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Laser Physics Letters

Nonadiabatic geometric quantum computation of W-state codes using invariant-based reverse engineering

Sheng Wang, Wen-Shu Ni, Zewen Chen, Bao Feng, Yu Ning, Yi‐Hao Kang, Yan Xia

Published Dec 8, 2022• 1 citation
Publisher

Abstract

Abstract In this paper, we propose a protocol to realize nonadiabatic geometric quantum computation (NGQC)of W-state codes in a spin system using invariant-based reverse engineering. The Heisenberg XY interaction of spin qubits provides a two-dimensional computational subspace spanned by a pair of W states. By applying a time-dependent magnetic on the spin qubits, we realize the effective Pauli operations for the computational subspace. Assisted by the invariant-based reverse engineering, the waveform of the control field is designed and the evolution paths for the NGQC is found. The performance of the protocol under the influence of experimental imperfections is estimated by the numerical simulations with available parameters. The results demonstrate that the protocol is robust against systematic error, random noise and decoherence. Therefore, the protocol may be promising to implement fast and robust manipulation of W states in spin systems.

DOI
10.1088/1612-202x/aca759

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Abstract In this paper, we propose a protocol to realize nonadiabatic geometric quantum computation (NGQC)of W-state codes in a spin system using invariant-based reverse engineering. The Heisenberg XY interaction of spin qubits provides a two-dimensional computational subspace spanned by a pair of W states. By applying a time-dependent magnetic on the spin qubits, we realize the effective Pauli operations for the computational subspace. Assisted by the invariant-based reverse engineering, the waveform of the control field is designed and the evolution paths for the NGQC is found. The performance of the protocol under the influence of experimental imperfections is estimated by the numerical simulations with available parameters. The results demonstrate that the protocol is robust against systematic error, random noise and decoherence. Therefore, the protocol may be promising to implement fast and robust manipulation of W states in spin systems.
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We propose a scheme to realize error-resistant nonadiabatic binomial-code geometric quantum computation using reverse engineering. A strong Kerr nonlinearity restricts the evolution in a computational subspace of the binomial code and a two-photon squeezing drive provides the connections between the logical states. The effective Hamiltonian possesses SU(2) dynamic structure and is analyzed through reverse engineering based on a dynamic invariant. By combining reverse engineering with the optimal control method, we find the evolution paths for nonadiabatic geometric quantum computation and derive the control field robust against the systematic error. Numerical simulations show that the scheme holds excellent resistance to the systematic error and is still well implemented in the presence of resonator leakage with the current superconducting nonlinear resonator technology. Therefore, the scheme may provide a promising approach for accurate nonadiabatic binomial-code geometric quantum computation.
Abstract In this paper, based on first given Lewis–Riesenfeld invariant depicted by a unit vector in parameter space, we inverse engineering the time-dependent Hamiltonian of a system with su(2) Lie algebraic structure. The introduced method is then applied to investigate nonadiabatic Abelian geometric quantum computation. We demonstrate that, by employing the nonadiabatic Berry phase generated through nonadiabatic periodic evolution, a driven two-level system which undergoes a single cyclic evolution along a loop path in Bloch space can realize a universal set of one-qubit gates. Subsequently, under consideration of the influence of the systematic error and dissipation on nonadiabatic process, the result reveals arbitrary one-qubit gate can be implemented with a high fidelity. Moreover, to complete the universal set, arbitrary controlled-U gate is designed by utilizing a driven system consisted of a pair of coupled spin subsystems.
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 XXX 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 ZZZ 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.
The binomial code is renowned for its parity-mediated loss immunity and loss-error recoverability, while geometric phases are widely recognized for their intrinsic resilience against noise. Capitalizing on their complementary merits, we propose a noise-resilient protocol to realize Nonadiabatic geometric quantum computation with binomial codes in a superconducting system composed of a microwave cavity %off-resonantly dispersively coupled to a %three-level qutrit. The control field %geometric quantum computation is designed by %combining geometric phases, integrating reverse engineering and optimal control. This design provides a customized control protocol featuring strong error-tolerance and inherent noise-resilience. Using experimentally accessible parameters in superconducting systems, numerical simulations show that the protocol yields relatively high average fidelity for geometric quantum gates based on binomial code, even in the presence of parameter fluctuations and decoherence. Thus, this protocol may provide a practical approach for realizing reliable Nonadiabatic geometric quantum computation with binomial codes in current technology.
In this paper, a flexible and effective scheme is proposed to realize nonadiabatic geometric quantum gates with the invariant based reverse engineering and the nonadiabatic holonomic quantum computation (NHQC+\mathrm{NHQC}+NHQC+) presented in recent work [B.-J. Liu et al., Phys. Rev. Lett. 123, 100501 (2019)] for extensible geometric quantum computation. The scheme provides variabilities for most of control parameters, and can build up multiple evolution paths with different geometric phases acquired in a cycling evolution. As the computational basis can be covered by the evolution paths, the realization of the nonadiabatic geometric quantum computation is possible without auxiliary levels. Moreover, multiple types of nonadiabatic geometric quantum gates can also be easily constructed by only adjusting boundary conditions of control parameters with the method. To show the applications of the scheme, we discuss the implementations of nonadiabatic geometric quantum gates of spin qubits in a double-quantum-dot system with numerical simulations. The results indicate that the scheme possesses robustness against the errors and noise. Therefore, the scheme may offer some interesting perspectives for the realization of the nonadiabatic geometric quantum computation.