Hybrid Quantum-Classical Machine Learning with String Diagrams
summary
Formal framework maps quantum CPTP superoperators through real matrices into smooth classical maps, using lax monoidal functor boxes that force multiple outputs to bundle into one so measurements yield a single classical probability. Integrates with ZX calculus (and ZXW for diagrammatic gradients) to enable in-place circuit optimization without separating quantum and classical parts. Applied to a 2018 parametrized circuit for multiclass classification as a worked example; no noise model yet.
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chapters (11)
- 0:00Hybrid quantum-classical ML intro
- 1:03Algorithms with string diagrams
- 2:26ZX calculus for circuits
- 3:09Category theory foundations
- 4:32Functors bridging domains
- 6:18Quantum systems to matrices
- 7:21Matrices to smooth maps
- 8:51Framework applied to QML
- 9:55Mathematical summary
- 10:37Gradient formalization future
- 11:23Q&A
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