Local Stochastic Factored Gradient Descent for Distributed Quantum State Tomography

We propose a distributed Quantum State Tomography (QST) protocol, named Local Stochastic Factored Gradient Descent (Local SFGD), to learn the low-rank factor of density matrix over set local machines. QST is canonical procedure characterize state quantum system, which we formulate as stochastic non-convex smooth optimization problem. Physically, estimation helps characterizing amount noise introduced by computation. Theoretically, prove convergence SFGD for general class restricted strongly convex/smooth loss functions. converges locally small neighborhood global optimum at linear rate with constant step size, while it exactly sub-linear diminishing sizes. With proper initialization, results imply convergence. validate our theoretical findings numerical simulations on Greenberger-Horne-Zeilinger (GHZ) state.