Local Stochastic Factored Gradient Descent for Distributed Quantum State Tomography

• URL: http://arxiv.org/abs/2203.11579v1
• Date: Tue, 22 Mar 2022 10:03:16 GMT
• Title: Local Stochastic Factored Gradient Descent for Distributed Quantum State Tomography
• Authors: Junhyung Lyle Kim, Mohammad Taha Toghani, C\'esar A. Uribe, Anastasios Kyrillidis
• Abstract summary: Local Factored Gradient Descent (Local SFGD) Quantum State Tomography (QST) protocol. Local SFGD converges locally to a small neighborhood of the global at a linear rate with a constant step size.
• Score: 10.623470454359431
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose a distributed Quantum State Tomography (QST) protocol, named Local Stochastic Factored Gradient Descent (Local SFGD), to learn the low-rank factor of a density matrix over a set of local machines. QST is the canonical procedure to characterize the state of a quantum system, which we formulate as a stochastic nonconvex smooth optimization problem. Physically, the estimation of a low-rank density matrix helps characterizing the amount of noise introduced by quantum computation. Theoretically, we prove the local convergence of Local SFGD for a general class of restricted strongly convex/smooth loss functions, i.e., Local SFGD converges locally to a small neighborhood of the global optimum at a linear rate with a constant step size, while it locally converges exactly at a sub-linear rate with diminishing step sizes. With a proper initialization, local convergence results imply global convergence. We validate our theoretical findings with numerical simulations of QST on the Greenberger-Horne-Zeilinger (GHZ) state.

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