A unitary encoder for surface codes

The quantum surface code is a promising candidate to achieve fault-tolerant quantum computation and has been realized in various hardware platforms including recently with Rydberg atom qubits. Rydberg-atom qubits in particular have demonstrated scalability and the capability of long-range interactions, but the measurements are more challenging. Consequently, the unitary encoder is a potential alternative for encoding logical information into surface codes, where the code size is increased by unitary gates instead of traditionally by stabilizer measurements.

In this work, we propose a unitary encoder circuit based on the unitary code conversion between rotated and regular surface codes. Our approach utilizes a depth-4 circuit to double the code size, offering a logarithmic time complexity in the final code size and with a 50% lower constant factor compared to the previous approach based on the multi-scale entanglement renormalization ansatz (MERA). While this approach, like other unitary encoding approaches, is not fault-tolerant, we numerically investigate its breakeven performance. We also explore the potential of our encoding scheme for applications such as magic state injection where the standard lattice-surgery-based method also has an overall code distance limited by the initial code size.