Fault-tolerant quantum computation with repetition cat-qubits.

Quantum error correcting codes provide, when operated below the threshold, an arbitrary good protection against noise, thus solving the decoherence problem for quantum information processing. However, the actual implementation of the most promising ones, such as the surface code, comes at the price of tremendous physical resources to reach a sufficient level of protection. We present a 1D repetition code based on the so-called cat-qubits as a viable candidate for a massive reduction in the hardware requirements for universal and fault-tolerant quantum computation. The cat-qubits that are stabilized by a two-photon driven dissipative process, exhibit a tunable noise bias where the effective bit-flips are exponentially suppressed with the average number of photons. Exploiting this noise bias, we build, at the level of the repetition cat-qubit, a universal set of fully protected logical gates. Remarkably, this construction avoids the costly magic states preparation, distillation and injection, even for non-Clifford gates.