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arXiv:2212.05519 · Physical Review Applied

Parasitic-Free Gate: An Error-Protected Cross-Resonance Switch in Weakly Tunable Architectures

Xuexin Xu, Mohammad H. Ansari

Published Feb 22, 2023• 12 citations
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Abstract

In two-qubit gates activated by microwave pulses, by turning the pulse on or off, the state of qubits is swapped between entangled or idle modes. In either mode, the presence of stray couplings makes qubits accumulate coherent phase error. However, the error rates in the two modes differ because qubits carry different stray coupling strengths in each mode; therefore, eliminating stray coupling from one mode does not remove it from the other. We propose to combine such a gate with a tunable coupler and show that both idle and entangled qubits can become free from stray couplings. This significantly increases the operational switch fidelity in quantum algorithms. We further propose a weakly tunable qubit as an optimum coupler to bring the two modes parametrically near each other. This remarkably enhances the tuning process by reducing its leakage.

DOI
10.1103/physrevapplied.19.024057

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In two-qubit gates activated by microwave pulses, by turning the pulse on or off, the state of qubits is swapped between entangled or idle modes. In either mode, the presence of stray couplings makes qubits accumulate coherent phase error. However, the error rates in the two modes differ because qubits carry different stray coupling strengths in each mode; therefore, eliminating stray coupling from one mode does not remove it from the other. We propose to combine such a gate with a tunable coupler and show that both idle and entangled qubits can become free from stray couplings. This significantly increases the operational switch fidelity in quantum algorithms. We further propose a weakly tunable qubit as an optimum coupler to bring the two modes parametrically near each other. This remarkably enhances the tuning process by reducing its leakage.
We propose a gate to switch superconducting qubit pairs in and out of a two-body interaction. This gate uses cross resonance driving on a tunable circuit with adjusted parameters and without accumulating residual ZZ interaction for idle and interacting qubits. It is imperative that this gate does not spread errors through the quantum register. Our detailed theoretical results show that these error-free modes do not necessarily require largely tunable circuits, such as magnetic modulation of qubits or couplers. We obtain the operational gate on weakly tuneable circuits as well and show that switching between them is remarkably fast.
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 ${10}^{\ensuremath{-}4}$.
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.
Tunable couplers have recently become one of the most powerful tools for implementing two-qubit gates between superconducting qubits.A tunable coupler typically includes a nonlinear element, such as a superconducting quantum interference device, which is used to tune the resonance frequency of an LC circuit connecting two qubits.Here we propose a complimentary approach where instead of tuning the resonance frequency of the tunable coupler by applying a quasistatic control signal, we excite by microwave the degree of freedom associated with the coupler itself.Because of strong effective longitudinal coupling between the coupler and the qubits, the frequency of this transition strongly depends on the computational state, leading to different phase accumulations in different states.Using this method, we experimentally demonstrate a controlled-Z gate of 44-ns duration on a fluxonium-based quantum processor, obtaining a fidelity of 97.6% ± 0.4% characterized by cross-entropy benchmarking.
High-fidelity parametric gates have been demonstrated with superconducting qubits via rf flux modulation of the qubit frequency. The modulation however leads to renormalization of the bare qubit-qubit coupling, thereby reducing the gate speed. Here, we realize a parametric-resonance gate, which is activated by bringing the average frequency of the modulated qubit in resonance with a static-frequency qubit while approximately retaining the bare qubit-qubit coupling. The activation of parametric-resonance gates does not depend on the frequency of modulation, allowing us to choose the modulation frequencies and avoid frequency collisions. Moreover, we show that this approach is compatible with tunable coupler architectures, which reduce always-on residual couplings. Using these techniques, we demonstrate iswap and controlled-ZZZ gates between two qubits coupled via a tunable coupler with average process fidelities as high as $99.3\mathrm{%}$ and $97.9\mathrm{%}$, respectively. The flexibility in activating parametric-resonance gates combined with a tunable coupler architecture provides a pathway for building large-scale quantum computers.
A register of quantum bits with fixed transition frequencies and weakly coupled to one another through simple linear circuit elements is an experimentally minimal architecture for a small-scale superconducting quantum information processor. Presently, the known schemes for implementing two-qubit gates in this system require microwave signals having amplitudes and frequencies precisely tuned to meet a resonance condition, leaving only the signal phases as free experimentally adjustable parameters. Here, we report a minimal and robust microwave scheme to generate fast, tunable universal two-qubit gates: simply irradiate one qubit (the ``control'') at the transition frequency of another (the ``target''). The effective coupling between them is then switched on by tuning only the frequency of this single drive tone; the drive amplitude adjusts the effective coupling strength; and the drive phase selects the particular two-qubit gate implemented. This cross-resonance effect turns on linearly with the ratio of the drive amplitude $\ensuremath{\Omega}$ to the qubit-qubit detuning $\ensuremath{\Delta}$, as compared with earlier proposals that turn on as ${(\ensuremath{\Omega}/\ensuremath{\Delta})}^{4}$.