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arXiv:2402.04495 · Physical Review X

Using Bifluxon Tunneling to Protect the Fluxonium Qubit

Waël Ardati, Sébastien Leger, Shelender Kumar, Vishnu Narayanan Suresh, Dorian Nicolas, Cyril Mori, Francesca d'Esposito, Tereza Vakhtel, O. Buisson, Quentin Ficheux, Nicolas Roch

Published Oct 16, 2024• 14 citations

Abstract

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

DOI: 10.1103/physrevx.14.041014

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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

We develop and characterize a symmetry-protected superconducting qubit that offers simultaneous exponential suppression of energy decay from charge and flux noises, and dephasing from flux noise.The qubit consists of a Cooper-pair box (CPB) shunted by a superinductor, forming a superconducting loop.Provided the offset charge on the CPB island is an odd number of electrons, the qubit potential corresponds to that of a cos (φ/2) Josephson element, preserving the parity of fluxons in the loop via Aharonov-Casher interference.In this regime, the logical-state wavefunctions reside in disjoint regions of Hilbert space, thereby ensuring protection against energy decay.By switching the protection on, we observe a tenfold increase of the decay time, reaching up to 100 μs.Though the qubit is sensitive to charge noise, the sensitivity is much reduced in comparison with the charge qubit, and the charge-noise-induced dephasing time of the current device exceeds 1 μs.Implementation of full dephasing protection can be achieved in the next-generation devices by combining several cos(φ/2) Josephson elements in a small array.

Fluxons in a superconducting loop can be coherently coupled by quantum phase slips occurring at a weak link such as a Josephson junction. If Cooper pair tunneling at the junction occurs through a resonant level, then $2\ensuremath{\pi}$ quantum phase slips are suppressed, and fluxons are predominantly coupled by $4\ensuremath{\pi}$ quantum phase slips. We analyze this scenario by computing the coupling between fluxons as the level is brought into resonance with the superconducting condensate. The results indicate that the $4\ensuremath{\pi}$-dominated regime can be observed directly in the transition spectrum for circuit parameters typical of a fluxonium qubit. We also show that if the inductive energy of the loop is much smaller than the plasma frequency of the junction, then the low-energy Hamiltonian of the circuit is dual to that of a topological superconducting island. These findings can inform experiments on bifluxon qubits as well as the design of novel types of protected qubits.

Encoding a qubit in logical quantum states with wave functions characterized by disjoint support and robust energies can offer simultaneous protection against relaxation and pure dephasing. One of the most promising candidates for such a fully protected superconducting qubit is the 0-π circuit [Brooks et al., Phys. Rev. A 87, 052306 (2013)]. Here we realize the proposed circuit topology in an experimentally obtainable parameter regime, where the ground-state degeneracy is lifted but the qubit is still largely noise protected. More precisely, the logical states of this qubit feature disjoint support and are exponentially protected against relaxation and exponentially (first order) protected against dephasing due to charge (flux) noise. We name the resultant device the "soft 0-π qubit."Multitone spectroscopy measurements reveal the energy-level structure of the system, which can be precisely described by a simple two-mode Hamiltonian. Using a Raman-type protocol, we exploit a higher-lying charge-insensitive energy level of the device to realize coherent population transfer and logical operations. The measured relaxation (T1 = 1.6 ms) and dephasing (TR = 9 μs, T2E = 25μs) times demonstrate that the soft 0-π circuit not only broadens the family of superconducting qubits but also constitutes an important step toward quantum computing with intrinsically protected superconducting qubits.

We describe a superconducting qubit derived from operating a properly designed fluxonium circuit in a zero magnetic field. The qubit has a frequency of about 4 GHz and an energy relaxation quality factor Q ≈ 0.7 × 10 7 , even though the dielectric loss quality factor of the circuit components is in the low- 10 5 range. The Ramsey coherence time exceeds 100 μ s , and the average fidelity of Clifford gates is benchmarked to F > 0.999 . These figures are expected to improve with optimized fabrication and measurement procedures. Our work establishes a ready-to-use “partially protected” superconducting qubit functioning in the frequency range of conventional transmons. Published by the American Physical Society 2024

High-coherence qubits, which can store and manipulate quantum states for long times with low error rates, are necessary building blocks for quantum computers. Here we propose a driven superconducting erasure qubit, the Floquet fluxonium molecule, which minimizes bit-flip rates through disjoint support of its qubit states and suppresses phase flips by a novel second-order insensitivity to flux-noise dephasing. We estimate the bit-flip, phase-flip, and erasure rates through numerical simulations, with predicted coherence times of approximately 50 ms in the computational subspace and erasure lifetimes of about 500 μ s . We also present a protocol for performing high-fidelity single-qubit rotation gates via additional flux modulation, on timescales of roughly 500 ns, and propose a scheme for erasure detection and logical readout. Our results demonstrate the utility of drives for building new qubits that can outperform their static counterparts. Published by the American Physical Society 2024

Coherence limitations of a Fourier-engineered

\cos(2\varphi)

transmon qubit

Intrinsically protected superconducting qubits are a promising route toward enhancing coherence times and advancing hardware towards applications in quantum computing. The

\cos(2\varphi)

qubit achieves protection against qubit relaxation by allowing only the coherent tunneling of pairs of Cooper pairs, resulting in Cooper-pair parity symmetry and thereby suppressing charge-induced errors. In this work, we experimentally realize a

\cos(2\varphi)

qubit by Fourier engineering the energy-phase relation in a multi-junction superconducting circuit. Using an interference-based architecture, we are able to suppress the odd harmonics of an effective qubit potential and we observe good agreement between the measured transition spectrum and the effective theoretical model. We further investigate the energy relaxation time as a function of external flux and find that the qubit lifetime at the flux symmetry point is limited by

1/f

flux noise. This strong sensitivity arises from residual fluctuations in the first harmonic, which possesses a large prefactor despite being nominally canceled. In contrast, a fluxonium qubit with a similar energy spectrum and noise amplitude is less affected by flux noise, highlighting a key challenge for interference-based protection schemes.