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Local Stochastic Factored Gradient Descent for Distributed Quantum State Tomography
- Source :
- IEEE Control Systems Letters. 7:199-204
- Publication Year :
- 2023
- Publisher :
- Institute of Electrical and Electronics Engineers (IEEE), 2023.
-
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.
- Subjects :
- FOS: Computer and information sciences
Quantum Physics
Computer Science - Machine Learning
Control and Optimization
Optimization and Control (math.OC)
Control and Systems Engineering
FOS: Mathematics
FOS: Physical sciences
Quantum Physics (quant-ph)
Mathematics - Optimization and Control
Machine Learning (cs.LG)
Subjects
Details
- ISSN :
- 24751456
- Volume :
- 7
- Database :
- OpenAIRE
- Journal :
- IEEE Control Systems Letters
- Accession number :
- edsair.doi.dedup.....59264f6c83b4ecd4def13eb5709d8dbb