Superconducting qubits now switch states in just 10 nanoseconds

Superconducting qubits have significantly contributed towards the development of a universal quantum computer. The team balanced the need for long coherence, reaching up to hours in a ‘heavy’ regime, with simplified control by introducing a qubit architecture featuring real-time tunable bit-flip protection. This approach uses base-band flux-pulses to realize high-fidelity single- and two-qubit gates. The researchers expect this concept of real-time wavefunction control will extend to other hardware-protected qubit designs.

Real-Time Bit-Flip Protection in Superconducting Qubits

Institute of Science and Technology Austria researchers achieved high-fidelity single- and two-qubit gates using base-band flux-pulses lasting approximately 10 nanoseconds, a speed previously difficult to attain without microwave signals. This control method distinguishes their approach to superconducting qubit design, focusing on real-time tunable bit-flip protection as a means of simultaneously maximizing coherence and simplifying control.

The team’s qubit architecture balances these traditionally conflicting goals through manipulation of wavefunction overlap and corresponding matrix elements, offering a novel pathway toward more stable and manageable quantum systems. The newly demonstrated control scheme operates in two distinct regimes, a ‘heavy’ regime prioritizing information storage and a ‘light’ regime facilitating rapid control, and the energy relaxation time in the ‘heavy’ regime can reach hours for fluxons positioned in near-degenerate ground states.

This extended coherence, recently detailed in a separate publication, is now coupled with the ability to perform gate operations on timescales previously reserved for more complex control systems. Simulations indicate that this performance is not achieved at the expense of phase coherence, a common trade-off in bit-flip protected cat qubits, and the team expects to be limited primarily by T₂ and potential relaxation errors during gate operations.

The qubit’s tunability stems from flux control of a dc-SQUID, which alters either the Josephson energy (E_J) or the charging energy (E_C) of the circuit, and the phase matrix element φ₀₁ is proportional to the charge matrix element =, serving as an indicator of protection from energy relaxation. The energy splitting of the qubit states, E₀₁, remains comparable across both qubit types as a function of, while φ₀₁ is substantially suppressed for the fluxonium.

This suppression is key to the architecture’s ability to maintain both long coherence and fast gate speeds, a combination that addresses a significant challenge in superconducting qubit development. “We proposed a new type of superconducting qubit: a fluxonium qubit with exponentially tunable bit-flip protection,” the team wrote in their publication, emphasizing the potential for broader application of their findings.

The tunability, they explain, is achieved through flux control of a dc-SQUID, and the qubits are operated in two regimes, with the ‘heavy’ regime demonstrating energy relaxation times estimated to scale exponentially with E_J. The team’s work represents a step toward more robust and versatile superconducting qubits capable of sustaining complex quantum computations.

Fluxonium Qubit Regimes: ‘Heavy’ and ‘Light’ Characteristics

Balancing information storage with active control capabilities is enabled by the architecture of these fluxonium qubits, allowing for operation in distinct regimes. In the ‘heavy’ regime, transitions between fluxon states are exponentially suppressed, a characteristic that intrinsically shields quantum information from decoherence. This protection, however, previously complicated efforts to actively manipulate the qubit’s state, a challenge now addressed through a novel approach to qubit design.

Simulations using parameters of E_C/h = 0. 25 GHz, E_L/h = 0. 5 GHz, and varying E_J/h from 1 to 12 GHz demonstrate this interplay between protection and control. This is accomplished by dynamically adjusting the qubit’s potential using flux control of a dc-SQUID, effectively switching between the ‘heavy’ and ‘light’ regimes as needed.

The circuit’s design allows it to operate between the limits of a heavy fluxonium and an IST-qubit, and for short durations, between a typical fluxonium and a flux qubit, optimizing performance for both storage and manipulation. The researchers detail how the capacitive coupling between qubits, defined by a Hamiltonian including terms for single qubit behavior and a coupling energy of E_Cg/h = 6. 67 GHz, further enhances control.

This allows for precise control over the qubit’s energy spectrum, as demonstrated by simulations showing the energy spectrum of two capacitively coupled qubits versus an external flux, with the flux of the first qubit fixed at = 0. 44Φ₀. 30 GHz, E_L1/h = 0. 52 GHz for the first qubit and similar values for the second, demonstrate the feasibility of this design.

The researchers found that the tunability of E_J/h, ranging from 1 to 12 GHz, is important for achieving this balance. The ability to switch between regimes allows for optimized performance during both information storage and gate operations.

Tunable Josephson Energy Enables Fast Gate Control

Researchers detail two distinct circuit designs enabling this control: a fluxonium where the Josephson energy is altered by manipulating an external magnetic flux, and a fluxonium employing a switchable capacitance. These circuits allow for rapid transitions between qubit states with disjoint support in the phase coordinate, a key characteristic for minimizing unwanted interactions. Simulations demonstrate the potential for high-fidelity single-qubit gates using the fluxonium, achieving a closed-system gate infidelity of 1-F_C = 2× 10^-5 with a 7. 5 nanosecond flat-top Gaussian pulse.

This pulse, with a full width at half maximum (FWHM) of 7. 5 ns and a flat-top duration of 1. 5 ns, was applied with the Josephson energy set to 0. 9872 GHz. The ability to implement a Hadamard gate, a π rotation around the axis σ_H = (σ_x + σ_z)/ √2, with such precision highlights the effectiveness of this approach.

The design of these tunable circuits addresses a long-standing challenge in superconducting qubit development: balancing long coherence times with simplified control capabilities. While previous work has explored similar concepts for oscillator-stabilized flux qubits and flux qubits, this approach offers a unique combination of features. The fluxonium, for example, uses a dc-SQUID to alter the effective Josephson energy, allowing for dynamic control of the qubit’s potential landscape. “Experimentally, fast flux control has already been used for the implementation of high-fidelity single qubit gates, by the means of non-adiabatic Landau-Zener transitions,” the researchers write.

Tunable-E_J Fluxonium Circuit Design and Hamiltonian

One approach uses a tunable Josephson energy within a fluxonium qubit, achieved by replacing a single Josephson junction with a dc-SQUID, a superconducting loop sensitive to external magnetic flux. Altering the flux through the dc-SQUID effectively changes the qubit’s Josephson energy, allowing for in-situ tuning of the potential landscape governing its behavior. An alternative design focuses on effectively switching a large capacitance connected to the fluxonium circuit, again using a dc-SQUID as the control element.

This ‘switch’ functions as a short circuit when the dc-SQUID’s flux approaches zero, and an open circuit at half-flux quantum, enabling dynamic modification of the qubit’s potential. The Hamiltonian for this fluxonium incorporates terms representing the charging energy, inductive energy and Josephson energy, alongside interactions between charge and flux variables. This manipulation of the potential, rather than directly altering the Josephson energy, increases the wavefunction overlap of the qubit states.

The team simulates time evolution using the Lindblad equation, accounting for multiple decay channels to extract the T₁ value. Although the population may not decay exponentially due to these multiple channels, other measurable quantities can be used to determine a single decay constant. The parameters of these new qubits are similar to those of the IST-qubit, suggesting comparable coherence properties. The ability to dynamically tune the qubit potential provides a novel method for balancing long coherence times with the demand for fast and precise control, an essential step toward building scalable and reliable quantum processors.

Tunable-E_C Fluxonium: Circuitry and Potential Landscape

The resulting circuits allow for fast gate operations between fluxon states with minimal overlap in the phase coordinate, a critical factor in qubit performance. This rapid control is facilitated by tuning the qubit to the ‘light’ regime, where a flux pulse lowers the potential barrier, effectively modifying the energy landscape. At a specific flux point of ${\Phi }_{ext}/{\Phi }_0$ = 0. 5, the potential approximates a double-well, localizing fluxon states in individual wells and defining the computational basis states.

In the heavy regime, transitions between the two lowest fluxon states are exponentially suppressed with the energy barrier separating them. This intrinsic protection however complicates active control of the qubit. In the light regime on the other hand, the matrix elements are substantially larger and the reduced energy dispersion leads to a smaller flux-noise sensitivity.

This regime – with the Blochnium being the most extreme – is more suitable for control at the cost of lower bit-flip protection. Physically, the qubit’s operation relies on identifying the symmetric and anti-symmetric superpositions of fluxon states as | + ⟩ and |-⟩, corresponding to the |0⟩ and |1⟩ computational basis states on the Bloch sphere, with only an exponentially small correction as seen in cat states.

10 Nanosecond Flux Pulses for High-Fidelity Gates

The approach relies on real-time, tunable bit-flip protection, allowing for rapid manipulation of qubit states without sacrificing stability. This fast control is facilitated by transitioning the qubit into a ‘light’ regime, where high-fidelity operations occur on nanosecond timescales, circumventing the need for traditional microwave signals. Researchers propose two distinct mechanisms for tuning the qubit’s potential, enabling the implementation of single- or two-qubit gates with precise control over local phase rotations.

Simulations, using parameters of E_C/h = 0. 25 GHz, E_L/h = 0. The architecture’s ability to decouple qubit subspaces in the ‘heavy’ regime, due to a vanishingly small charge matrix element, further enhances its performance. When operating in this mode, the qubits exhibit minimal interaction, preserving coherence. Conversely, tuning both qubits to the ‘light’ regime induces hybridization of their states, enabling fast, high-fidelity two-qubit gates.

Analysis reveals a substantial difference, a factor of approximately ${10}^5$ to ${10}^6$, in energy relaxation times between the ‘heavy’ and ‘light’ regimes around the working points of the single- and two-qubit gates. The team anticipates that this approach will allow for the creation of more robust and scalable quantum systems.

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