Nearly Time-Optimal Pure State Tomography with Pauli Measurements

TL;DR

This paper presents a nearly time-optimal algorithm for pure state tomography using only single-qubit Pauli measurements, achieving high fidelity with minimal copies and efficient runtime.

Contribution

It introduces the first pure state tomography algorithm that attains near-optimal time complexity with simple Pauli measurements and nonadaptive measurement strategies.

Findings

Uses $ ilde{O}(2^n/\epsilon)$ copies of the state.

Runs in $ ilde{O}(2^n/\epsilon)$ time.

Outputs a state with fidelity at least $1-\epsilon$.

Abstract

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