Repetition-Cat Codes
Stacking a classical repetition code on bit-flip-protected cat qubits corrects the remaining phase flips, giving a lean path to a logical qubit.
A biased-noise architecture
A repetition-cat code combines two ideas. The inner layer is a set of cat qubits whose bit-flip rate is exponentially suppressed by the coherent-state amplitude. The outer layer is a simple classical repetition code that corrects the one error type the cat qubits still suffer, phase flips. Because only one error type remains, a one-dimensional repetition code suffices where a full two-dimensional surface code would otherwise be required.
Why one dimension is enough
A repetition code against phase flips has distance equal to the number of cat qubits in the chain. As long as the inner bit-flip rate stays negligible, the logical error rate falls exponentially with chain length. The whole scheme has an effective threshold on the phase-flip rate, and the qubit count grows linearly with the desired distance rather than quadratically.
- Inner cat qubits suppress bit flips exponentially in photon number.
- Outer repetition code handles the surviving phase flips.
- Overhead scales linearly with distance, not quadratically.
- Correctness depends on gates preserving the noise bias.
The appeal is overhead. If the bias is strong and stable, a modest chain of cat qubits reaches a low logical error rate with far fewer physical modes than an unbiased 2D code. This is one of the most concrete proposals for reducing the resource cost of a first useful logical qubit.
The risks are all about the assumptions. If gates leak bit-flip error back in, or if the achievable amplitude is limited, the bias weakens and the one-dimensional shortcut no longer holds, forcing a fallback to a two-dimensional code. The engineering effort therefore concentrates on bias-preserving CNOT and measurement operations.