Efficient Learning of Quantum States Prepared With Few Non-Clifford Gates II: Single-Copy Measurements

Recent work has shown that $n$-qubit quantum states output by circuits with at most $t$ single-qubit non-Clifford gates can be learned to trace distance $\epsilon$ using $\mathsf{p}\mathsf{o}\mathsf{l}\mathsf{y}(n,2^t,1\mathrm{/}\epsilon )$ time and samples. All prior algorithms achieving this runtime use entangled measurements across two copies of the input state. In this work, we give a similarly efficient algorithm that learns the same class of states using only single-copy measurements.