Learning t-doped stabilizer states

In this paper, we present a learning algorithm aimed at learning states obtained from computational basis states by Clifford circuits doped with a finite number t of T-gates. The algorithm learns an exact tomographic description of t-doped stabilizer states in terms of Pauli observables. This is possible because such states are countable and form a discrete set. To tackle the problem, we introduce a novel algebraic framework for t-doped stabilizer states, which extends beyond T-gates and includes doping with any kind of local non-Clifford gate. The algorithm requires resources of complexity poly(n,2t) and exhibits an exponentially small probability of failure.