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arXiv:2303.16622 · Physical Review Applied

Control of the ZZ coupling between Kerr cat qubits via transmon couplers

Takaaki Aoki, Taro Kanao, Hayato Goto, Shiro Kawabata, Shumpei Masuda

Published Jan 18, 2024• 15 citations
arXivHTMLPDF

Abstract

Kerr cat qubits are a promising candidate for fault-tolerant quantum computers owing to the biased nature of their errors. The $ZZ$ coupling between the qubits can be utilized for a two-qubit entangling gate, but the residual coupling called $ZZ$ crosstalk is detrimental to precise computing. In order to resolve this problem, we propose a tunable $ZZ$-coupling scheme using two transmon couplers. By setting the detunings of the two couplers at opposite values, the residual $ZZ$ couplings via the two couplers cancel each other out. We also apply our scheme to the ${R}_{ZZ}(\mathrm{\ensuremath{\Theta}})$ gate ($ZZ$ 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.

DOI
10.1103/physrevapplied.21.014030

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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 RZZ(\ensuremathΘ){R}_{ZZ}(\mathrm{\ensuremath{\Theta}})RZZ​(\ensuremathΘ) gate (ZZZZZZ rotation with angle \ensuremathΘ\mathrm{\ensuremath{\Theta}}\ensuremathΘ), one of the two-qubit entangling gates. We numerically show that the fidelity of the RZZ(\ensuremath−\ensuremathπ/2){R}_{ZZ}(\ensuremath{-}\ensuremath{\pi}/2)RZZ​(\ensuremath−\ensuremathπ/2) gate is higher than 99.9% in a case of 16-ns gate time and without decoherence.
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.
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.
Eliminating residual ZZ interactions in a two-qubit system is essential for reducing coherent errors during quantum operations. In a superconducting circuit platform, coupling two transmon qubits via a transmon coupler has been shown to effectively suppress residual ZZ interactions. However, in such systems, perfect cancellation usually requires the qubit-qubit detuning to be smaller than the individual qubit anharmonicities, which exacerbates frequency crowding and microwave crosstalk. To address this limitation, we introduce TFT (Transmon-Fluxonium-Transmon) architecture, wherein two transmon qubits are coupled via a fluxonium qubit. The coupling mediated by the fluxonium eliminates residual ZZ interactions even for transmons detuned larger than their anharmonicities. We experimentally identified zero-ZZ interaction points at qubit-qubit detunings of 409 MHz and 616 MHz from two distinct TFT devices. We then implemented an adiabatic, coupler-flux-biased controlled-Z gate on both devices, achieving CZ gate fidelities of 99.64(6)% and 99.68(8)%.
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.
High-fidelity single- and two-qubit gates are essential building blocks for a fault-tolerant quantum computer. While there has been much progress in suppressing single-qubit gate errors in superconducting qubit systems, two-qubit gates still suffer from error rates that are orders of magnitude higher. One limiting factor is the residual ZZ-interaction, which originates from a coupling between computational states and higher-energy states. While this interaction is usually viewed as a nuisance, here we experimentally demonstrate that it can be exploited to produce a universal set of fast single- and two-qubit entangling gates in a coupled transmon qubit system. To implement arbitrary single-qubit rotations, we design a new protocol called the two-axis gate that is based on a three-part composite pulse. It rotates a single qubit independently of the state of the other qubit despite the strong ZZ-coupling. We achieve single-qubit gate fidelities as high as 99.1% from randomized benchmarking measurements. We then demonstrate both a CZ gate and a CNOT gate. Because the system has a strong ZZ-interaction, a CZ gate can be achieved by letting the system freely evolve for a gate time tg=53.8t_g=53.8tg​=53.8 ns. To design the CNOT gate, we utilize an analytical microwave pulse shape based on the SWIPHT protocol for realizing fast, low-leakage gates. We obtain fidelities of 94.6% and 97.8% for the CNOT and CZ gates respectively from quantum progress tomography.
Striving for higher gate fidelity is crucial not only for enhancing existing noisy intermediate-scale quantum devices, but also for unleashing the potential of fault-tolerant quantum computation through quantum error correction. A recently proposed theoretical scheme, the double-transmon coupler (DTC), aims to achieve both suppressed residual interaction and a fast high-fidelity two-qubit gate simultaneously, particularly for highly detuned qubits. Harnessing the state-of-the-art fabrication techniques and a model-free pulse-optimization process based on reinforcement learning, we translate the theoretical DTC scheme into reality, attaining fidelities of 99.90% for a controlled- Z gate and 99.98% for single-qubit gates. The performance of the DTC scheme demonstrates its potential as a competitive building block for superconducting quantum processors. Published by the American Physical Society 2024