Stabilizer Tensor Networks with Magic State Injection

This Letter augments the recently introduced stabilizer tensor network (STN) protocol with magic state injection, reporting a new framework with significantly enhanced ability to simulate circuits with an extensive number of non-Clifford operations. Specifically, for random T-doped N-qubit Clifford circuits the computational cost of circuits prepared with magic state injection scales as O[poly(N)] when the circuit has t≲N T gates compared to an exponential scaling for the STN approach, which is demonstrated in systems of up to 200 qubits. In the case of the hidden bit shift circuit, a paradigmatic benchmarking system for extended stabilizer methods with a tunable amount of magic, we report that our magic state injected STN framework can efficiently simulate 4000 qubits and 320T gates. These findings provide a promising outlook for the use of this protocol in the classical modeling of quantum circuits that are conventionally difficult to simulate efficiently.