Förster resonance induced by strong dipole-dipole interaction between two Rydberg atoms, which provides a selective coupling mechanism to simply the dynamics of system. Moreover, for improving the fidelity of the scheme, the optimal control method is introduced to enhance the gate robustness against systematic errors. Numerical simulations show the scheme is robust against the random noise in control fields, the deviation of dipole-dipole interaction, the Förster defect, and the spontaneous emission of atoms. Therefore, the scheme may provide some useful perspectives for the realization of quantum computation with Rydberg atoms.
In this paper, we propose a scheme for implementing the nonadiabatic holonomic quantum computation (NHQC+) of two Rydberg atoms by using invariant-based reverse engineering (IBRE). The scheme is based on Förster resonance induced by strong dipole-dipole interaction between two Rydberg atoms, which provides a selective coupling mechanism to simply the dynamics of system. Moreover, for improving the fidelity of the scheme, the optimal control method is introduced to enhance the gate robustness against systematic errors. Numerical simulations show the scheme is robust against the random noise in control fields, the deviation of dipole-dipole interaction, the Förster defect, and the spontaneous emission of atoms. Therefore, the scheme may provide some useful perspectives for the realization of quantum computation with Rydberg atoms.
We propose a protocol to realize atomic nonadiabatic holonomic quantum computation (NHQC) with two computational atoms and an auxiliary atom. Dynamics of the system is analyzed in the regime of Rydberg blockade, and robust laser pulses are designed via reverse engineering, so that quantum gates can be easily realized with hig h fidelities. In addition, we also study the evolution suffering from dissipation with a master equation. The result indicates that decays of atoms can be heralded by measuring the state of the auxiliary atom, and nearly perfect unitary evolution can be obtained if the auxiliary atom remains in its Rydberg state. Therefore, the protocol may be helpful to realize NHQC in a dissipative environment.
Nonadiabatic holonomic quantum computation (NHQC) provides an essential way to construct robust and high-fidelity quantum gates due to its geometric features. However, NHQC is more sensitive to decay and dephasing errors than a conventional dynamical gate since it requires an ancillary intermediate state. Here, we utilize the Hamiltonian reverse engineering technique to study the influence of intermediate-state decoherence on NHQC gate fidelity, and propose schemes to construct an arbitrary single-qubit holonomic gate and nontrivial two-qubit holonomic gate with high fidelity and robustness to the decoherence. Although the proposed method is generic and can be applied to many experimental platforms, such as superconducting qubits, trapped ions, and quantum dots, here we take a nitrogen-vacancy center as an example to show that the gate fidelity can be significantly enhanced from 89% to 99.6% in contrast to recent experimental NHQC schemes [Phys. Rev. Lett. 119, 140503 (2017); Nat. Photonics 11, 309 (2017); Opt. Lett. 43, 2380 (2018)], and the robustness against decoherence can also be significantly improved. All in all, our scheme provides a promising way for fault-tolerant 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.