Symbolic Execution of Hadamard-Toffoli Quantum Circuits
summary
Classical symbolic evaluation models Hadamard-created superpositions as symbolic boolean variables and runs reversible parts forward and backward to produce constraints; with careful formula representations (lists → maps → bitset/bitmap representation) and a tiny DSL the system symbolically executes textbook algorithms and returns exact answers. Results: circuits with millions of gates (reported up to 4 million gates in seconds) execute quickly for many instances (Deutsch, Grover, Shor’s small cases), but some small adversarial circuits still cause exponential-time constraint solving.
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chapters (17)
- 0:00Symbolic quantum circuit execution
- 2:34Reversible gates basics
- 6:09Hadamard and superposition circuits
- 8:16Deutsch-Jozsa algorithm
- 10:00Grover’s search algorithm
- 10:43Reusable quantum circuit code
- 13:12Optimizing circuit representations
- 17:27Symbolic execution results
- 18:53Cryptographic function constraints
- 19:15Grover’s constraints and optimizations
- 20:16Shor’s algorithm factoring 15
- 21:41Symbolic execution performance
- 23:07Timing comparisons
- 24:37Complexity and successes
- 25:41Classical quantum algorithm implications
- 26:06Q&A: Unitary matrices
- 27:51Q&A: Qubit count and scalability
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