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arXiv:2003.02775 · Physical Review Letters

Suppression of Unwanted Z Z Interactions in a Hybrid Two-Qubit System

Jaseung Ku, Xuexin Xu, Markus Brink, David C. McKay, Jared Hertzberg, Mohammad H. Ansari, B. L. T. Plourde

Published Nov 11, 2020• 111 citations
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Abstract

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.

DOI
10.1103/physrevlett.125.200504

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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.
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)%.
For building a scalable quantum processor with superconducting qubits, the ZZ interaction is of great concert because of relevant for implementing two-qubit gates, and the close contact between gate infidelity and its residual. Two-qubit gates with fidelity beyond fault-tolerant thresholds have been demonstrated using the ZZ interaction. However, as the performance of quantum processor improves, the residual static-ZZ can also become a performance-limiting factor for quantum gate operations and quantum error correction. Here, we introduce a scalable superconducting architecture for addressing this challenge. We demonstrate that by coupling two superconducting qubits with opposite-sign anharmonicities together, high-contrast ZZ interaction can be realized in this architecture. Thus, we can control ZZ interaction with high on/off ratio for implementing two-qubit CZ gate, or suppress it during the two-qubit gate operations using XY interaction (e.g. iSWAP). Meanwhile, the ZZ crosstalk related to neighboring spectator qubits can also be heavily suppressed in fixed coupled multi-qubit systems. This architecture could provide a promising way towards scalable superconducting quantum processor with high gate fidelity and low qubit crosstalk.
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.
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.
The superconducting transmon qubit is currently a leading qubit modality for quantum computing, but the gate performance in a quantum processor with transmons is often insufficient to support the running of complex algorithms for practical applications. It is thus highly desirable to further improve gate performance. Due to the weak anharmonicity of a transmon, a static ZZZZZZ interaction between coupled transmons commonly exists, undermining the gate performance and, in the long term, it can become performance limiting. Here, we theoretically explore a promising parameter region in an all-transmon system to address this issue. We show that a feasible parameter region, where the ZZZZZZ interaction is heavily suppressed, while leaving the XYXYXY interaction with an adequate strength to implement two-qubit gates, can be found for all-transmon systems. Thus, two-qubit gates, such as a cross-resonance gate or an iswap gate, can be realized without a detrimental effect from the static ZZZZZZ interaction. To illustrate this, we demonstrate that an iswap gate with a fast gate speed and dramatically lower conditional phase error can be achieved. By scaling up to a large-scale transmon quantum processor, especially for cases with fixed coupling, addressing errors, idling errors, and crosstalk that arise from the static ZZZZZZ interaction can also be strongly suppressed.