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Physica Scripta

Selective-resonance-based fast CZ gate on transmon qubits with untraditional periodic relationships among Rabi oscillations

Ming Hua, Ming‐Jie Tao

Published May 1, 2025• 0 citations
Publisher

Abstract

Abstract We propose a new effect on the system composed of two superconducting qubits (q 1 and q 2) coupled to a 1D superconducting resonator—the selective resonance, coming from the qubit-state-dependent resonator transition frequency caused by q 1. The effect means q 2 can selectively resonate with different frequencies (determined by the state of q 1) of the resonator. By utilizing the large coupling strength of q 1 to enlarge this effect, considering the existence of the third energy level of the q 1, and using specific period relation between the desired and undesired Rabi oscillations of q 2 and the resonator, which is differs from the traditional method to completely avoid the undesired Rabi oscillation, we propose a fast, high-fidelity (∼99.7%) one-step controlled-σ z gate on q 1 and q 2 with a gate time close to 10 ns which is approaching the operation time of a single-qubit gate.

DOI
10.1088/1402-4896/add2a0

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arXiv:2510.09461•Physical Review A•Feb 23, 2026•0 citations
Abstract We propose a new effect on the system composed of two superconducting qubits (q 1 and q 2) coupled to a 1D superconducting resonator—the selective resonance, coming from the qubit-state-dependent resonator transition frequency caused by q 1. The effect means q 2 can selectively resonate with different frequencies (determined by the state of q 1) of the resonator. By utilizing the large coupling strength of q 1 to enlarge this effect, considering the existence of the third energy level of the q 1, and using specific period relation between the desired and undesired Rabi oscillations of q 2 and the resonator, which is differs from the traditional method to completely avoid the undesired Rabi oscillation, we propose a fast, high-fidelity (∼99.7%) one-step controlled-σ z gate on q 1 and q 2 with a gate time close to 10 ns which is approaching the operation time of a single-qubit gate.
We present a fast quantum entangling operation on superconducting qubits assisted by a resonator in the quasi-dispersive regime with a new effect --- the selective resonance coming from the amplified qubit-state-dependent resonator transition frequency and the tunable period relation between a wanted quantum Rabi oscillation and an unwanted one. This operation does not require any kind of drive fields and the interaction between qubits. More interesting, the non-computational third excitation states of the charge qubits can play an important role in shortening largely the operation time of the entangling gates. All those features provide an effective way to realize much faster quantum entangling gates on superconducting qubits than previous proposals.
Engineering high-fidelity two-qubit gates is an indispensable step toward practical quantum computing. For superconducting quantum platforms, one important setback is the stray interaction between qubits, which causes significant coherent errors. For transmon qubits, protocols for mitigating such errors usually involve fine-tuning the hardware parameters or introducing usually noisy flux-tunable couplers. In this work, we propose a simple scheme to cancel these stray interactions. The coupler used for such cancellation is a driven high-coherence resonator, where the amplitude and frequency of the drive serve as control knobs. Through the resonator-induced-phase (RIP) interaction, the static ZZ coupling can be entirely neutralized. We numerically show that such a scheme can enable short and high-fidelity entangling gates, including cross-resonance CNOT gates within 40 ns and adiabatic CZ gates within 140 ns. Our architecture is not only ZZ free but also contains no extra noisy components, such that it preserves the coherence times of fixed-frequency transmon qubits. With the state-of-the-art coherence times, the error of our cross-resonance CNOT gate can be reduced to below 1e-4.
Single-flux-quantum (SFQ) digital circuitry has great potential in building a scalable control system of superconducting qubits. In this work, we describe a practical SFQ-based two-qubit gate for transmon qubits. The controlled-ZZZ (CZ) gate is activated by near-resonant SFQ-pulse trains near the target transition involving the second excited state. Numerical simulations show that the fidelity of a SFQ-activated CZ gate in excess of 99.9% is achievable within 100-ns gate time. We evaluate the CZ gate error caused by leakage and SFQ-pulse width. Combined with the proposed feasible expansion methods, this work is a supplement to the scalable and integratable superconducting-qubit control system based on SFQ digital logic.
A possible building block for a scalable quantum computer has recently been demonstrated [Mariantoni et al., Science 334, 61 (2011)]. This architecture consists of superconducting qubits capacitively coupled both to individual memory resonators as well as a common bus. In this work we study a natural primitive entangling gate for this and related resonator-based architectures, which consists of a controlled-${\ensuremath{\sigma}}^{z}$ (cz) operation between a qubit and the bus. The cz gate is implemented with the aid of the noncomputational qubit $|2\ensuremath{\rangle}$ state [Strauch et al., Phys. Rev. Lett. 91, 167005 (2003)]. Assuming phase or transmon qubits with 300 MHz anharmonicity, we show that by using only low frequency qubit-bias control it is possible to implement the qubit-bus cz gate with 99.9% (99.99%) fidelity in about 17ns17\phantom{\rule{0.16em}{0ex}}\mathrm{ns}17ns (23ns23\phantom{\rule{0.16em}{0ex}}\mathrm{ns}23ns) with a realistic two-parameter pulse profile, plus two auxiliary zzz rotations. The fidelity measure we refer to here is a state-averaged intrinsic process fidelity, which does not include any effects of noise or decoherence. These results apply to a multiqubit device that includes strongly coupled memory resonators. We investigate the performance of the qubit-bus cz gate as a function of qubit anharmonicity, identify the dominant intrinsic error mechanism and derive an associated fidelity estimator, quantify the pulse shape sensitivity and precision requirements, simulate qubit-qubit cz gates that are mediated by the bus resonator, and also attempt a global optimization of system parameters including resonator frequencies and couplings. Our results are relevant for a wide range of superconducting hardware designs that incorporate resonators and suggest that it should be possible to demonstrate a 99.999.9%99.9 cz gate with existing transmon qubits, which would constitute an important step towards the development of an error-corrected superconducting quantum computer.
Engineering high-fidelity two-qubit gates is an indispensable step toward practical quantum computing. For superconducting quantum platforms, one important setback is the stray interaction between qubits, which causes significant coherent errors. For transmon qubits, protocols for mitigating such errors usually involve fine-tuning the hardware parameters or introducing usually noisy flux-tunable couplers. In this work, we propose a simple scheme to cancel these stray interactions. The coupler used for such cancelation is a driven high-coherence resonator, where the amplitude and frequency of the drive serve as control knobs. Through the resonator-induced-phase interaction, the static ZZZZZZ coupling can be entirely neutralized. We numerically show that such a scheme can enable short and high-fidelity entangling gates, including cross-resonance controlled-not (cnot) gates within 40 ns and adiabatic controlled-ZZZ gates within 140 ns. Our architecture is not only ZZZZZZ-free, but also contains no extra noisy components, such that it preserves the coherence times of fixed-frequency transmon qubits. With the state-of-the-art coherence times, the error of our cross-resonance cnot gate can be reduced to below ${10}^{\ensuremath{-}4}$.
In superconducting quantum circuits, decoherence errors in qubits constitute a critical factor limiting quantum gate performance. To mitigate decoherence-induced gate infidelity, rapid implementation of quantum gates is essential. Here we propose a scheme for rapid controlled-Z (CZ) gate implementation through energy-level engineering, which leverages Rabi oscillations between the ∣11⟩\left|11\right\rangle∣11⟩ state and the non-computational state in a tunable-coupler architecture. Numerical simulations achieved a 22 ns\mathrm{22~ns}22 ns nonadiabatic CZ gate with fidelity over 99.99%99.99\%99.99%. We further investigated the performance of the CZ gate in the presence of anharmonicity offsets. The results demonstrate that a high-fidelity CZ gate with an error rate below 10−410^{-4}10−4 remains achievable even with finite anharmonicity variations. Furthermore, the detrimental impact of spectator qubits in different quantum states on the fidelity of CZ gate is effectively suppressed by incorporating a tunable coupler. This scheme exhibits potential for extending the circuit execution depth constrained by coherence time limitations.