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Acta Physica Sinica

Quantum phase gate on a single superconducting Λ-type three-level and two superconducting resonators

Liu Chao, Wu Yun-Wen

Published Jan 1, 2018• 1 citation
Publisher

Abstract

Quantum phase gate is a necessary quantum component for quantum coding and quantum computing. Compared with the traditional gate circuit, quantum phase gate has the characteristics of unitarity and reversibility. Therefore, we construct a model of mutual coupling between a single Λ -type three-level atom and two superconducting resonators, which is connected by a capacitor. By separately controlling the disconnection time and connection time of the two superconducting resonators in the model as well as by controlling the magnetic flux of the superconducting quantum interference device (SQUID) to make a certain transition energy level of the Λ -type three-level atom equal the relevant resonance energy level, the interaction between the two levels can be achieved and the system can be manipulated. Afterwards, we propose four control schemes for implementing the controlled-Z gate through a three-step operation, and two operation schemes for implementing swap gate through a four-step operation. At the same time, the numerical simulations of fidelity are implemented for the first operation scheme for controlling the Z-gate. The results of fidelity discussion show that the fidelity of this scheme is 96.67% through the running time of 20.83 ns, thus it proves that this scheme is theoretically feasible. The increase in the three attenuation parameters, i.e., attenuation rate, relaxation rate, and phase shift ratio, will reduce the fidelity of the system, while the increase in coupling strength will cut down the time of system operation, thus reducing the influence of attenuation parameters and improving the system fidelity.In this paper we present a quantum phase gate scheme in which two superconducting resonators and a Λ -type three-level atom are coupled with two capacitors. Since the experimental setup is simplified, it is important to reduce the coherence between devices. In addition, the solution has no restriction on the strength of the classic pulse principally, through which the system operates faster and the fidelity of the phase gate is improved effectively.

DOI
10.7498/aps.67.20180830

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Quantum phase gate is a necessary quantum component for quantum coding and quantum computing. Compared with the traditional gate circuit, quantum phase gate has the characteristics of unitarity and reversibility. Therefore, we construct a model of mutual coupling between a single Λ -type three-level atom and two superconducting resonators, which is connected by a capacitor. By separately controlling the disconnection time and connection time of the two superconducting resonators in the model as well as by controlling the magnetic flux of the superconducting quantum interference device (SQUID) to make a certain transition energy level of the Λ -type three-level atom equal the relevant resonance energy level, the interaction between the two levels can be achieved and the system can be manipulated. Afterwards, we propose four control schemes for implementing the controlled-Z gate through a three-step operation, and two operation schemes for implementing swap gate through a four-step operation. At the same time, the numerical simulations of fidelity are implemented for the first operation scheme for controlling the Z-gate. The results of fidelity discussion show that the fidelity of this scheme is 96.67% through the running time of 20.83 ns, thus it proves that this scheme is theoretically feasible. The increase in the three attenuation parameters, i.e., attenuation rate, relaxation rate, and phase shift ratio, will reduce the fidelity of the system, while the increase in coupling strength will cut down the time of system operation, thus reducing the influence of attenuation parameters and improving the system fidelity.In this paper we present a quantum phase gate scheme in which two superconducting resonators and a Λ -type three-level atom are coupled with two capacitors. Since the experimental setup is simplified, it is important to reduce the coherence between devices. In addition, the solution has no restriction on the strength of the classic pulse principally, through which the system operates faster and the fidelity of the phase gate is improved effectively.
We propose a one-step scheme for implementing multi-qubit phase gates on microwave photons in multiple resonators mediated by a superconducting bus in circuit quantum electrodynamics (QED) system. In the scheme, multiple single-mode resonators carry quantum information with their vacuum and single-photon Fock states, and a multi-level artificial atom acts as a quantum bus which induces the indirect interaction among resonators. The method of pulse engineering is used to shape the coupling strength between resonators and the bus so as to improve the fidelity and robustness of the scheme. We also discuss the influence of finite coherence time for the bus and resonators on gate fidelity respectively. Finally, we consider the suppression of unwanted transitions and propose the method of optimized detuning compensation for offsetting unwanted transitions, showing the feasibility of the scheme within the current experiment technology.
We propose a way for realizing a two-qubit controlled phase gate with superconducting quantum interference devices (SQUIDs) coupled to a superconducting resonator. In this proposal, the two lowest levels of each SQUID serve as the logical states and two intermediate levels of each SQUID are used for the gate realization. We show that neither adjustment of SQUID level spacings during the gate operation nor uniformity in SQUID parameters is required by this proposal. In addition, this proposal does not require the adiabatic passage or a second-order detuning and thus the gate is much faster.
We construct a novel Λ-type system via the dressed states formed by the coupling between a superconducting qubit and a transmission line resonator (TLR). Compared with the conventional three-level structure, our model averts the decay of excited states. We choose the two lowest energy dressed states as the logical states. The single qubit quantum gate can be realized by the adiabatic passage and three-step operation method, respectively. Based on realistic parameters, the feasibility of the adiabatic passage method is discussed. Also, we calculate the fidelity (0.9996) of realizing the single qubit gate with the three-step operation method.
Applications for noisy intermediate-scale quantum computing devices rely on the efficient entanglement of many qubits to reach a potential quantum advantage. Although entanglement is typically generated using two-qubit gates, direct control of strong multiqubit interactions can improve the efficiency of the process. Here, we investigate a system of three superconducting transmon-type qubits coupled via a single flux-tunable coupler. Tuning the frequency of the coupler by adiabatic flux pulses enables us to control the conditional energy shifts between the qubits and directly realize multiqubit interactions. To accurately adjust the resulting controlled relative phases, we describe a gate protocol involving refocusing pulses and adjustable interaction times. This enables the implementation of the full family of pairwise controlled-phase and controlled-controlled-phase gates. Numerical simulations result in fidelities around 99% and gate times below 300 ns using currently achievable system parameters and decoherence rates.
We present a scheme to realize the basic two-qubit logic gates such as the quantum phase gate and SWAP gate using a detuned microwave cavity interacting with three-level superconducting-quantum-interference-device (SQUID) qubit(s), by placing SQUID(s) in a two-mode microwave cavity and using adiabatic passage methods. In this scheme, the two logical states of the qubit are represented by the two lowest levels of the SQUID and the cavity fields are treated as quantized. Compared with the previous method, the complex procedures of adjusting the level spacing of the SQUID and applying the resonant microwave pulse to the SQUID to create transformation are not required. Based on superconducting device with relatively long decoherence time and simplified operation procedure, the gates operate at a high speed, which is important in view of decoherence.