mlsanityData to 7 Oct 2026

Local Stochastic Factored Gradient Descent for Distributed Quantum State Tomography

arXiv 2203.11579 ↗First posted 22 Mar 2022quant-ph cs.LG math.OCcited by 1

Not on the map. Why?

Abstract (arXiv)

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.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 19 of its 33 references that are in the map. First posted on arXiv 22 Mar 2022.

Builds on

19 of 33 references.

References · 19

  1. 2017Accurate, Large Minibatch SGD: Training ImageNet in 1 Hourcited by 1,479
  2. 2016Optimization Methods for Large-Scale Machine Learningcited by 1,140
  3. 2016TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systemscited by 660
  4. 2018Local SGD Converges Fast and Communicates Littlecited by 595
  5. 2021Sparsity in Deep Learning: Pruning and growth for efficient inference and training in neural networkscited by 521
  6. 2017Deep Gradient Compression: Reducing the Communication Bandwidth for Distributed Trainingcited by 471
  7. 2019Tighter Theory for Local SGD on Identical and Heterogeneous Datacited by 266
  8. 2018Nonconvex Optimization Meets Low-Rank Matrix Factorization: An Overviewcited by 159
  9. 2020Is Local SGD Better than Minibatch SGD?cited by 151
  10. 2016QSGD: Communication-Efficient SGD via Gradient Quantization and Encodingcited by 147
  11. 2018Cooperative SGD: A unified Framework for the Design and Analysis of Communication-Efficient SGD Algorithmscited by 106
  12. 2019Local SGD with Periodic Averaging: Tighter Analysis and Adaptive Synchronizationcited by 106
7 more
  1. 2015Low-rank Solutions of Linear Matrix Equations via Procrustes Flowcited by 97
  2. 2018SGD and Hogwild! Convergence Without the Bounded Gradients Assumptioncited by 94
  3. 2017On the convergence properties of a K-step averaging stochastic gradient descent algorithm for nonconvex optimizationcited by 91
  4. 2017Communication-Efficient Algorithms for Decentralized and Stochastic Optimizationcited by 42
  5. 2015Dropping Convexity for Faster Semi-definite Optimizationcited by 40
  6. 2016Finding Low-Rank Solutions via Non-Convex Matrix Factorization, Efficiently and Provablycited by 22
  7. 2021Fast quantum state reconstruction via accelerated non-convex programmingcited by 5

Built on by

Cited by year

Citing papers per year: 2023: 1.

1 paper.

  1. 2023Adaptive Federated Learning with Auto-Tuned Clientscited by 7