Magic state injection on the rotated surface code

Fault-tolerant quantum computing based on the surface code requires magic states to achieve universality. The initially prepared magic states have low fidelity and need to be purified by a costly procedure called magic state distillation. The high spatial-temporal cost for distillation can be reduced by improving the fidelity of initial magic states. Prior works have investigated state injection approaches on the regular surface code. In this work, we propose a magic state injection method for the rotated surface code that requires fewer physical qubits to encode one logical qubit. Analytical results show that our method could achieve lower logical error rates than the state-of-the-art approach for the regular surface code in 1. When both the two-qubit gate and single-qubit operation error rates are p, the new method results in a logical error rate to 34p/15 compared to 46p/15 in 1. This fidelity improvement and fewer qubit encoding requirement would help reduce the overhead of fault-tolerant quantum computation, which is crucial for practical implementation in the near term.