Optimal compilation of parametrised quantum circuits
summary
Shows that minimizing parameters is NP-hard in general, but when circuits are Clifford apart from parametrised phase gates and each parameter is used only once there is an efficient, constructive algorithm that provably finds the optimal parameter count. Proof and extraction use the ZX-calculus and a rewrite system; the 2019 ZX-based optimisation is shown to be optimal under affine, parsimonious reductions. Key caveat: allowing parameter copying or non‑affine transforms destroys tractability.
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chapters (11)
- 0:00Introduction
- 1:49Circuit optimization needs ZX
- 3:34Automating ZX with PyZX
- 6:21T-count reduction
- 7:45Comparing with Zeng and Chin
- 10:13Parameter optimization beyond T
- 11:15Affine parameter reduction
- 13:23Optimal parameter count
- 14:47PyZX achieves optimality
- 15:50Parameter minimization problems
- 16:37Q&A
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