Nearly Time-Optimal Pure State Tomography with Pauli Measurements

Abstract

We give an algorithm for pure state tomography with near-optimal copy and time complexity using only single-qubit measurements. Specifically, given $\tilde{O}(2^n/ϵ)$ copies of an unknown $n$-qubit pure state $|\psi ⟩$, the algorithm performs only nonadaptive Pauli measurements, runs in time $\tilde{O}(2^n/ϵ)$, and outputs $|\hat{\psi }⟩$ with fidelity at least $1-ϵ$ with $|\psi ⟩$ with high probability. This is the first algorithm for pure state tomography that achieves near-optimal running time.