Towards a Hierarchical Quantum Circuit Language
summary
Introduces a hierarchical circuit language that adds two concrete connectives: subcircuit exponentiation (matrix power via log/exp) and a novel control product (log-tensor-divide-exponentiate) built by a category-theoretic prop construction. Proves the control product generalizes controlled unitaries, gives a one-qubit-universal gate-set construction, derives a reusable circuit identity useful for optimization, rewrites the operation as a phase-selection primitive, and shows examples (Grover, parity-controlled CNOT). Reports that lowering to standard circuits requires a diagonalization step and leaves efficient diagrammatic diagonalization as an open problem.
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chapters (13)
- 0:00Hierarchical quantum circuits
- 1:03Quantum control flow
- 2:50Mathematical formalism
- 5:18Subcircuit exponentiation
- 6:21Control product operation
- 8:10New circuit operations
- 9:53Nested control products
- 10:14Universal gate set
- 12:01Phase-based circuits
- 13:48Control operation semantics
- 15:35Compiler applications
- 17:20Quantum literature examples
- 18:23Q&A
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