mlsanityData to 13 Oct 2026

Quantum activation functions for quantum neural networks

arXiv 2201.03700 ↗First posted 10 Jan 2022quant-ph cs.AIcited by 10

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Abstract (arXiv)

The field of artificial neural networks is expected to strongly benefit from recent developments of quantum computers. In particular, quantum machine learning, a class of quantum algorithms which exploit qubits for creating trainable neural networks, will provide more power to solve problems such as pattern recognition, clustering and machine learning in general. The building block of feed-forward neural networks consists of one layer of neurons connected to an output neuron that is activated according to an arbitrary activation function. The corresponding learning algorithm goes under the name of Rosenblatt perceptron. Quantum perceptrons with specific activation functions are known, but a general method to realize arbitrary activation functions on a quantum computer is still lacking. Here we fill this gap with a quantum algorithm which is capable to approximate any analytic activation functions to any given order of its power series. Unlike previous proposals providing irreversible measurement--based and simplified activation functions, here we show how to approximate any analytic function to any required accuracy without the need to measure the states encoding the information. Thanks to the generality of this construction, any feed-forward neural network may acquire the universal approximation properties according to Hornik's theorem. Our results recast the science of artificial neural networks in the architecture of gate-model quantum computers.

Key facts. Cited by 10 papers in the map (data through 13 Oct 2026). Builds on 11 of its 48 references that are in the map. First posted on arXiv 10 Jan 2022.

Builds on

11 of 48 references.

References · 11

  1. 2018Barren plateaus in quantum neural network training landscapescited by 627
  2. 2019Parameterized quantum circuits as machine learning modelscited by 332
  3. 2016Quantum Machine Learningcited by 326
  4. 2019Efficient Learning for Deep Quantum Neural Networkscited by 160
  5. 2017Quantum Neuron: an elementary building block for machine learning on quantum computerscited by 34
  6. 2020Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuitscited by 26
  7. 2020Satellite Image Classification with Deep Learningcited by 12
  8. 2016Quantum perceptron over a field and neural network architecture selection in a quantum computercited by 7
  9. 2018A Simple Quantum Neural Net with a Periodic Activation Functioncited by 7
  10. 2017Neural Networks Architecture Evaluation in a Quantum Computercited by 2
  11. 2016Weightless neural network parameters and architecture selection in a quantum computercited by 1

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Cited by year

Citing papers per year: 2023: 2; 2024: 6; 2025: 2.

10 papers.

  1. 2024Learning with SASQuaTCh: a Novel Variational Quantum Transformer Architecture with Kernel-Based Self-Attentioncited by 5
  2. 2024Quantum-Cognitive Neural Networks: Assessing Confidence and Uncertainty with Human Decision-Making Simulationscited by 4
  3. 2023Enabling Non-Linear Quantum Operations through Variational Quantum Splinescited by 3
  4. 2023Assessing the Impact of Noise on Quantum Neural Networks: An Experimental Analysiscited by 3
  5. 2024Quantum Machine Learning in Drug Discovery: Applications in Academia and Pharmaceutical Industriescited by 3
  6. 2024Efficient Quantum Circuits for Machine Learning Activation Functions including Constant T-depth ReLUcited by 2
  7. 2024A Tutorial on the Use of Physics-Informed Neural Networks to Compute the Spectrum of Quantum Systemscited by 2
  8. 2025Hybrid Quantum Neural Networks for Efficient Protein-Ligand Binding Affinity Predictioncited by 1
  9. 2024Training quantum machine learning models on cloud without uploading the datacited by 0
  10. 2025Solving the encoding bottleneck: of the HHL algorithm, by the HHL algorithmcited by 0