Diagrammatic Differentiation for Quantum Machine Learning

  title={Diagrammatic Differentiation for Quantum Machine Learning},
  author={Alexis Toumi and Richie Yeung and Giovanni de Felice},
We introduce diagrammatic differentiation for tensor calculus by generalising the dual number construction from rigs to monoidal categories. Applying this to ZX diagrams, we show how to calculate diagrammatically the gradient of a linear map with respect to a phase parameter. For diagrams of parametrised quantum circuits, we get the well-known parameter-shift rule at the basis of many variational quantum algorithms. We then extend our method to the automatic differentation of hybrid classical… 

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