Performance Analysis of a Repetition Cat Code Architecture: Computing 256-bit Elliptic Curve Logarithm in 9 Hours with 126133 Cat Qubits

Understand

Cat qubits provide appealing building blocks for quantum computing.

• They exhibit a tunable noise bias yielding an exponential suppression of bit flips with the average photon number and a protection against the remaining phase errors can be ensured by a simple repetition code.
• We here quantify the cost of a repetition code and provide valuable guidance for the choice of a large scale architecture using cat qubits by realizing a performance analysis based on the computation of discrete logarithms on an elliptic curve with Shor's algorithm.
• By focusing on a 2D grid of cat qubits with neighboring connectivity, we propose to implement 2-qubit gates via lattice surgery and Toffoli gates with off-line fault-tolerant preparation of magic states through projective measurements and subsequent gate teleportations.