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arXiv:2009.00485 · Physical Review Applied

ZZ Freedom in Two-Qubit Gates

Xuexin Xu, Mohammad H. Ansari

Published Jun 29, 2021• 33 citations
arXivHTMLPDF

Abstract

Superconducting qubits on a circuit exhibit an always-on state-dependent phase error. This error is due to sub-MHz parasitic interaction that repels computational levels from noncomputational ones. We study a general theory to evaluate the ``static'' repulsion between seemingly idle qubits as well as the ``dynamical'' repulsion between entangled qubits under microwave driving gate. By combining qubits of either the same or opposite anharmonicity signs we find the characteristics of static and dynamical $ZZ$ freedoms. The latter universally eliminate the parasitic repulsion, leading us to mitigate high-fidelity gate operation. Our theory introduces the opportunities for making perfect entangled and unentangled states, which is extremely useful for quantum technology.

DOI
10.1103/physrevapplied.15.064074

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Superconducting qubits on a circuit exhibit an always-on state-dependent phase error. This error is due to sub-MHz parasitic interaction that repels computational levels from noncomputational ones. We study a general theory to evaluate the static'' repulsion between seemingly idle qubits as well as the dynamical'' repulsion between entangled qubits under microwave driving gate. By combining qubits of either the same or opposite anharmonicity signs we find the characteristics of static and dynamical ZZZZZZ freedoms. The latter universally eliminate the parasitic repulsion, leading us to mitigate high-fidelity gate operation. Our theory introduces the opportunities for making perfect entangled and unentangled states, which is extremely useful for quantum technology.
Generating high-fidelity, tunable entanglement between qubits is crucial for realizing gate-based quantum computation. In superconducting circuits, tunable interactions are often implemented using flux-tunable qubits or coupling elements, adding control complexity and noise sources. Here, we realize a tunable ZZ interaction between two transmon qubits with fixed frequencies and fixed coupling, induced by driving both transmons off resonantly. We show tunable coupling over 1 order of magnitude larger than the static coupling, and change the sign of the interaction, enabling cancellation of the idle coupling. Further, this interaction is amenable to large quantum processors: the drive frequency can be flexibly chosen to avoid spurious transitions, and because both transmons are driven, it is resilient to microwave cross talk. We apply this interaction to implement a controlled phase (CZ) gate with a gate fidelity of 99.43(1)% as measured by cycle benchmarking, and we find the fidelity is limited by incoherent errors.
Mitigating crosstalk errors, whether classical or quantum mechanical, is critically important for achieving high-fidelity entangling gates in multiqubit circuits. For weakly anharmonic superconducting qubits, unwanted ZZ interactions can be suppressed by combining qubits with opposite anharmonicity. We present experimental measurements and theoretical modeling of two-qubit gate error for gates based on the cross resonance interaction between a capacitively shunted flux qubit and a transmon, and demonstrate the elimination of the ZZ interaction.
For building a scalable quantum processor with superconducting qubits, ZZ interaction is of great concern because its residual has a crucial impact to two-qubit gate fidelity. Two-qubit gates with fidelity meeting the criterion of fault-tolerant quantum computation have been demonstrated using ZZ interaction. However, as the performance of quantum processors improves, the residual static ZZ can become a performance-limiting factor for quantum gate operation and quantum error correction. Here, we introduce a superconducting architecture using qubits with opposite-sign anharmonicity, a transmon qubit, and a C-shunt flux qubit, to address this issue. We theoretically demonstrate that by coupling the two types of qubits, the high-contrast ZZ interaction can be realized. Thus, we can control the interaction with a high on-off ratio to implement two-qubit controlled-Z gates, or suppress it during two-qubit gate operation using XY interaction (e.g., an iSWAP gate). The proposed architecture can also be scaled up to multiqubit cases. In a fixed coupled system, ZZ crosstalk related to neighboring spectator qubits could also be heavily suppressed.
Generating high-fidelity, tunable entanglement between qubits is crucial for realizing gate-based quantum computation. In superconducting circuits, tunable interactions are often implemented using flux-tunable qubits or coupling elements, adding control complexity and noise sources. Here, we realize a tunable ZZZZZZ interaction between two transmon qubits with fixed frequencies and fixed coupling, induced by driving both transmons off-resonantly. We show tunable coupling over one order of magnitude larger than the static coupling, and change the sign of the interaction, enabling cancellation of the idle coupling. Further, this interaction is amenable to large quantum processors: the drive frequency can be flexibly chosen to avoid spurious transitions, and because both transmons are driven, it is resilient to microwave crosstalk. We apply this interaction to implement a controlled phase (CZ) gate with a gate fidelity of 99.43(1)%99.43(1)\%99.43(1)% as measured by cycle benchmarking, and we find the fidelity is limited by incoherent errors.
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 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.