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arXiv:2511.11056

High-speed $R_{ZZ}$ gates in Kerr-cat qubits via fast-forward scaling

Takaaki Aoki, Shumpei Masuda

quant-phSubmitted Nov 14, 2025• Announced Nov 17, 2025• 0 citations• Revised Sep 10, 2026 (v3)
v1 · Nov 14, 2025v2 · Apr 9, 2026v3 · Sep 10, 2026
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Abstract

Kerr parametric oscillators can encode Kerr-cat qubits, whose biased-noise nature can reduce the hardware overhead required for fault-tolerant quantum computation. In a recently proposed $R_{ZZ}$-gate scheme for Kerr-cat qubits, a tunable coupler must be displaced while avoiding nonadiabatic excitation. To address this challenge, we propose and theoretically analyze a protocol that applies fast-forward scaling to the coupler displacement. The protocol suppresses nonadiabatic excitation of the coupler and enables high speed $R_{ZZ}$ gates.

Comments
16 pages, 7 figures

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Kerr cat qubits are a promising candidate for fault-tolerant quantum computers owing to the biased nature of their errors. The ZZZZZZ coupling between the qubits can be utilized for a two-qubit entangling gate, but the residual coupling called ZZZZZZ crosstalk is detrimental to precise computing. In order to resolve this problem, we propose a tunable ZZZZZZ-coupling scheme using two transmon couplers. By setting the detunings of the two couplers at opposite values, the residual ZZZZZZ couplings via the two couplers cancel each other out. We also apply our scheme to the ${R}_{ZZ}(\mathrm{\ensuremath{\Theta}})$ gate (ZZZZZZ rotation with angle $\mathrm{\ensuremath{\Theta}}$), one of the two-qubit entangling gates. We numerically show that the fidelity of the ${R}_{ZZ}(\ensuremath{-}\ensuremath{\pi}/2)$ gate is higher than 99.9% in a case of 16-ns gate time and without decoherence.
Kerr-cat qubits offer a hardware-efficient route to fault-tolerant quantum computing by suppressing bit-flip errors exponentially, while phase-flip errors increase only linearly with the mean photon number. To maintain this protection, entangling operations must be bias-preserving, ensuring that phase-flip errors occurring during the gate do not propagate into bit-flip errors. In this paper, we propose an asymmetrically threaded SQUID (ATS) parametric coupler to implement high-fidelity, bias-preserving entangling gates between Kerr-cat qubits. By engineering a photon-number asymmetry between the control and target modes, we enable fast gate operations that suppress non-adiabatic leakage without complex pulse shaping. Through numerical simulations of the full circuit Hamiltonian, we demonstrate a bias-preserving CX gate achieving 99.69% fidelity in the absence of photon loss for a gate duration of 50 ns. Under a single-photon loss rate of 100 kHz, our protocol yields a noise bias of 9922, exceeding the noise bias of a naive non-bias-preserving CX implementation by approximately a factor of 570. These results support the ATS coupler as a valuable building block for concatenated cat-qubit architectures.
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Kerr parametric oscillators (KPOs), which can be implemented with superconducting parametrons possessing large Kerr nonlinearity, have been attracting much attention in terms of their applications to quantum annealing, universal quantum computation, and studies of quantum many-body systems. It is of practical importance for these studies to realize fast and accurate tunable coupling between KPOs in a simple manner. We develop a simple scheme of fast tunable coupling of KPOs with high tunability in speed and amplitude using the fast transitionless rotation of a KPO in the phase space based on the shortcuts to adiabaticity. Our scheme enables rapid switching of the effective coupling between KPOs, and can be implemented with always-on linear coupling between KPOs, by controlling the phase of the pump field and the resonance frequency of the KPO without controlling the amplitude of the pump field nor using additional drive fields and couplers. We apply the coupling scheme to a two-qubit gate, and show that our scheme realizes high gate fidelity compared with a purely adiabatic one, by mitigating undesired nonadiabatic transitions.