Learning t-doped stabilizer states

Understand

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.