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arXiv:2303.01102 · Physical Review Research

Fast universal control of a flux qubit via exponentially tunable wave-function overlap

Svend Krøjer, Anders Enevold Dahl, Kasper Sangild Christensen, Morten Kjærgaard, Karsten Flensberg

Published Apr 18, 2024• 8 citations
arXivHTMLPDF

Abstract

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

DOI
10.1103/physrevresearch.6.023064

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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
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.
Fully tunable flux qubits offer in-situ and independent controls of their energy potential asymmetry and tunnel barrier, making them versatile tools for quantum computation and the study of decoherence sources. However, only short coherence times have been demonstrated so far with this type of qubit. Here, we present a capacitively shunted flux qubit featuring improved relaxation times up to T1_11​ = 25 μ s and a 20-GHz wide theoretical frequency tunability range at the flux-insensitive sweet spot, of which a 3-GHz range was shown. As a model application, we demonstrate detection of two-level tunneling defects in a frequency range spanning one octave.
Abstract Fully tunable flux qubits offer in-situ and independent controls of their energy potential asymmetry and tunnel barrier, making them versatile tools for quantum computation and the study of decoherence sources. However, only short coherence times have been demonstrated so far with this type of qubit. Here, we present a capacitively shunted flux qubit featuring improved relaxation times up to T 1 = 25 μ s and a 20-GHz wide theoretical frequency tunability range at the flux-insensitive sweet spot, of which a 3-GHz range was shown. As a model application, we demonstrate detection of two-level tunneling defects in a frequency range spanning one octave.
Encoding quantum information in quantum states with disjoint wave-function support and noise-insensitive energies is the key behind the idea of qubit protection. While fully protected qubits are expected to offer exponential protection against both energy relaxation and pure dephasing, simpler circuits may grant partial protection with currently achievable parameters. Here, we study a fluxonium circuit in which the wave functions are engineered to minimize their overlap while benefiting from a first-order-insensitive flux sweet spot. Taking advantage of a large superinductance ( L ∼ 1 μ H ), our circuit incorporates a resonant tunneling mechanism at zero external flux that couples states with the same fluxon parity, thus enabling bifluxon tunneling. The states | 0 ⟩ and | 1 ⟩ are encoded in wave functions with parities 0 and 1, respectively, ensuring a minimal form of protection against relaxation. Two-tone spectroscopy reveals the energy-level structure of the circuit and the presence of 4 π quantum-phase slips between different potential wells corresponding to m = ± 1 fluxons, which can be precisely described by a simple fluxonium Hamiltonian or by an effective bifluxon Hamiltonian. Despite suboptimal fabrication, the measured relaxation ( T 1 = 177 ± 3 μ s ) and dephasing ( T 2 E = 75 ± 5 μ s ) times not only demonstrate the relevance of our approach but also open an alternative direction toward quantum computing using partially protected fluxonium qubits. Published by the American Physical Society 2024
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.