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Fast Gates for Bit-Flip Protected Superconducting Qubits

C. A. Siegele, А. Соколова, Lucky N. Kapoor, Farid Hassani, J. M. Fink

Published Jul 31, 2026• 0 citations
Publisher

Abstract

Superconducting qubits offer an unprecedentedly high degree of flexibility in terms of circuit encoding and parameter choices. However, in designing the qubit parameters, one typically faces the conflicting goals of long coherence times and simple control capabilities. Both are determined by the wavefunction overlap of the qubit basis states and the corresponding matrix elements. Here, we address this problem by introducing a qubit architecture with real-time tunable bit-flip protection. In the first, the “heavy” regime, the energy relaxation time can be on the order of hours for fluxons located in two near-degenerate ground states, as recently demonstrated in Ref. [Hassani ., (2023)]. The second, “light” regime, facilitates high-fidelity control on nanosecond timescales without the need for microwave signals. We propose two different tuning mechanisms of the qubit potential and show that base-band flux-pulses of around 10 ns are sufficient to realize a universal set of high-fidelity single- and two-qubit gates. This realizes a hardware-efficient and strongly noise-biased qubit platform with analogies to cat qubits with the potential for efficient quantum error correction. We expect that the introduced concept of fast and real-time wavefunction control can also be applied to other hardware-protected qubit designs.

DOI
10.1103/1kmf-6fz9

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Superconducting qubits offer an unprecedentedly high degree of flexibility in terms of circuit encoding and parameter choices. However, in designing the qubit parameters, one typically faces the conflicting goals of long coherence times and simple control capabilities. Both are determined by the wavefunction overlap of the qubit basis states and the corresponding matrix elements. Here, we address this problem by introducing a qubit architecture with real-time tunable bit-flip protection. In the first, the “heavy” regime, the energy relaxation time can be on the order of hours for fluxons located in two near-degenerate ground states, as recently demonstrated in Ref. [Hassani ., (2023)]. The second, “light” regime, facilitates high-fidelity control on nanosecond timescales without the need for microwave signals. We propose two different tuning mechanisms of the qubit potential and show that base-band flux-pulses of around 10 ns are sufficient to realize a universal set of high-fidelity single- and two-qubit gates. This realizes a hardware-efficient and strongly noise-biased qubit platform with analogies to cat qubits with the potential for efficient quantum error correction. We expect that the introduced concept of fast and real-time wavefunction control can also be applied to other hardware-protected qubit designs.
Superconducting qubits offer an unprecedentedly high degree of flexibility in terms of circuit encoding and parameter choices. However, in designing the qubit parameters one typically faces the conflicting goals of long coherence times and simple control capabilities. Both are determined by the wavefunction overlap of the qubit basis states and the corresponding matrix elements. Here, we address this problem by introducing a qubit architecture with real-time tunable bit-flip protection. In the first, the `heavy' regime, the energy relaxation time can be on the order of hours for fluxons located in two near-degenerate ground states, as recently demonstrated in Ref. [Hassani et al., Nat.~Commun.~14 (2023)]. The second, `light' regime, on the other hand facilitates high-fidelity control on nanosecond timescales without the need for microwave signals. We propose two different tuning mechanisms of the qubit potential and show that base-band flux-pulses of around 10 ns are sufficient to realize a universal set of high-fidelity single- and two-qubit gates. We expect that the concept of real-time wavefunction control can also be applied to other hardware-protected qubit designs.
Quantum bits (qubits) are prone to several types of errors due to uncontrolled interactions with their environment. Common strategies to correct these errors are based on architectures of qubits involving daunting hardware overheads. A hopeful path forward is to build qubits that are inherently protected against certain types of errors, so that the overhead required to correct remaining ones is significantly reduced. However, the foreseen benefit rests on a severe condition: quantum manipulations of the qubit must not break the protection that has been so carefully engineered. A recent qubit - the cat-qubit - is encoded in the manifold of metastable states of a quantum dynamical system, thereby acquiring continuous and autonomous protection against bit-flips. Here, in a superconducting circuit experiment, we implement a cat-qubit with bit-flip times exceeding 10 seconds. This is a four order of magnitude improvement over previous cat-qubit implementations. We prepare and image quantum superposition states, and measure phase-flip times above 490 nanoseconds. Most importantly, we control the phase of these quantum superpositions without breaking bit-flip protection. This experiment demonstrates the compatibility of quantum control and inherent bit-flip protection at an unprecedented level, showing the viability of these dynamical qubits for future quantum technologies.
The heavy-fluxonium circuit is a promising building block for superconducting quantum processors due to its long relaxation and dephasing time at the flux-frustration point. However, the suppressed charge matrix elements and low transition frequency make it challenging to perform fast single-qubit gates using standard protocols. We report on new protocols for reset, fast coherent control,and readout that allow high-quality operation of the qubit with a 14 MHz transition frequency, an order of magnitude lower in energy than the ambient thermal energy scale. We utilize higher levels of the fluxonium to read out the qubit state and to initialize the qubit with 97% fidelity corresponding to cooling it to 190 μK. Instead of using standard microwave pulses, we control the qubit only with fast-flux pulses, generating control fields much larger than the qubit frequency. We develop a universal set of gates based on nonadiabatic Landau-Zener transitions that act in 20-60 ns, less than the single-qubit Larmor period. We measure qubit coherence of T1,T2e∼300 μs for a fluxonium in a 2D architecture and realize single-qubit gates with an average gate fidelity of 99.8% as characterized by randomized benchmarking.
The Kerr-cat qubit is a bosonic qubit in which multiphoton Schrödinger cat states are stabilized by applying a two-photon drive to an oscillator with a Kerr nonlinearity. The suppressed bit-flip rate with increasing cat size makes this qubit a promising candidate to implement quantum error correction codes tailored for noise-biased qubits. However, achieving strong light-matter interactions necessary for stabilizing and controlling this qubit has traditionally required strong microwave drives that heat the qubit and degrade its performance. In contrast, increasing the coupling to the drive port removes the need for strong drives at the expense of large Purcell decay. By integrating an effective band-block filter on chip, we overcome this trade-off and realize a Kerr-cat qubit in a scalable 2D superconducting circuit with high coherence. This filter provides 30 dB of isolation at the qubit frequency with negligible attenuation at the frequencies required for stabilization and readout. We experimentally demonstrate quantum nondemolition readout fidelity of 99.6% for a cat with eight photons. Also, to have high-fidelity universal control over this qubit, we combine fast Rabi oscillations with a new demonstration of the X ( π / 2 ) gate through phase modulation of the stabilization drive. Finally, the lifetime in this architecture is examined as a function of the cat size of up to ten photons in the oscillator, achieving a bit-flip time higher than 1 ms and only a linear increase in the phase-flip rate, in good agreement with the theoretical analysis of the circuit. Our qubit shows promise as a building block for fault-tolerant quantum processors with a small footprint. Published by the American Physical Society 2024
Fast, high-fidelity control and readout of protected superconducting qubits are fundamentally challenging due to their inherent insensitivity. We propose a flux qubit variation which enjoys a tunable level of protection against relaxation to resolve this outstanding issue. Our qubit design, the double-shunted flux qubit (DSFQ), realizes a generic double-well potential through its three-junction ring geometry. One of the junctions is tunable, making it possible to control the barrier height and thus the level of protection. We analyze single- and two-qubit gate operations that rely on lowering the barrier. We show that this is a viable method that results in high-fidelity gates as the noncomputational states are not occupied during operations. Further, we show how the effective coupling to a readout resonator can be controlled by adjusting the externally applied flux while the DSFQ is protected from decaying into the readout resonator. Finally, we also study a double-loop gradiometric version of the DSFQ which is exponentially insensitive to variations in the global magnetic field, even when the loop areas are nonidentical. Published by the American Physical Society 2024
Abstract Achieving fast gates and long coherence times for superconducting qubits presents challenges, typically requiring either a stronger coupling of the drive line or an excessively strong microwave signal to the qubit. To address this, we introduce on-chip filters of the qubit drive exhibiting a stopband at the qubit frequency, thus enabling long coherence times and strong coupling at the subharmonic frequency, facilitating fast single-qubit gates, and reduced thermal load. The filters exhibit an extrinsic relaxation time of a few seconds while enabling sub-10-ns gates with subharmonic control. Here we show up to 200-fold improvement in the measured relaxation time at the stopband. Furthermore, we implement subharmonic driving of Rabi oscillations with a π pulse duration of 12 ns. Our demonstration of on-chip filters and efficient subharmonic driving in a two-dimensional quantum processor paves the way for a scalable qubit architecture with reduced thermal load and noise from the control line.