mlsanityData to 14 Oct 2026

Stochastic noise can be helpful for variational quantum algorithms

arXiv 2210.06723 ↗First posted 13 Oct 2022quant-ph cs.LGcited by 16

Not on the map. Why?

Abstract (arXiv)

Saddle points constitute a crucial challenge for first-order gradient descent algorithms. In notions of classical machine learning, they are avoided for example by means of stochastic gradient descent methods. In this work, we provide evidence that the saddle points problem can be naturally avoided in variational quantum algorithms by exploiting the presence of stochasticity. We prove convergence guarantees and present practical examples in numerical simulations and on quantum hardware. We argue that the natural stochasticity of variational algorithms can be beneficial for avoiding strict saddle points, i.e., those saddle points with at least one negative Hessian eigenvalue. This insight that some levels of shot noise could help is expected to add a new perspective to notions of near-term variational quantum algorithms.

Key facts. Cited by 16 papers in the map (data through 14 Oct 2026). Builds on 16 of its 54 references that are in the map. First posted on arXiv 13 Oct 2022.

Builds on

16 of 54 references.

References · 16

  1. 2020Variational Quantum Algorithmscited by 692
  2. 2018Barren plateaus in quantum neural network training landscapescited by 630
  3. 2020Noise-Induced Barren Plateaus in Variational Quantum Algorithmscited by 193
  4. 2017Non-convex Optimization for Machine Learningcited by 133
  5. 2021Noisy intermediate-scale quantum (NISQ) algorithmscited by 79
  6. 2017Gradient Descent Can Take Exponential Time to Escape Saddle Pointscited by 74
  7. 2019Stochastic gradient descent for hybrid quantum-classical optimizationcited by 59
  8. 2021Representation Learning via Quantum Neural Tangent Kernelscited by 40
  9. 2021Capacity and quantum geometry of parametrized quantum circuitscited by 32
  10. 2016Gradient Descent Converges to Minimizerscited by 25
  11. 2022Analytic theory for the dynamics of wide quantum neural networkscited by 21
  12. 2017First-order Methods Almost Always Avoid Saddle Pointscited by 14
4 more
  1. 2021Adaptive shot allocation for fast convergence in variational quantum algorithmscited by 12
  2. 2022Laziness, Barren Plateau, and Noise in Machine Learningcited by 10
  3. 2021Variational Quantum Algorithms for Semidefinite Programmingcited by 8
  4. 2022Bayesian Learning of Parameterised Quantum Circuitscited by 3

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 1; 2023: 4; 2024: 5; 2025: 1; 2026: 5.

16 papers.

Sort:

By area:

  1. 2024Barren Plateaus in Variational Quantum Computingcited by 133
  2. 2024Curriculum reinforcement learning for quantum architecture search under hardware errorscited by 37
  3. 2023Towards provably efficient quantum algorithms for large-scale machine-learning modelscited by 32
  4. 2023Thermodynamic AI and the fluctuation frontiercited by 15
  5. 2022SnCQA: A hardware-efficient equivariant quantum convolutional circuit architecturecited by 7
  6. 2024Method for noise-induced regularization in quantum neural networkscited by 7
  7. 2023Assessing the Impact of Noise on Quantum Neural Networks: An Experimental Analysiscited by 3
  8. 2024Image Classification with Rotation-Invariant Variational Quantum Circuitscited by 3
  9. 2024Enhancing the Trainability of Variational Quantum Circuits with Regularization Strategiescited by 2
  10. 2026How to find expressible and trainable parameterized quantum circuits?cited by 2
  11. 2025Escaping Barren Plateaus in Variational Quantum Algorithms Using Negative Learning Rate in Quantum Internet of Thingscited by 1
  12. 2026Quantum End-to-End Learning for Contextual Combinatorial Optimizationcited by 1
4 more
  1. 2023Noisy Tensor Ring approximation for computing gradients of Variational Quantum Eigensolver for Combinatorial Optimizationcited by 0
  2. 2026Simplicity Suffices for Parameter Noise Injection in Stochastic Gradient Descentcited by 0
  3. 2026Representational separation between unitary and channel quantum generative models via shared classical randomness at shallow depthcited by 0
  4. 2026A Theory of Finite-Noise Optima and Generalization in Quantum Machine Learningcited by 0