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arXiv:2408.16617 · Physical Review Letters

Long-Range Z Z Interaction via Resonator-Induced Phase in Superconducting Qubits

Xiang Bo Deng, Wen Zheng, Xudong Liao, Haoyu Zhou, Yangyang Ge, Jie Zhao, Dong Lan, Xinsheng Tan, Yu Zhang, Shaoxiong Li, Yang Yu

Published Jan 16, 2025• 17 citations
arXivHTMLPDF

Abstract

Superconducting quantum computing emerges as one of the leading candidates for achieving quantum advantage. However, a prevailing challenge is the coding overhead due to limited quantum connectivity, constrained by nearest-neighbor coupling among superconducting qubits. Here, we propose a novel multimode coupling scheme using three resonators driven by two microwaves, based on the resonator-induced phase gate, to extend the ZZ interaction distance between qubits. We demonstrate a controlled-Z (cz) gate fidelity exceeding 99.9% within 160 ns at a free spectral range (FSR) of 1.4 GHz, and by optimizing driving pulses, we further reduce the residual photon to nearly 10^{-3} within 100 ns at a FSR of 0.2 GHz. These facilitate the long-range cz gate over separations reaching submeters, thus significantly enhancing qubit connectivity and making a practical step toward the scalable integration and modularization of quantum processors. Specifically, our approach supports the implementation of quantum error correction codes requiring high connectivity, such as low-density parity check codes that pave the way to achieving fault-tolerant quantum computing.

DOI
10.1103/physrevlett.134.020801

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Superconducting quantum computing emerges as one of the leading candidates for achieving quantum advantage. However, a prevailing challenge is the coding overhead due to limited quantum connectivity, constrained by nearest-neighbor coupling among superconducting qubits. Here, we propose a novel multimode coupling scheme using three resonators driven by two microwaves, based on the resonator-induced phase gate, to extend the ZZ interaction distance between qubits. We demonstrate a controlled-Z (cz) gate fidelity exceeding 99.9% within 160 ns at a free spectral range (FSR) of 1.4 GHz, and by optimizing driving pulses, we further reduce the residual photon to nearly 10^{-3} within 100 ns at a FSR of 0.2 GHz. These facilitate the long-range cz gate over separations reaching submeters, thus significantly enhancing qubit connectivity and making a practical step toward the scalable integration and modularization of quantum processors. Specifically, our approach supports the implementation of quantum error correction codes requiring high connectivity, such as low-density parity check codes that pave the way to achieving fault-tolerant quantum computing.
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.
Scalable superconducting quantum processors require balancing critical constraints in coherence, control complexity, and spectral crowding. Fixed-frequency architectures suppress flux noise and simplify control via all-microwave operations but remain limited by residual ZZ crosstalk. Here we propose a microwave-activated three-qubit gate protocol for fixed-frequency transmon qubits in the large-detuning regime (∣Δ∣≫g|Δ| \gg g∣Δ∣≫g), leveraging the third-order nonlinear interaction to coherently exchange ∣001⟩↔∣110⟩\ket{001} \leftrightarrow \ket{110}∣001⟩↔∣110⟩ states. By incorporating a phase-compensated optimization protocol, numerical simulations demonstrate a high average gate fidelity exceeding 99.9%99.9\%99.9%. Systematic error analysis identifies static long-range ZZ coupling as the dominant error source in multi-qubit systems, which can be suppressed via operations in the large-detuning regime (∼1\sim 1∼1 GHz). The protocol maintains process fidelities exceeding 98%98\%98% under decoherence, while demonstrating intrinsic robustness to fabrication-induced parameter variations and compatibility with existing all-microwave two-qubit gate architectures. This hardware-efficient strategy advances scalable quantum computing systems by improving coherence properties, reducing spectral congestion, and expanding the experimental toolkit for error-resilient quantum operations in the noisy intermediate-scale quantum era.
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.
Entangling gates between neighboring physical qubits are essential for quantum error correction. Implementing them in an all-microwave manner simplifies signal routing and control apparatus of superconducting quantum processors. We propose and experimentally demonstrate an all-microwave controlled-Z (CZ) gate that achieves high fidelity while suppressing residual ZZ interactions. Our approach utilizes a fixed-frequency transmon coupler and multi-path coupling, thereby sufficiently reducing the net transverse interaction between data transmons to suppress residual ZZ interactions. The controlled phase arises from the dispersive frequency shift of the ∣gf⟩|gf\rangle∣gf⟩$\unicode{x2013}$∣eg⟩|eg\rangle∣eg⟩ transition between the coupler and one of the data transmons conditioned on the state of the other data transmon. Driving the transitions at the midpoint of two dispersively shifted resonance frequencies induces state-dependent geometric phases to achieve the CZ gate. Crucially, with this scheme, we can maintain a small net transverse interaction between two data transmons while increasing the coupling between the data and coupler transmons to accelerate the CZ-gate speed. Additionally, we measure the coupler state after the gate to detect a subset of decoherence-induced failures that occur during the gate operation. These events constitute erasure errors with known locations, enabling erasure-aware quantum error-correcting codes to improve future logical qubit performance.
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.
Superconducting quantum processors offer a promising path toward practical quantum computing. However, building a fault-tolerant quantum computer with millions of superconducting qubits is hindered by wiring density, packaging constraints, and fabrication yield. Interconnecting medium-scale processors via low-loss superconducting links provides a promising alternative. Yet, achieving high-fidelity two-qubit gates across such channels remains difficult. Here, we show that a multimode coaxial cable can mediate high-contrast interaction between spatially separated superconducting qubits. Leveraging interference between cable modes, we can implement high-fidelity controlled-Z and ZZ-free iSWAP gates by simply modulating qubit frequencies. Numerical simulations under realistic coherence and coupling parameters predict fidelities above 99% for both gate schemes. Our approach provides a versatile building block for modular superconducting architectures and facilitates distributed quantum error correction and large-scale fault-tolerant quantum computing.