Table 5 Analysis of state fidelity (\(\mathcal {F}_S\)) derived from \({\mathcal {QST}}\) experiments conducted on the GSA, encompassing both single-search and two-search oracles. The experiments are performed across various environments: Noise-free, Noisy, and on IBM Quantum’s 127-qubit superconducting quantum computers. Furthermore, the analysis includes hypothesis testing and \(95\%\) CI for the population mean (\(\mu\)) and variance (\(\sigma ^2\)).
From: Characterizing Grover search algorithm on large-scale superconducting quantum computers
Marked State | \(\mathcal {F}_S\) \({\mathcal {QST}}\) (Noise-free) | \(\mathcal {F}_S\) \({\mathcal {QST}}\) (Noisy settings) | \(\mathcal {F}_S\) \({\mathcal {QST}}\) (IBM Quantum) |
|---|---|---|---|
Single-search (010) | 0.9946673 | 0.7394261 | 0.4923291 |
Single-search (101) | 0.9946291 | 0.7380571 | 0.5388754 |
Two-search (000, 111) | 0.9956002 | 0.7827690 | 0.5721854 |
Two-search (101, 110) | 0.9922922 | 0.8085018 | 0.4923291 |
Two-search (111, 101) | 0.9921588 | 0.8376049 | 0.6894187 |
Mean | 0.993870 | 0.7813 | 0.5432 |
StDev | 0.001551 | 0.0434 | 0.0990 |
SE Mean | 0.000694 | 0.01194 | 0.0443 |
t-test (95% CI) | (0.9919, 0.9957) | (0.7274, 0.8352) | (0.4205, 0.6661) |
Hypothesis tests (Mean\(^1\)) | P-value: 0.999 | 0.999 | 1.000 |
95% CI StDev | (0.00093, 0.00446) | (0.0260, 0.1247) | (0.05930, 0.02845) |
95% CI Variance | (0.000001, 0.00002) | (0.00068, 0.01556) | (0.00352, 0.08093) |
Hypothesis tests (Variance\(^2\)) | P-value: 0.812 | 0.812 | 0.812 |
