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Cat qubits provide appealing building blocks for quantum computing. Theyexhibit a tunable noise bias yielding an exponential suppression of bit flipswith the average photon number and a protection against the remaining phaseerrors can be ensured by a simple repetition code. We here quantify the cost ofa repetition code and provide valuable guidance for the choice of a large scalearchitecture using cat qubits by realizing a performance analysis based on thecomputation of discrete logarithms on an elliptic curve with Shor's algorithm.By focusing on a 2D grid of cat qubits with neighboring connectivity, wepropose to implement 2-qubit gates via lattice surgery and Toffoli gates withoff-line fault-tolerant preparation of magic states through projectivemeasurements and subsequent gate teleportations. All-to-all connectivitybetween logical qubits is ensured by routing qubits. Assuming a ratio betweensingle- and two-photon losses of 1e-5 and a cycle time of 500 ns, we showconcretely that such an architecture can compute a 256-bit elliptic curvelogarithm in 9 h with 126133 cat qubits and on average 19 photons by cat state.We give the details of the realization of Shor's algorithm so that the proposedperformance analysis can be easily reused to guide the choice of architecturefor others platforms.

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