Fig. 6: Qubit dynamics and filtered clause readout signals under the heralded Algorithm 2.
From: Solving k–SAT problems with generalized quantum measurement
The SAT problem here is the same as the one defined in Eq. (33b). We set the measurement collapse time τ = 1 and the total dragging time Tf = 100. The filter response time is set to be \({T}_{be}=\max \{2\tau ,0.1{T}_{f}\}\), and the threshold is \({r}_{th}=-2.5/\sqrt{{T}_{be}}\). a Shows the evolution of a successful run, where the filtered signals \(\bar{r}\) Eq. (21) never reach the threshold value and the reduced conditional qubit dynamics (inset) diffuse relatively cleanly towards the correct solution state. b Shows the evolution of a failed run. In this example, qubit 0 is collapsed into an incorrect subspace near t/τ ≈ 50 (see inset) and the filtered signal 1 reaches the threshold near t/τ ≈ 60, heralding violation of a particular clause, and therefore a failure of the algorithm. The failure is detected when the threshold is crossed: the algorithm is terminated at this point. We also show the evolution for some time past this point, up to t = Tf, for illustrative purposes.
