Hybrid quantum-classical circuit simplification with the ZX-calculus
summary
A complete optimization procedure targets hybrid quantum-classical circuits with classical parity logic (NOT and XOR), translating them into ZX⏚ (ZX-ground) diagrams in a strict graph-like form and preserving focused gFlow so extraction back to a circuit succeeds. gFlow-preserving rewrite rules include deleting degree‑1 ground spiders and removing phase 0 or π spiders connected to grounds (Discarding and Ground‑Pauli Pivot), while Gauss elimination on the biadjacency matrix finds zero or single‑one rows to expose more deletions. Extraction yields pure-quantum internals plus a PyZX extension that detects and replaces classically implementable wires with classical gates.
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chapters (12)
- 0:00Intro
- 0:12The setting
- 2:38Pure ZX optimization
- 3:30The ZX-calculus
- 4:17Quantum circuits as ZX-diagrams
- 5:26Underlying open-graph
- 6:43Zx diagram optimization rules
- 7:25Ground-related optimizations
- 8:09Finding optimizations on the ground-cut diagram
- 9:29Optimization algorithm
- 10:24Circuit extraction
- 12:42Detecting classical wires
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