  One of the primary objectives in the field of quantum state learning is to
develop algorithms that are time-efficient for learning states generated from
quantum circuits. Earlier investigations have demonstrated time-efficient
algorithms for states generated from Clifford circuits with at most $\log(n)$
non-Clifford gates. However, these algorithms necessitate multi-copy
measurements, posing implementation challenges in the near term due to the
requisite quantum memory. On the contrary, using solely single-qubit
measurements in the computational basis is insufficient in learning even the
output distribution of a Clifford circuit with one additional $T$ gate under
reasonable post-quantum cryptographic assumptions. In this work, we introduce
an efficient quantum algorithm that employs only nonadaptive single-copy
measurement to learn states produced by Clifford circuits with a maximum of
$O(\log n)$ non-Clifford gates, filling a gap between the previous positive and
negative results.
