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New Journal of Physics

Effective implementation of nonadiabatic geometric quantum gates of cat-state qubits using an auxiliary qutrit

Yi‐Hao Kang, Yang Xiao, Zhi‐Cheng Shi, Yu Wang, Jianqun Yang, Jie Song, Yan Xia

Published Mar 1, 2023• 22 citations
Publisher

Abstract

Abstract We propose an effective protocol for the implementation of nonadiabatic geometric quantum gates of cat-state qubits in Kerr-nonlinear resonators driven by two-photon squeezing drives. Coupling the Kerr-nonlinear resonators with an auxiliary qutrit with proper coupling strengths, the selective transition of the auxiliary qutrit is realized. The selective transition can be exploited in the implementation of a set of useful quantum gates, including the phase gates, the NOT gates, the controlled-phase gates, the controlled NOT gates, and the Toffoli gates. Numerical simulations show the implementations of different types of gates are robust against systematic errors, random noise, and decoherence. Therefore, the protocol may be helpful for robust and scalable quantum computation based on cat-state qubits.

DOI
10.1088/1367-2630/acc2de

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Abstract We propose an effective protocol for the implementation of nonadiabatic geometric quantum gates of cat-state qubits in Kerr-nonlinear resonators driven by two-photon squeezing drives. Coupling the Kerr-nonlinear resonators with an auxiliary qutrit with proper coupling strengths, the selective transition of the auxiliary qutrit is realized. The selective transition can be exploited in the implementation of a set of useful quantum gates, including the phase gates, the NOT gates, the controlled-phase gates, the controlled NOT gates, and the Toffoli gates. Numerical simulations show the implementations of different types of gates are robust against systematic errors, random noise, and decoherence. Therefore, the protocol may be helpful for robust and scalable quantum computation based on cat-state qubits.
ABSTRACT We propose a feasible approach to implement nonadiabatic geometric SWAP and Fredkin gates for cat‐state qubits using Kerr‐nonlinear resonators driven by two‐photon squeezing fields. By coupling an auxiliary ququart (a four‐level system) to the resonators, a resonator‐selective transition of the ququart is achieved through precise optical control. This selective transition enables conditional flipping of the states of target cat‐state qubits based on the state of control qubits, forming the basis for high‐fidelity multi‐qubit gate operations. Leveraging this mechanism, both SWAP and Fredkin gates are realized through a fixed operational sequence, with the number of steps remaining constant regardless of the number of involved cat‐state qubits. Numerical simulations confirm robust performance under realistic conditions, including parameter inaccuracies, imbalanced couplings, inter‐resonator crosstalk, and decoherence. Therefore, this approach offers a robust and practical method for implementing nonadiabatic geometric SWAP and Fredkin gates with cat‐state qubits.
Abstract Photonic cat states stored in high-Q resonators show great promise for hardware efficient universal quantum computing. We propose an approach to efficiently prepare such cat states in a Kerr-nonlinear resonator by the use of a two-photon drive. Significantly, we show that this preparation is robust against single-photon loss. An outcome of this observation is that a two-photon drive can eliminate undesirable phase evolution induced by a Kerr nonlinearity. By exploiting the concept of transitionless quantum driving, we moreover demonstrate how non-adiabatic initialization of cat states is possible. Finally, we present a universal set of quantum logical gates that can be performed on the engineered eigenspace of such a two-photon driven resonator and discuss a possible realization using superconducting circuits. The robustness of the engineered subspace to higher-order circuit nonlinearities makes this implementation favorable for scalable quantum computation.
We propose a protocol to realize nonadiabatic geometric quantum computation of small-amplitude Schr\"odinger cat qubits via invariant-based reverse engineering. We consider a system with a two-photon driven Kerr nonlinearity, which can generate a pair of dressed even and odd coherent states (i.e., Schr\"odinger cat states) for fault-tolerant quantum computations. An additional coherent field is applied to linearly drive a cavity mode, to induce oscillations between dressed cat states. By designing this linear drive with invariant-based reverse engineering, we show how to implement nonadiabatic geometric quantum computation with cat qubits. The performance of the protocol is estimated by taking into account the influence of systematic errors, additive white Gaussian noise, 1/f1/f1/f noise, and decoherence including photon loss and dephasing. Numerical results demonstrate that our protocol is robust against these negative factors. Therefore, this protocol may provide a feasible method for nonadiabatic geometric quantum computation in bosonic systems.
Abstract We propose a protocol for nonadiabatic holonomic quantum computation based on squeezed cat states. By exponentially enhancing the Kerr nonlinearity of a harmonic oscillator via a tailored driving scheme, we enable the fast, nonadiabatic generation of squeezed coherent states through shortcuts to adiabaticity. These squeezed coherent states serve as the building blocks for squeezed cat states, which are then utilized as logical qubits in our holonomic framework. Numerical simulations show that our state-preparation mechanism is approximately five times faster than conventional adiabatic approaches, thereby providing a practical route to accelerate the realization of holonomic gates. Leveraging the robustness of geometric phases and the nonclassical features of squeezed cat states, our scheme offers a promising platform for high-speed, fault-tolerant quantum computation.
Nonadiabatic geometric phases have important applications in quantum computation, as they depend only on the global properties of the evolution paths, and thus are robust against certain types of local noise. Experimental implementation is challenging, though, due to the need for complex control of multilevel or multiple quantum systems. This study proposes a delicate gate implementation to solve the problem, based on parametrically tunable resonant coupling between two superconducting transmon qubits, without introducing any auxiliary state. This approach is promising for high-fidelity geometric manipulation and robust solid-state quantum computing.
We propose a protocol to implement multi-qubit geometric gates (i.e., the Molmer-Sorensen gate) using photonic cat qubits. These cat qubits stored in high-QQQ resonators are promising for hardware-efficient universal quantum computing. Specifically, in the limit of strong two-photon drivings, phase-flip errors of the cat qubits are effectively suppressed, leaving only a bit-flip error to be corrected. A geometric evolution guarantees the robustness of the protocol against stochastic noise along the evolution path. Moreover, by changing detunings of the cavity-cavity couplings at a proper time, the protocol can be robust against control imperfections (e.g., the total evolution time) without introducing extra noises into the system. As a result, the gate can produce multi-mode entangled cat states in a short time with high fidelities.