Quantum Assertion Testing Without Mid-Circuit Measurement: Strategies and Lower Bounds
summary
Defines FirstFail and exist-fail tasks and proves concrete time‑space limits: any strategy without mid‑circuit measurement satisfies T × S = Ω(log n). Provides a single‑run algorithm that uses O(log n) ancilla qubits (one 1‑bit flag plus a log n index register) and records the first failing assertion by reversible controlled swaps after each oracle toggle. Shows this matches the lower bound and that mid‑circuit measurement gives only an O(log n) advantage, not O(n).
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chapters (12)
- 0:00Quantum assertion testing intro
- 1:06Measuring quantum states challenges
- 3:11Research question and problems
- 5:41Runtime assertion with ancilla
- 7:46Single-run vs multi-run
- 9:51Mid-circuit measurement limits
- 10:31Problem setting and oracles
- 12:39Single-run failure lower bound
- 15:13First failing assertion bound
- 16:58Multi-run lower bounds
- 17:39Results and future impact
- 18:29Q&A
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