Flux qubits achieve all-to-all links via adiabatic ZZ interactions.

The work proposes a baseband-driven adiabatic ZZ gate that achieves all-to-all qubit connectivity without relying on tunable couplers. This approach uses a common cavity to entangle any selected qubit pair, maintaining dc-biasing at the qubits’ flux sweet spot, and remains effective even with many qubits coupled to the cavity. The protocol is robust against frequency fluctuations and simulations show comparable fidelities for two simultaneous gates within a four-qubit register.

Flux Qubit Architecture for All-to-All Connectivity

Flux qubits sidestep wiring complexities through a newly detailed gate design. This level of precision, demonstrated through numerical simulations, suggests a viable path toward reducing error rates in quantum computations and scaling superconducting processors. This approach maintains direct current biasing at the qubits’ flux sweet spot, a critical operating point for stability and performance. By applying strong drives selectively through local flux lines at frequencies far below qubit transitions, the system adiabatically tilts quantization axes, generating an effective longitudinal ZZ interaction.

The strength of this coupling is not determined by resonance conditions, but rather by the amplitudes and relative phase of the applied drives, offering a significant degree of control and flexibility. This method of control also addresses a common challenge in scaling quantum processors: frequency crowding and spectral collisions. As the number of qubits increases, their transition frequencies tend to cluster, leading to unwanted interactions and errors.

The adiabatic ZZ gate, however, avoids the need to tune qubit frequencies away from their optimal operating points, mitigating these issues. The design inherently suppresses static ZZ crosstalk, a phenomenon where unintended interactions occur between qubits sharing a common cavity. Simulations involving a 20-qubit processor, with qubit frequencies spanning 7-8 GHz in 50 MHz increments, indicate a residual ZZ coupling contributing an infidelity of order ${10}^{–7}$ over a 55 ns gate duration.

The robustness of this architecture extends to fluctuations in qubit frequencies. The quasi-static flux noise, a common source of error, is actively refocused by the drive itself, shifting the noise sensitivity away from low-frequency components. This is achieved through the harmonic structure of the applied drive, which contains only odd harmonics of the drive frequency. The resulting second-order shift, estimated to be less than 1/(2Δ_k) where ${\Delta }_k$ is the qubit transition frequency, remains minimal even under noisy conditions.

This capability suggests that the architecture is not limited to sequential processing, potentially increasing computational speed and efficiency. The gate duration of 55 ns, used in the simulations, is sufficiently short that the resulting gate error remains below the thresholds required for leading quantum error correction codes. For a gradiometer flux qubit with a relaxation time (T_1) of 50 microseconds, the error associated with this gate duration is approximately ${10}^{–3}$.

The design’s reliance on a shared cavity bus, combined with low-frequency adiabatic control and frequency-selective activation, provides a pathway to highly connected superconducting processors. The use of a common cavity, while enabling all-to-all connectivity, does not introduce significant crosstalk, maintaining the integrity of quantum information. Elena Lupo, Nguyen H. Le, Eran Ginossar, and Michael Stern’s work offers a promising alternative to existing architectures, potentially simplifying the construction and control of larger, more powerful quantum computers.

The ability to maintain high fidelity even with a large number of qubits coupled to the cavity is a key advantage of this approach. The simulations demonstrate that the protocol remains effective even as the processor scales, suggesting a viable path toward building truly scalable quantum systems. This is particularly important as the demand for increased qubit connectivity grows, driven by the need to tackle increasingly complex computational problems. The findings suggest that flux qubits, with their large anharmonicities, offer a compelling platform for realizing highly connected and robust quantum processors.

Adiabatic ZZ Gate via Baseband-Driven Flux Qubits

Numerical simulations reveal that this baseband-driven adiabatic ZZ gate achieves coherent gate errors below ${10}^{–4}$, a level of precision essential for scalable quantum computation, by carefully controlling the interaction between flux qubits. This performance stems from a design that avoids resonance conditions, a common limitation in other gate architectures, and instead relies on the precise amplitude and phase of applied drives to tune coupling strength.

The protocol’s success hinges on maintaining qubits at their flux sweet spot, a point of minimal sensitivity to control errors, throughout the gate operation. The architecture achieves all-to-all connectivity without the need for tunable couplers, a departure from many current superconducting processor designs, by using a shared cavity to mediate interactions between any selected qubit pair.

This approach simplifies the physical wiring and control complexity typically associated with scaling up quantum processors, as the coupling strength is determined by drive parameters rather than physical tuning elements. This method also mitigates the impact of low-frequency flux noise, a significant source of decoherence in superconducting qubits, by refocusing the noise through the drive itself. “The low drive frequencies have a further practical advantage: they lie outside the stop band of the Bragg filters used to suppress near-resonant spontaneous emission,” the paper states.

The researchers modeled flux qubits as effective two-level systems transversely coupled to a single cavity mode, using a Hamiltonian that incorporates the qubit transition frequencies, applied drives and qubit-cavity coupling strengths. By carefully selecting the drive frequencies to be an integer multiple of a period, the local rotations and conditional displacements induced by the drives cancel out, leaving only the desired ZZ rotation.

This adiabatic approach allows for precise control over the qubit interactions without requiring precise tuning of qubit frequencies or resonance conditions. “A flux fluctuation $\delta {\epsilon }_k$ enters as $\delta {\epsilon }_k{\sigma }_k^x/2$, whose longitudinal component in the adiabatic frame, (ε_k/η_k) $\delta {\epsilon }_k{\sigma }_k^z/2$, sets the first-order flux sensitivity of the driven qubit,” the paper explains.

The residual second-order shift, resulting from this refocusing, is shown to be comparable to that of a static sweet spot, indicating that the drive does not compromise the inherent noise protection of the flux qubit design. This architecture allows for all-to-all intra-core connectivity, enabling efficient implementation of complex quantum algorithms.

Mitigation of Crosstalk in Superconducting Flux Qubits

This approach envisions multiple multi-qubit registers, each a “core” with its own cavity bus, linked by frequency-tunable couplers enabling long-range interactions between qubits residing in different cores. The design allows for the creation of a 400-qubit quantum processor by interconnecting 20 cores, each housing 20 flux qubits, a significant increase over current architectures. The use of these frequency-tunable couplers, specifically SQUID-tunable superconducting resonators, allows for activation, tuning, or deactivation of the effective interaction between cavity modes, creating nonlocal bosonic modes that couple flux qubits across cores.

Applying matched, low-frequency drives to a selected inter-core qubit pair then generates an adiabatic ZZ interaction, extending pair-selective entanglement beyond a single core. This modularity addresses the wiring and control overhead that typically accompany scaling, as it reduces the need for extensive direct connections between every qubit in the system.

The researchers detail how activating an inter-core coupler hybridizes resonator modes, creating delocalized normal modes spanning the two cores and mediating longitudinal interactions between flux qubits in different cores. This contrasts with architectures reliant on tunable couplers directly connecting neighboring qubits, which can introduce spectral collisions and parasitic ZZ interactions as processor size increases. The team’s approach uses the intrinsic properties of flux qubits, specifically their large anharmonicity and gradiometric designs, to suppress static ZZ crosstalk, a critical factor for maintaining coherence in highly connected processors.

Quantifying this crosstalk, the work defines a metric ζ = $E_{11}–E_{10}–E_{01}$ + $E_{00}$, where the energies include shifts induced by the cavity, spectator qubits and higher qubit levels. These shifts can be estimated perturbatively, and the researchers demonstrate that the nearly two-level character of flux qubits minimizes this effect, essential for scaling to highly connected processors.

The design also benefits from operating qubits at their flux sweet spots, where transition frequencies exhibit first-order insensitivity to flux noise, further enhancing coherence. The team’s proposed gate design is not limited to intra-core connectivity; it extends to inter-core entanglement through the tunable couplers. The ability to selectively activate interactions between arbitrary qubit pairs, without relying on resonance conditions or precise frequency tuning, simplifies control and calibration requirements.

This provides a more robust and flexible approach to qubit control, reducing the sensitivity to variations in qubit frequencies and other system parameters. The researchers suggest that current flux qubit fabrication technologies are capable of supporting a system comprising up to 20 interconnected cores, each with 20 flux qubits, demonstrating the feasibility of this approach.

The work explicitly notes that the scheme is well suited to qubits that closely approximate ideal two-level systems, and flux qubits provide a natural superconducting implementation. This is because the suppression of leakage, even under strong driving, is important for maintaining the fidelity of quantum operations. “Varying the coupler frequency allows the effective interaction between the cavity modes to be activated, tuned, or parked near zero,” the team writes, outlining the dynamic control offered by this modular design.

This performance was established for two simultaneous gates operating within a four-qubit register, indicating the potential for parallel quantum operations. The simulations assessed gate fidelity within the cavity’s 0-photon subspace, a critical parameter for evaluating the viability of this architecture. The simulations reveal broad regions where infidelity remains below the ${10}^{–4}$ threshold, even when an additional “spectator” qubit shares the cavity, confirming that idle qubits do not substantially degrade gate performance under typical conditions. However, sharp peaks in infidelity do emerge, attributable to resonance between the spectator qubit and those actively undergoing gate operations.

The results highlight a diagonal feature in the gate error map where pair selectivity is lost when both pairs are driven at the same frequency, alongside additional narrow features arising from these Floquet sidebands. The simulations demonstrate that the frequency-selection mechanism effectively distinguishes between the two pairs, enabling simultaneous operations without introducing unwanted cross-pair phases.

The researchers found that the overall increase in gate infidelity with decreasing detuning can be attributed to hybridization of the two qubits via a static cavity-mediated XX interaction. This effect is further detailed in the supporting materials, providing a deeper understanding of the underlying physics governing the gate performance.

The amplitude of the drives, denoted as A, was optimized alongside local Z rotations to minimize infidelity, ensuring the highest possible gate fidelity for the simulated conditions. The simulations used identical drives with $A_1$ = $A_2$ = A, a parameter that fixes the $R_k^x$ rotations within the gate decomposition. The protocol’s robustness extends beyond the presence of spectator qubits.

This scalability is key for building larger, more complex quantum processors capable of tackling increasingly challenging computational problems. The adiabatic nature of the gate, achieved by slowly tilting the quantization axes of the qubits, minimizes the impact of noise and fluctuations, contributing to the high fidelity observed in the simulations.

The simulations employed a specific set of parameters, including a detuning of ${\Delta }_1/2\pi$ = 7. 00 GHz and a frequency fluctuation of ${\delta }_{12}/2\pi$ = 250 MHz, to assess the gate’s performance under realistic conditions. The gate duration and drive frequency were consistent with those used in the two-qubit analysis, allowing for a direct comparison of the results. The optimized gate error was then mapped as a function of the drive frequencies for the two entangled pairs, revealing the regions of highest fidelity and identifying potential sources of error.

“There are wide regions where the infidelity remains below ${10}^{–4}$, comparable to the spectator-free result of at similar parameters, confirming that an idle qubit sharing the cavity does not degrade the gate under generic conditions,” the researchers report. This finding emphasises the robustness of the design and its potential for scaling to larger qubit registers.

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