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Add Parameter-Shift Differentiation for Hybrid Quantum-Classical Algorithms #9

Description

@gstenzel

The qandle library supports hybrid quantum-classical machine learning workflows, particularly via integration with PyTorch. Currently, gradient computation (backward pass) is implemented in a way that leverages PyTorch's autodiff, but does not provide access to quantum-native differentiation methods.

To enhance flexibility and research opportunities, we should implement parameter-shift differentiation, which is a quantum-compatible method for computing gradients of expectation values with respect to gate parameters. This involves:

  • Adding parameter-shift rules for supported gates (e.g., RX, RY, RZ, etc.).
  • Integrating parameter-shift differentiation as an option for the backward pass in hybrid workflows, potentially allowing to disable PyTorch-based gradient tracking.
  • Providing documentation and examples comparing parameter-shift and classical autodiff approaches.
  • Benchmarking the performance and accuracy trade-offs for relevant quantum machine learning tasks.

This feature will support research into variational quantum algorithms and hybrid training strategies, making qandle more competitive with other quantum ML frameworks.

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