Cat-qubit-stabilization scheme using a voltage-biased Josephson junction

Abstract

dc voltage–biased Josephson junctions have recently been used in superconducting circuits for Hamiltonian engineering, demonstrating microwave amplification, single-photon sources, and entangled photon generation. Compared with more conventional approaches based on parametric pumps, this solution typically enables larger interaction strengths. In the context of quantum information, a two-to-one photon interaction can stabilize cat qubits, where bit-flip errors are exponentially suppressed, promising significant resource savings for quantum error correction. This work investigates how the dc bias approach to Hamiltonian engineering can benefit cat qubits. We find a simple circuit design that is predicted to showcase a two-to-one photon exchange rate larger than that of the parametric pump–based implementation while dynamically averaging typically resonant parasitic terms such as Kerr terms and cross-Kerr-terms. In addition to addressing qubit stabilization, we propose using injection locking with a cat qubit–adapted frequency filter to prevent long-term drifts of the cat qubit angle associated with dc voltage noise. The whole scheme is simulated without rotating-wave approximations, highlighting the amplitude of related oscillatory effects in cat-qubit-stabilization schemes. This study lays the groundwork for the experimental realization of such a circuit.

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