Cost of Classical Strong Simulation of the T-Gate Magic State

The stabilizer rank of qubit T-gate magic state has been postulated to grow slowest with increasing number of qubits, suggesting that the T-gate is in this sense the most efficient state outside the Clifford subtheory that can be simulated by classical strong simulation that nevertheless extends this subtheory to quantum universality. Unfortunately, the T-gate magic state’s stabilizer rank scaling is not formally known and has only been found numerically for up to seven qubits. We examine this problem from the perspective of the cost of strong classical simulation of discrete Wigner functions in systems with odd dimension and compare with the known results for qubits. To accomplish this, we develop and exploit relationships between the number of critical points of quantum states’ Wigner functions in a periodized stationary phase approximation and spanning decompositions of stabilizer states that are closely related to the stabilizer rank. We report on the trends we observe.