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arXiv:2410.00431 · Applied Physics Letters

Residual-ZZ-coupling suppression and fast two-qubit gate for Kerr-cat qubits based on level-degeneracy engineering

Takaaki Aoki, Akiyoshi Tomonaga, Kosuke Mizuno, Shumpei Masuda

Published Jan 27, 2025• 3 citations
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Abstract

Building large-scale quantum computers requires an interqubit-coupling scheme with a high on–off ratio to avoid unwanted crosstalk coming from residual coupling and to enable fast multi-qubit operations. We propose a ZZ-coupling scheme for two Kerr-cat qubits with a frequency-tunable coupler. By making four relevant states of the two Kerr-cat qubits quadruply degenerate, we can switch off the ZZ coupling. By partially lifting the level degeneracy, we can switch it on. We theoretically show that an experimentally feasible circuit model suppresses the residual ZZ coupling. Moreover, our circuit can realize RZZ(−π/2)-gate fidelity higher than 99.9% within 18 ns when decoherence is ignored. Our model includes the first-order terms in expansion beyond the rotating-wave approximation.

DOI
10.1063/5.0241315

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Building large-scale quantum computers requires an interqubit-coupling scheme with a high on–off ratio to avoid unwanted crosstalk coming from residual coupling and to enable fast multi-qubit operations. We propose a ZZ-coupling scheme for two Kerr-cat qubits with a frequency-tunable coupler. By making four relevant states of the two Kerr-cat qubits quadruply degenerate, we can switch off the ZZ coupling. By partially lifting the level degeneracy, we can switch it on. We theoretically show that an experimentally feasible circuit model suppresses the residual ZZ coupling. Moreover, our circuit can realize RZZ(−π/2)-gate fidelity higher than 99.9% within 18 ns when decoherence is ignored. Our model includes the first-order terms in expansion beyond the rotating-wave approximation.
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.
High-speed RZZR_{ZZ}RZZ​ gates in Kerr-cat qubits via fast-forward scaling
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 RZZR_{ZZ}RZZ​-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 RZZR_{ZZ}RZZ​ gates.
High fidelity two-qubit gates exhibiting low cross talk are essential building blocks for gate-based quantum information processing. In superconducting circuits, two-qubit gates are typically based either on rf-controlled interactions or on the in situ tunability of qubit frequencies. Here, we present an alternative approach using a tunable cross-Kerr-type ZZ interaction between two qubits, which we realize with a flux-tunable coupler element. We control the ZZ-coupling rate over 3 orders of magnitude to perform a rapid (38 ns), high-contrast, low leakage (0.14±0.24%) conditional phase CZ gate with a fidelity of 97.9±0.7% as measured in interleaved randomized benchmarking without relying on the resonant interaction with a noncomputational state. Furthermore, by exploiting the direct nature of the ZZ coupling, we easily access the entire conditional phase gate family by adjusting only a single control parameter.
Tunable couplers, which turn on and off the interaction between qubits, have emerged as a key means to achieve low error rates in superconducting quantum computers. Conventional devices using one transmon qubit exhibit unwanted residual coupling, though, especially at the high detuning that is desirable for suppressing crosstalk errors. To solve this critical problem, the author proposes a tunable coupler based on two transmons that satisfies the ideal conditions of no residual coupling and fast two-qubit gate operations at high detuning. This double-transmon coupler is expected to become standard for superconducting architectures by eliminating unwanted coupling during idle time.
We propose a theoretical scheme of using two fixed-frequency resonator couplers to tune the interaction between two Xmon qubits. The indirect interaction between two qubits induced by two resonators can cancel each other, so direct qubit-qubit coupling is not essential for the switching off. So, we can suppress the static ZZ coupling with the weak direct qubit-qubit coupling and even eliminate the static ZZ coupling through the destructive interferences of the double-path couplers. The cross-Kerr resonance can induce additional poles for the static ZZ coupling which should be kept away during the two-qubit gates. The double-resonator couplers scheme could unfreeze some restrictions during the design of superconducting quantum chips and mitigate the static ZZ coupling, which might supply a promising platform for future superconducting quantum chips.
High-fidelity two-qubit gates at scale are a key requirement to realize the full promise of quantum computation and simulation. The advent and use of coupler elements to tunably control two-qubit interactions has improved operational fidelity in many-qubit systems by reducing parasitic coupling and frequency crowding issues. Nonetheless, two-qubit gate errors still limit the capability of near-term quantum applications. The reason, in part, is the existing framework for tunable couplers based on the dispersive approximation does not fully incorporate three-body multi-level dynamics, which is essential for addressing coherent leakage to the coupler and parasitic longitudinal (ZZZZZZ) interactions during two-qubit gates. Here, we present a systematic approach that goes beyond the dispersive approximation to exploit the engineered level structure of the coupler and optimize its control. Using this approach, we experimentally demonstrate CZ and ZZZZZZ-free iSWAP gates with two-qubit interaction fidelities of 99.76±0.0799.76 \pm 0.0799.76±0.07% and 99.87±0.2399.87 \pm 0.2399.87±0.23%, respectively, which are close to their T1T_1T1​ limits.