Dissipatively Stabilized 0-n Fock Qubits for Noise-Biased Quantum Computing
Noise-biased qubits have bit-flip errors that are exponentially suppressed relative to phase-flip errors, and offer a promising route toward fault-tolerant quantum computing. However, this bias can be compromised during gate operations with non-biased control qubits. To address this limitation, we propose a "0-n" Fock qubit architecture that maintains the noise bias by encoding information in the ground state and n-th excited state of a nonlinear multi-level system, such as a transmon. This encoding is achieved via a dissipative stabilization that acts as decay and gain for lower and upper intermediate levels, respectively. We first analytically demonstrate that bit-flip errors are exponentially suppressed with the number of levels. Then, we present a practical implementation using a multi-mode lossy filter to achieve the frequency-selective dissipation. Finally, we numerically demonstrate that bit-flip probabilities approaching $10^{-8}$ are achievable for controlled-X gates on cat qubits using the 0-n qubit as an ancilla with $n \geq 9$ (i.e. ten or more levels), for realistic experimental parameters. Building on this, we simulate syndrome extraction in a repetition code, achieving logical error rates in the megaquop regime with only a distance of $d=9$.