mlsanityData to 14 Oct 2026

Learning Unitaries by Gradient Descent

arXiv 2001.11897 ↗First posted 31 Jan 2020quant-ph cs.LG math-phcited by 20

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Abstract (arXiv)

We study the hardness of learning unitary transformations in U(d) via gradient descent on time parameters of alternating operator sequences. We provide numerical evidence that, despite the non-convex nature of the loss landscape, gradient descent always converges to the target unitary when the sequence contains d2 or more parameters. Rates of convergence indicate a "computational phase transition." With less than d2 parameters, gradient descent converges to a sub-optimal solution, whereas with more than d2 parameters, gradient descent converges exponentially to an optimal solution.

Key facts. Cited by 20 papers in the map (data through 14 Oct 2026). First posted on arXiv 31 Jan 2020.

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Citing papers per year: 2021: 4; 2022: 4; 2023: 6; 2024: 2; 2025: 3; 2026: 1.

20 papers.

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  1. 2023Challenges and Opportunities in Quantum Machine Learningcited by 203
  2. 2024Barren Plateaus in Variational Quantum Computingcited by 133
  3. 2021Theory of overparametrization in quantum neural networkscited by 100
  4. 2024A comprehensive review of Quantum Machine Learning: from NISQ to Fault Tolerancecited by 32
  5. 2022projUNN: efficient method for training deep networks with unitary matricescited by 27
  6. 2021Exponentially Many Local Minima in Quantum Neural Networkscited by 22
  7. 2022Analytic theory for the dynamics of wide quantum neural networkscited by 21
  8. 2022Symmetric Pruning in Quantum Neural Networkscited by 21
  9. 2022A Convergence Theory for Over-parameterized Variational Quantum Eigensolverscited by 15
  10. 2023Quantum Machine Learning on Near-Term Quantum Devices: Current State of Supervised and Unsupervised Techniques for Real-World Applicationscited by 14
  11. 2021Learning quantum data with the quantum Earth Mover's distancecited by 13
  12. 2025A Primer on Quantum Machine Learningcited by 12
8 more
  1. 2023Generalization of Quantum Machine Learning Models Using Quantum Fisher Information Metriccited by 10
  2. 2023Effects of noise on the overparametrization of quantum neural networkscited by 9
  3. 2025Double descent in quantum kernel methodscited by 9
  4. 2023Quantum Neural Estimation of Entropiescited by 6
  5. 2021Entanglement Diagnostics for Efficient Quantum Computationcited by 2
  6. 2023Dynamical transition in controllable quantum neural networks with large depthcited by 2
  7. 2025Connecting phases of matter to the flatness of the loss landscape in analog variational quantum algorithmscited by 0
  8. 2026Gradient descent reliably finds depth- and gate-optimal circuits for generic unitariescited by 0