Putting the Magic in Surface Codes

Quantum computing devices are noisy, and hence large-scale quantum computation will require error correction to perform large scale fault tolerant computation. As such, classical simulation of error correction protocols is of great interest to study their performance and prepare for large devices. One such error correction protocol is the surface code, where several physical qubits are used to implement a single logical qubit. Despite the large number of qubits and entanglement required, the surface code consists only of Clifford gates, and as such can be simulated efficiently using stabilizer simulator methods. However, stabilizer simulators are not able to simulate non-Clifford gates, such as the T gate, and cannot simulate arbitrary quantum circuits. While there are techniques to extend stabilizer simulators to support T gates, these tend to scale poorly with the number of T gates. Here we use the Stabilizer Tensor Network simulator [Masot-Llima et al, arXiv:2403.08724], which can simulate many more T gates before scaling exponentially badly, to simulate magic state distillation, injection, and full algorithms on the surface code.