Fault-tolerant encoders for a high-rate symplectic double code

Last year, we proposed an efficient fault-tolerant encoder for a [[30,6,5]] symplectic double code[1]. The advantage of this code is its compactness, in addition to its high encoding rate (20%), allowing for early experimental realization. However, naive fault-tolerant preparation of logical states encoded with this code requires large numbers of ancilla qubits. In this work, our encoder can reduce resource overheads while keeping low logical error rates by detecting crucial errors during encoding with as few auxiliary qubits as possible. We also developed an arbitrary-state encoder for this code to enable universal quantum computation with the [[30,6,5]] code.

[1] N. Kanomata and H. Goto, arXiv:2509.15457 (2025).