Efficient Learning of Quantum States Prepared With Few Non-Clifford Gates

arXiv:2305.13409v4 Announce Type: replace-cross
Abstract: We give a pair of algorithms that efficiently learn a quantum state prepared by Clifford gates and $O(\log n)$ non-Clifford gates. Specifically, for an $n$-qubit state $|\psi\rangle$ prepared with at most $t$ non-Clifford gates, our algorithms use $\mathsf{poly}(n,2^t,1/\varepsilon)$ time and copies of $|\psi\rangle$ to learn $|\psi\rangle$ to trace distance at most $\varepsilon$.
The first algorithm for this task is more efficient, but requires entangled measurements across two copies of $|\psi\rangle$. The second algorithm uses only …

abstract algorithms arxiv cs.lg gates learn quant-ph quantum qubit state type