Researchers have demonstrated a new control strategy for fluxonium qubits using picosecond single-flux-quantum (SFQ) pulses generated by Josephson digital circuits. The team overcame a key limitation in controlling these qubits, where standard protocols for transmon qubits prove inefficient, leading to signal leakage or slow processing speeds. Multilevel simulations show single-qubit gate fidelities exceeding 99.99% with two complementary protocols, one robust to qubit variations and another that substantially accelerates gate operation, establishing SFQ-based control as a viable path toward scalable quantum computation.

Fluxonium Qubit Characteristics: Anharmonicity and Energy Scales

This configuration highlights a key characteristic of fluxonium qubits: strong anharmonicity, where the energy difference between the first and second excited states is significantly larger than that between the ground and first excited states, $E_{2} - E_{1}$ ≫ $E_{1} - E_{0}$ . This pronounced anharmonicity effectively isolates the computational subspace comprised of the |0⟩ and |1⟩ states from higher-energy levels, minimizing errors during quantum operations.

The fluxonium qubit’s unique properties stem from its design, combining aspects of both flux and charge qubits, and relies on a large inductive shunt to suppress sensitivity to static offset charge fluctuations. The ratio of Josephson energy to inductive energy, E_J/E_L, dictates the number of potential wells in the qubit’s landscape, while the ratio of Josephson to charging energy, E_J/E_C, governs the tunneling rate between these wells.

SFQ Control Challenges for Low-Frequency Fluxonium

Low-frequency fluxonium qubits benefit from a digital control approach that uses picosecond single-flux-quantum (SFQ) pulse packets, circumventing limitations inherent in traditional transmon qubit control methods. Standard SFQ protocols prove inefficient for these qubits due to an asymmetry in flux and charge couplings, resulting in either excessive leakage from the qubit’s computational states or unacceptably long gate times. This inefficiency stems from the unique spectral properties of fluxonium qubits, which are defined by low characteristic frequencies and require stringent filtering and isolation from technical and thermal noise.

The development of SFQ-based cryogenic control represents an attractive route for realizing the full potential of fluxonium qubits in scalable processors, moving beyond analog microwave control techniques. While SFQ control has already proven viable for transmon qubits, adapting it to fluxonium demands new solutions that address the qubit’s low-frequency spectrum and the imbalance between charge and flux degrees of freedom.

Simulations demonstrate that optimized pulse sequences can achieve single-qubit gate fidelities above 99.99%; the simpler protocol remains robust under moderate variations of qubit parameters and flux bias, while the combined protocol preserves high fidelity while substantially accelerating the gate. These results are based on numerical simulations using parameters including $A_{φ} / h$ = 0.03 GHz and a pulse duration of τ = 15 ps. The simulations tracked the populations of the qubit basis states, $P_{0, 1} (t)$ and higher leakage levels, $P_{2, 3} (t)$ , confirming the suppression of unwanted transitions.

The ability to drive these qubits with high-frequency SFQ pulse packets offers a simple, analytically transparent and robust approach to high-fidelity single-qubit control, capitalizing on the strong anharmonicity of fluxonium qubits. This anharmonicity effectively suppresses leakage to non-computational states, a critical factor in maintaining coherence and minimizing errors.

High-Frequency Flux-Only SFQ Pulse Protocol for Control

Fluxonium qubits now benefit from control sequences employing 13 precisely timed single-flux-quantum pulses within each qubit period, a method yielding improved fidelity over previous attempts. Adapting control strategies from transmon qubits proved inefficient for these low-frequency systems, resulting in either unacceptable signal leakage or prolonged gate durations, a challenge the researchers directly addressed through protocol optimization. The team’s work focuses on overcoming limitations stemming from the asymmetry between flux and charge couplings within the fluxonium qubit itself, a key factor in achieving reliable quantum operations.

The newly developed control scheme uses high-frequency SFQ pulse packets delivered through the flux channel, providing a robust and analytically transparent approach to single-qubit control, and demonstrating a significant departure from conventional microwave techniques. Simulations reveal that increasing the frequency of the pulse generator, the rate at which pulses are repeated, directly improves gate fidelity, a critical metric for quantum computation.

Specifically, the optimized sequence, using 15 cycles of these pulses, achieves a gate fidelity exceeding the 10^-4 threshold, even with moderate variations in qubit parameters. The system parameters used in these simulations include a Josephson energy of 5. 71 GHz, a charging energy of 1. 3 GHz, and an inductive energy of 0. 59 GHz, values representative of current fluxonium qubit designs. Numerical results confirm that the X_π gate fidelity meets the established criterion under these conditions, indicating a viable path toward scalable manipulation.

Further analysis focused on the impact of the high-frequency generator frequency, revealing a direct correlation between pulse repetition rate and gate fidelity. The researchers note the importance of precise timing in achieving high-performance quantum gates.

Across the representative parameter sets, this combined approach realizes X_π gates in approximately 17-27 nanoseconds, and X_(π/2) and Y_(π/2) gates in approximately 8. 5-13. 5 nanoseconds, consistently maintaining fidelities at or above 99. This high-frequency approach offers a simpler, more analytically transparent method for controlling fluxonium qubits compared to earlier strategies that relied on “on-ramp” and “off-ramp” segments to improve fidelity, but still resulted in longer gate times. The combined effect of optimized pulse structure and high-frequency control establishes a foundation for faster, more accurate, and scalable fluxonium qubit manipulation.

Multilevel Simulations Demonstrate 99.99% Single-Qubit Fidelity

Multilevel simulations revealed single-qubit gate fidelities exceeding 99. 99% using two distinct control protocols for fluxonium qubits, a result that pushes the boundaries of accuracy in quantum computation. The high fidelity was evaluated using a metric that considers both the accuracy of the gate operation and the suppression of unwanted transitions to higher energy states within the qubit. One protocol relies on high-frequency, phase-shifted single-flux-quantum (SFQ) pulse packets applied to both flux and charge control channels, achieving a quadrature configuration that enhances the resonant drive while minimizing unwanted interactions.

The simulations also revealed the importance of spectral filtering in minimizing leakage, a common source of error in quantum gates. This effect is fully accounted for in the multilevel simulations. The work highlights the potential of digital control techniques to overcome limitations in controlling complex qubits like the fluxonium.

Combined Phase-Shifted Flux and Charge Control Protocol

The combined protocol detailed in this work achieves single-qubit gate fidelities exceeding 99.99% by strategically applying phase-shifted flux and charge pulse sequences, a significant advancement in controlling fluxonium qubits. This approach enhances the resonant drive while simultaneously reducing the time required to complete a quantum gate operation, addressing a key limitation of earlier control methods. Researchers focused on optimizing control despite the low transition frequency and asymmetric couplings inherent in fluxonium qubits, a challenge that previously hindered efficient digital control.

This systematic approach revealed that the optimal control sequences consistently used differing numbers of flux and charge pulses, effectively treating each as independent control variables. The team considered three representative sets of fluxonium parameters during optimization, ensuring the protocol’s adaptability to a range of qubit designs.

SFQ-Based Control as a Route to Scalable Fluxonium Manipulation

The ability to precisely manipulate quantum states hinges on the speed and accuracy of control signals, and a new approach uses picosecond single-flux-quantum (SFQ) pulses to accelerate operations on fluxonium qubits. To address these limitations, researchers developed two complementary protocols, each designed to optimize control over the fluxonium qubit. The first protocol employs high-frequency SFQ pulse packets, repeating them once per qubit period to provide a straightforward and robust method for single-qubit control.

The second protocol takes a more detailed approach, combining phase-shifted flux and charge pulse sequences to enhance the resonant drive and significantly reduce the duration of each gate operation. 99%. The simpler, high-frequency packet protocol prioritizes stability, while the combined protocol focuses on speed, preserving high fidelity while substantially accelerating the gate. “These results demonstrate that picosecond SFQ pulses can enable fluxonium control that is both fast and precise,” the researchers report, highlighting the potential for scalable quantum processors.

The integration of fluxonium qubits with digital SFQ control offers a promising framework for addressing challenges in qubit manipulation and system integration. Researchers also intend to explore independently tunable generators for the two control quadratures and to develop two-qubit gates within the same framework, ultimately aiming to experimentally benchmark the protocols in a real-world quantum computing environment. The numerical results were obtained using the Lobachevsky supercomputer with the support of the program for the development of regional scientific and educational mathematical centers.

Fluxonium Circuit Model: Josephson Junction Parameters

Fluxonium qubits exhibit a unique energy profile stemming from a large inductive component within their circuit design, typically realized through Josephson junction arrays or superconducting nanowires. The Josephson energy, defined as E_J =, where I_c is the critical current and *Φ₀ = h/2e* represents the magnetic flux quantum, is a key parameter in establishing this characteristic. Fluxonium qubits are designed with a charging energy significantly larger than the inductive energy, E_L ≪ E_C, to create a strongly anharmonic spectrum and well-defined, low-lying energy levels.

Typical ratios fall within the range of ~ 2-10, with all energies satisfying E_L < E_C < E_J. The potential governing the fluxonium’s behavior is described by U(φ) = – E_J cosφ, where φ denotes the phase difference across the Josephson junction.

Deviations from ideal parameter values, however, can introduce vulnerabilities; specifically, they reduce first-order protection against low-frequency magnetic noise, although the control matrix elements n₍₀₁₎ and *φ₍₀₁₎* remain relatively stable for small variations. To account for these shifts, control amplitude recalculations are performed for each parameter variation, with changes in E_L directly impacting L_q and subsequently A_φ. This performance is further enhanced by a second protocol that combines independently optimized flux and charge single-flux-quantum (SFQ) pulse packets with a relative quarter-period shift to amplify the resonant drive.

👉 More information
🗞 High-Speed Control of a Fluxonium Qubit via Picosecond Pulses from Josephson Digital Circuits
✍️ M. V. Bastrakova and D. S. Pashin (Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia); V. A. Vozhakov (Joint venture Quantum Technologies, Moscow, Russia); N. V. Klenov (Moscow Technical University of Communications and Informatics, Moscow, Russia); I. I. Soloviev (Russian Quantum Center, Skolkovo, Moscow, Russia)
🧠 ArXiv: https://arxiv.org/abs/2611.14358

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