The Quantum Gradient Algorithm is (almost) Optimal for Quantum State Tomography

Abstract

Quantum state tomography is the process of obtaining a description of an unknown quantum state. We show that when we have access to a state-preparation unitary, modifications of the quantum gradient algorithm yield (almost) optimal algorithm, improving the dependence on precision of previously known tomography algorithm. This has important applications in some quantum optimization algorithms, where obtaining a description of the quantum state allows us to recover a description of the solution.