Learning t-doped stabilizer states

Abstract

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 , 2 t ) and exhibits an exponentially small probability of failure.