Algorithm family
Quantum phase estimation
Estimation of an eigenphase with an m-qubit counting register: dyadic phases representable in m bits are returned with certainty; non-representable phases concentrate on the nearest bin with probability at least 4/pi^2. The registry's reference runs sweep m = 3..8 for both regimes.
Assumptions and execution semantics
The registry implementation is a STATEVECTOR SIMULATION of the textbook circuit (Hadamards, controlled-phase ladder, inverse QFT) with Born-rule sampling; noiseless and exact by construction. Gate counts are of the constructed circuit. No hardware execution.
Implementations
| Engine | Method | Backend | Abstraction level | Semantics |
|---|---|---|---|---|
| ketqat-runner | statevector | ketqat-statevector-python | gate-level circuit, exact simulation | SIMULATED Simulated — a circuit was executed on a classical simulator phase_is_representable is recorded per point, so the certain and nearest-bin regimes are never conflated |
Problem and sizes
- Instance types
- eigenphase
- Size axis
- qubit_count (counting-register width m)
- Sizes measured
- n = 3n = 4n = 5n = 6n = 7n = 8
- Parameters
- phase, shots, seed
Suites and runs
Benchmark suites
Hash-verified runs
Quality and resources across size
One row per measured point; every row traces to its run. Semantics per the implementation table — nothing here mixes modelled and simulated values in one aggregate.
| n | Success probability | Depth | Gates (2q) | Runtime (s) | Run |
|---|---|---|---|---|---|
| 3 | 1.000000 | 7 | 9 (3) | 0.0000 | phase-estimation-reference-dyadic |
| 3 | 0.697510 | 7 | 9 (3) | 0.0000 | phase-estimation-reference-nondyadic |
| 4 | 1.000000 | 9 | 14 (6) | 0.0000 | phase-estimation-reference-dyadic |
| 4 | 0.678955 | 9 | 14 (6) | 0.0000 | phase-estimation-reference-nondyadic |
| 5 | 1.000000 | 11 | 20 (10) | 0.0000 | phase-estimation-reference-dyadic |
| 5 | 0.672607 | 11 | 20 (10) | 0.0000 | phase-estimation-reference-nondyadic |
| 6 | 1.000000 | 13 | 27 (15) | 0.0000 | phase-estimation-reference-dyadic |
| 6 | 0.683105 | 13 | 27 (15) | 0.0000 | phase-estimation-reference-nondyadic |
| 7 | 1.000000 | 15 | 35 (21) | 0.0000 | phase-estimation-reference-dyadic |
| 7 | 0.672607 | 15 | 35 (21) | 0.0000 | phase-estimation-reference-nondyadic |
| 8 | 1.000000 | 17 | 44 (28) | 0.0000 | phase-estimation-reference-dyadic |
| 8 | 0.699707 | 17 | 44 (28) | 0.0000 | phase-estimation-reference-nondyadic |
References
- Kitaev, Quantum measurements and the Abelian Stabilizer Problem — arXiv:quant-ph/9511026
- Cleve, Ekert, Macchiavello, Mosca, Quantum algorithms revisited — arXiv:quant-ph/9708016
Next action
Sweep additional non-representable phases and plot the nearest-bin probability against the 4/pi^2 bound across register widths.