Quantum Circuits Are Just a Phase
summary
Defines a tiny language with a single numerical primitive pH(theta) (global phase) plus a quantum pattern match iflet that picks bases via patterns as isometries. Proves universality by deriving a universal gate set, encodes CX, Hadamard, Grover, QFT, QSP and QET concisely, and gives categorical (Hilbert-space) denotational semantics. Ships a prototype compiler that emits circuits, handles inverses and fractional powers (square roots), and is proven sound with artifacts available.
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chapters (14)
- 0:00Quantum circuits introduction
- 1:30Quantum circuit model recap
- 4:43Challenges with quantum gates
- 8:10Phase as quantum primitive
- 9:35Pattern matching with iflet
- 12:43Diagonal gates like Z S T
- 13:27Pattern matching on X gates
- 14:53Quantum phase language
- 16:35Meta operations inverses exponentiation
- 18:19Type system and semantics
- 19:21Semantic equalities and algorithms
- 20:24Future beyond unitaries
- 21:49Q&A basis selection
- 25:43Q&A phase manipulation
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