Table 1 Numerical simulations of various phase estimation algorithms were performed. The indices \(^1\), \(^2\), and \(^3\) denote algorithms that (i) do not use, (ii) fully use, and (iii) partially use the already measured field, respectively. The parameters were set to \(\tau ^* = 512\) and \({\Delta t} = 1\).
From: Phase estimation algorithms for quantum enhanced magnetometry with artificial atoms
Algorithm | \(N_\textrm{tests}\) | \(N_\textrm{errors}\) | \(\sigma ^2\) | \(\sum \limits _k^m N_\textrm{k}\) | \(N_\mathrm{{\tau = \tau ^*}}\) | \(t_\mathrm{{min}}\) |
|---|---|---|---|---|---|---|
K | 10, 000 | 3734 | \(38.2 \pm 0.9\) | 263 | 123 | 1 |
\(\text {K}^1\) | 10, 000 | 44 | \(26.6 \pm 0.4\) | 263 | 115 | 1 |
\(\text {K}^2\) | 10, 000 | 11 | \(15.0 \pm 0.2\) | 263 | 123 | 1 |
F | 10, 000 | 3528 | \(40.8 \pm 0.8\) | 263 | 123 | 1 |
\(\text {F}^2\) | 10, 000 | 876 | \(39.0 \pm 0.7\) | 263 | 123 | 1 |
\(\text {SRK}^3\) | 10, 000 | 9 | \(15.4 \pm 0.2\) | 263 | 120 | 8 |
\(\text {RK}^1\) | 10, 000 | 6 | \(13.0 \pm 0.2\) | 263 | 41 | 256 |
\(\text {RK}^2\) | 10, 000 | 161 | \(9.1 \pm 0.1\) | 263 | 41 | 256 |
\(\text {RK}^3\) | 10, 000 | 18 | \(11.4 \pm 0.2\) | 263 | 41 | 256 |
\(\text {ELAMA}^2\) | 10, 000 | 0 | \(8.2 \pm 0.1\) | 263 | 8 | 256 |
\(\text {K}^2\) | 10, 000 | 0 | \(6.3 \pm 0.1\) | 512 | 278 | 1 |
\(\text {F}^2\) | 10, 000 | 352 | \(23.6 \pm 0.5\) | 512 | 278 | 1 |
\(\text {SRK}^3\) | 10, 000 | 1 | \(6.3 \pm 0.1\) | 512 | 275 | 8 |
\(\text {RK}^2\) | 10, 000 | 35 | \(4.4 \pm 0.1\) | 512 | 144 | 256 |
\(\text {RK}^3\) | 10, 000 | 0 | \(5.3 \pm 0.1\) | 512 | 144 | 256 |
\(\text {ELAMA}^2\) | 10, 000 | 0 | \(3.9 \pm 0.1\) | 512 | 256 | 257 |
\(\text {LAMA}^2\) | 10, 000 | 0 | \(6.5 \pm 0.1\) | 512 | 1 | 1 |
