Computing 256-bit elliptic curve discrete logarithms in 26 days on a fault-tolerant trapped-ion quantum computer with 20,000 qubits

One of the strengths of our recently proposed Walking Cat Architecture for a trapped-ion quantum computer is that it is straightforward to extend and optimize for a specific application. As a proof-of-concept, here we present such optimizations for solving the $256$-bit elliptic curve discrete logar