Table 1 Tabulated values of \(s\cdot p_{G}\), where s is the quantile of the distribution of the required number of shots to find all solutions. The column headers contain the probabilities p, and each row contains the values of \(s \cdot p_{G}\) such that \({\mathbb{P}}(X_{M-1, M} \leq s) = p\) for a given value of M. Assume, for example, that the user wants a probability 0.9 of finding all the \(M = 100\) solutions to their search problem, the table indicates that \(s\cdot p_{G}\) should be 686. If \(p_{G}\), see (1), has a value of 0.8 for example, it follows that approximately 857 shots are required
From: Determination of the number of shots for Grover’s search algorithm
M | Probability p | |||||
|---|---|---|---|---|---|---|
0.50 | 0.70 | 0.80 | 0.90 | 0.95 | 0.99 | |
5 | 10.36 | 13.69 | 16.03 | 19.78 | 23.38 | 31.53 |
6 | 13.44 | 17.42 | 20.24 | 24.74 | 29.06 | 38.84 |
7 | 16.68 | 21.33 | 24.61 | 29.86 | 34.90 | 46.31 |
8 | 20.06 | 25.37 | 29.12 | 35.13 | 40.89 | 53.93 |
9 | 23.56 | 29.54 | 33.77 | 40.52 | 47.00 | 61.67 |
10 | 27.18 | 33.83 | 38.52 | 46.02 | 53.22 | 69.52 |
20 | 67.74 | 81.03 | 90.41 | 105.42 | 119.81 | 152.41 |
30 | 113.53 | 133.46 | 147.53 | 170.04 | 191.64 | 240.54 |
40 | 162.71 | 189.29 | 208.05 | 238.07 | 266.86 | 332.06 |
50 | 214.43 | 247.65 | 271.10 | 308.62 | 344.61 | 426.11 |
75 | 351.80 | 401.63 | 436.81 | 493.09 | 547.08 | 669.32 |
100 | 497.67 | 564.11 | 611.01 | 686.05 | 758.04 | 921.03 |
200 | 1133.47 | 1266.35 | 1360.15 | 1510.24 | 1654.20 | 1980.19 |
300 | 1821.59 | 2020.91 | 2161.62 | 2386.74 | 2602.69 | 3091.68 |
400 | 2543.69 | 2809.46 | 2997.06 | 3297.23 | 3585.16 | 4237.15 |
500 | 3291.06 | 3623.27 | 3857.77 | 4232.99 | 4592.90 | 5407.88 |
1000 | 7274.77 | 7939.19 | 8408.20 | 9158.62 | 9878.45 | 11,508.40 |
2000 | 15,935.33 | 17,264.17 | 18,202.18 | 19,703.04 | 21,142.70 | 24,402.60 |