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Physical Review A

One-step parity measurement of N cat-state qubits via reverse engineering and optimal control

Dong-Sheng Li, Yi‐Hao Kang, Ye‐Hong Chen, Yang Liu, Cheng Zhang, Yu Wang, Jie Song, Yan Xia

Published Feb 26, 2024• 13 citations
Publisher

Abstract

In this paper, a one-step protocol is proposed for the parity measurement of $N$ cat-state qubits which are encoded on the cat states of the modes in superconducting Kerr-nonlinear cavities. The parity measurement is performed with the help of an auxiliary qutrit. Especially, the auxiliary qutrit can (cannot) be excited to the higher-energy levels when the cat-state qubits are in the even- (odd-) parity state. By designing the Rabi frequency of the classical fields via reverse engineering and optimal control, the qutrit is driven to an excited dressed state in the even-parity case, which is robust to the systematic errors of the qutrit-cavity coupling strengths. Accordingly, the parity of the cat-state qubits can be distinguished with high accuracy by measuring the final population of the ground state of the auxiliary qutrit. Numerical simulations also show that the protocol is insensitive to the systematic errors of the classical fields, the inhomogeneity of the coupling strengths, intercavity cross talk, unwanted qutrit transitions, and decoherence. Therefore, the protocol may provide an effective approach for parity measurement of multiple cat-state qubits.

DOI
10.1103/physreva.109.022437

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Abstract In this paper, a protocol for nondestructive parity meter (NPM) of two cat‐state qubits is proposed. The physical model contains two cavities and an auxiliary qubit. For each cavity, the quantum information is encoded on the odd and even cat state, forming a cat‐state qubit. By adjusting the strength of the driving field on the auxiliary qubit, an effective Hamiltonian for cavity‐selective transition is derived. Moreover, reverse engineering based on the effective Hamiltonian is applied to find the evolution path, and the systematic‐error‐sensitivity nullification method is used to select proper parameters of the evolution path. In this way, robust control fields are designed to combat the influence of the systematic errors. Furthermore, the effects of random noise and decoherence on the fidelity of the protocol are considered. Numerical simulations show that the protocol is insensitive to the experimental imperfection, including systematic errors, random noise and decoherence. Therefore, the protocol is expected to expand the vision of realizing NPM.
We propose a scheme for realizing parity measurement of cat-state qubits based on a topological quantum phase transition. The cat-state qubits, formed by the bosonic modes in the Kerr-nonlinear resonators with two-photon squeezing drives, couple with a superconducting qubit in the center. We demonstrate that the resonator-qubit couplings with proper strengths can induce a topological quantum phase transition when the cat-state qubits are initial in the even-parity states. The topological quantum phase transition provides an approach to distinguish the even-parity states from the odd-parity states by measuring a topological invariant, namely the Chern number. Due to the robustness of the Chern number, the scheme shows great tolerance for multiple types of disturbing factors, including the systematic errors of the control fields and the coupling strengths, the inter-resonator crosstalk, and decoherence. Therefore, the scheme may be useful to construct an error-tolerant parity detector of cat-state qubits.
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.
We propose a single-step implementation of a muti-target-qubit controlled phase gate with one catstate qubit ( cqubit ) simultaneously controlling n –1 target cqubits . The two logic states of a cqubit are represented by two orthogonal cat states of a single cavity mode. In this proposal, the gate is implemented with n microwave cavities coupled to a superconducting transmon qutrit. Because the qutrit remains in the ground state during the gate operation, decoherence caused due to the qutrit’s energy relaxation and dephasing is greatly suppressed. The gate implementation is quite simple because only a single-step operation is needed and neither classical pulse nor measurement is required. Numerical simulations demonstrate that high-fidelity realization of a controlled phase gate with one cqubit simultaneously controlling two target cqubits is feasible with present circuit QED technology. This proposal can be extended to a wide range of physical systems to realize the proposed gate, such as multiple microwave or optical cavities coupled to a natural or artificial three-level atom.
The engineering of Kerr interactions is of great interest for processing quantum information in multipartite quantum systems and for investigating many-body physics in a complex cavity-qubit network. We study how coupling multiple different types of superconducting qubits to the same cavity modes can be used to modify the self- and cross-Kerr effects acting on the cavities and demonstrate that this type of architecture could be of significant benefit for quantum technologies. Using both analytical perturbation theory results and numerical simulations, we first show that coupling two superconducting qubits with opposite anharmonicities to a single cavity enables the effective self-Kerr interaction to be diminished, while retaining the number splitting effect that enables control and measurement of the cavity field. We demonstrate that this reduction of the self-Kerr effect can maintain the fidelity of coherent states and generalised Schrödinger cat states for much longer than typical coherence times in realistic devices. Next, we find that the cross-Kerr interaction between two cavities can be modified by coupling them both to the same pair of qubit devices. When one of the qubits is tunable in frequency, the strength of entangling interactions between the cavities can be varied on demand, forming the basis for logic operations on the two modes. Finally, we discuss the feasibility of producing an array of cavities and qubits where intermediary and on-site qubits can tune the strength of self- and cross-Kerr interactions across the whole system. This architecture could provide a way to engineer interesting many-body Hamiltonians and be a useful platform for quantum simulation in circuit quantum electrodynamics.
Abstract In this paper, a robust and accurate protocol is proposed to realize nondestructive parity measurement of artificial atoms using a superconducting resonator and homodyne measurement. With the help of an additional microwave driving field, the cavity field evolves into a coherent state or remains in a vacuum state according to the parity of the atoms. Consequently, the parity information of atoms can be read out by a homodyne measurement on the cavity. Parity information can be obtained without destroying the original state of the system, which means that the state can be further applied to other quantum information processing tasks after a parity measurement. The numerical simulation results show that the protocol is robust against systematic error, random noise, and decoherence. Therefore, this protocol can provide a feasible viewpoint for nondestructive parity measurement.