Bias-Preserving Entanglement of Kerr-Cat Qubits with an ATS Coupler

Introduction

Kerr‑cat qubits have emerged as a promising platform for fault‑tolerant quantum computing because their logical states are protected against bit‑flip errors by an exponential suppression that grows with the photon number. The remaining challenge is to perform two‑qubit gates that preserve this bias: phase‑flip errors that occur during the gate must not be converted into bit‑flips, which would erode the advantage of the cat encoding. The recent work by Yurtseven et al. proposes a hardware solution—a novel asymmetrically threaded SQUID (ATS) parametric coupler—that delivers high‑fidelity, bias‑preserving entangling operations without the need for intricate pulse shaping.

The ATS Coupler Concept

The ATS coupler is built from a superconducting quantum interference device whose two loops are threaded with different magnetic fluxes. This asymmetry translates into a photon‑number‑dependent interaction strength between the control and target Kerr‑cat modes. By deliberately engineering a larger coupling for the control mode than for the target, the authors create a situation where the dominant interaction swaps excitations only when the control is in the logical "1" state, while leaving the target largely untouched otherwise. The resulting effective Hamiltonian implements a controlled‑X (CX) gate that respects the cat‑qubit bias: phase‑flip errors remain confined to the phase degree of freedom and do not induce unwanted bit‑flips.

Performance Highlights from Simulation

Using a full circuit‑level Hamiltonian, the authors numerically simulate the gate dynamics under realistic parameters:

• Gate time: 50 ns, substantially faster than adiabatic schemes that require hundreds of nanoseconds to avoid leakage.
• Intrinsic fidelity: 99.69 % in the absence of photon loss, indicating that non‑adiabatic leakage is already well suppressed by the photon‑number asymmetry.
• Noise bias: With a single‑photon loss rate of 100 kHz, the protocol yields a bias of ≈9.9 × 10³, more than 500‑fold improvement over a conventional, non‑bias‑preserving CX gate.

These numbers demonstrate that the ATS coupler can serve as a practical building block for concatenated cat‑qubit error‑correction schemes, where maintaining a high noise bias across many layers is essential.

Practical Implications and Outlook

The ATS approach sidesteps several engineering hurdles that have limited previous bias‑preserving gate proposals. Because the asymmetry is built into the static circuit layout, the gate does not rely on finely tuned, time‑dependent pulse envelopes; a simple resonant drive suffices. This simplicity reduces calibration overhead and improves robustness against control‑line imperfections. Moreover, the fast gate duration mitigates the impact of photon loss, which scales with the total operation time.

For experimental teams working with superconducting cat qubits, integrating an ATS coupler involves adding a modestly sized SQUID with two independent flux bias lines. The required flux offsets are within the range of standard cryogenic flux‑bias hardware, and the coupler can be fabricated using existing planar processes. Future work will likely explore scaling to multi‑qubit lattices, where a network of ATS couplers could enable parallel, bias‑preserving entanglement across a processor.

Conclusion

The asymmetrically threaded SQUID coupler offers a clear path toward fast, high‑fidelity, bias‑preserving two‑qubit gates for Kerr‑cat qubits. By leveraging photon‑number asymmetry, the design achieves >99.6 % intrinsic fidelity in 50 ns and sustains a noise bias near 10⁴ under realistic loss rates. These results reinforce the viability of cat‑qubit architectures for scalable, fault‑tolerant quantum computing and provide a concrete hardware component that experimental groups can adopt without extensive pulse‑shaping complexity.