mlsanityData to 14 Oct 2026

Toward Super-polynomial Quantum Speedup of Equivariant Quantum Algorithms with SU(d) Symmetry

arXiv 2207.07250 ↗First posted 15 Jul 2022quant-ph cs.AI cs.LGcited by 4

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Abstract (arXiv)

We introduce a framework of the equivariant convolutional quantum algorithms which is tailored for a number of machine-learning tasks on physical systems with arbitrary SU(d) symmetries. It allows us to enhance a natural model of quantum computation -- permutational quantum computing (PQC) -- and define a more powerful model: PQC+. While PQC was shown to be efficiently classically simulatable, we exhibit a problem which can be efficiently solved on PQC+ machine, whereas no classical polynomial time algorithm is known; thus providing evidence against PQC+ being classically simulatable. We further discuss practical quantum machine learning algorithms which can be carried out in the paradigm of PQC+.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 10 of its 80 references that are in the map. First posted on arXiv 15 Jul 2022.

Builds on

10 of 80 references.

References · 10

  1. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 746
  2. 2018On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groupscited by 300
  3. 2019Cormorant: Covariant Molecular Neural Networkscited by 263
  4. 2018Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Networkcited by 171
  5. 2020Lorentz Group Equivariant Neural Network for Particle Physicscited by 121
  6. 2022Exploiting symmetry in variational quantum machine learningcited by 69
  7. 2022Group-Invariant Quantum Machine Learningcited by 56
  8. 2021Speeding up Learning Quantum States through Group Equivariant Convolutional Quantum Ans"atzecited by 29
  9. 2017Convolutional Networks for Spherical Signalscited by 18
  10. 2022Linear programming with unitary-equivariant constraintscited by 3

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Cited by year

Citing papers per year: 2022: 4.

4 papers.

  1. 2022Theory for Equivariant Quantum Neural Networkscited by 62
  2. 2022Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networkscited by 52
  3. 2022Symmetric Pruning in Quantum Neural Networkscited by 21
  4. 2022SnCQA: A hardware-efficient equivariant quantum convolutional circuit architecturecited by 7