  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
$\text{poly}(n,2^t)$ and exhibits an exponentially small probability of
failure.
