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Differentiating and Integrating ZX Diagrams with Applications to Quantum Machine Learning

arXiv 2201.13250 ↗First posted 31 Jan 2022quant-ph cs.LGcited by 1

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Abstract (arXiv)

ZX-calculus has proved to be a useful tool for quantum technology with a wide range of successful applications. Most of these applications are of an algebraic nature. However, other tasks that involve differentiation and integration remain unreachable with current ZX techniques. Here we elevate ZX to an analytical perspective by realising differentiation and integration entirely within the framework of ZX-calculus. We explicitly illustrate the new analytic framework of ZX-calculus by applying it in context of quantum machine learning for the analysis of barren plateaus.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 13 of its 56 references that are in the map. First posted on arXiv 31 Jan 2022.

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13 of 56 references.

References · 13

  1. 2018Barren plateaus in quantum neural network training landscapescited by 624
  2. 2014The Loss Surfaces of Multilayer Networkscited by 278
  3. 2021QNLP in Practice: Running Compositional Models of Meaning on a Quantum Computercited by 65
  4. 2020Foundations for Near-Term Quantum Natural Language Processingcited by 51
  5. 2021lambeq: An Efficient High-Level Python Library for Quantum NLPcited by 43
  6. 2021Analyzing the barren plateau phenomenon in training quantum neural networks with the ZX-calculuscited by 30
  7. 2019Graph-theoretic Simplification of Quantum Circuits with the ZX-calculuscited by 20
  8. 2020Diagrammatic Design and Study of Ans"atze for Quantum Machine Learningcited by 5
  9. 2021Diagrammatic Differentiation for Quantum Machine Learningcited by 5
  10. 2015A Diagrammatic Axiomatisation for Qubit Entanglementcited by 4
  11. 2017The ZX calculus is a language for surface code lattice surgerycited by 4
  12. 2021Kindergarden quantum mechanics graduates (...or how I learned to stop gluing LEGO together and love the ZX-calculus)cited by 4
1 more
  1. 2017Generalised Mermin-type non-locality argumentscited by 2

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