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 $\mathsf{poly}(n,2^t,1/\epsilon)$ 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.

使用单次测量，以多项式时间和样本量来学习由具有最多 t 个单量子比特非克利福德门的电路输出的 n 量子比特态的得到的跟踪距离为 ε 的最新算法。

少非克利福门单比特态高效学习二：单次测量

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

We give an algorithm that efficiently learns a quantum state prepared by
Clifford gates and $O(\log(n))$ non-Clifford gates. Specifically, for an
$n$-qubit state $\lvert \psi \rangle$ prepared with at most $t$ non-Clifford
gates, we show that $\mathsf{poly}(n,2^t,1/\epsilon)$ time and copies of
$\lvert \psi \rangle$ suffice to learn $\lvert \psi \rangle$ to trace distance
at most $\epsilon$. This result follows as a special case of an algorithm for
learning states with large stabilizer dimension, where a quantum state has
stabilizer dimension $k$ if it is stabilized by an abelian group of $2^k$ Pauli
operators. We also develop an efficient property testing algorithm for
stabilizer dimension, which may be of independent interest.

本研究报告提出了一种有效的算法，可以通过使用 Clifford 门和 O (log (n)) 非 Clifford 门来高效地学习一个量子态，并介绍了一种用于学习大稳定子维度的算法，其中量子态的稳定子维度使用一个由 2^k 个 Pauli 操作符的交换群来稳定。此外，我们还开发了一种有效的质检算法来测试稳定子维度。