Fig. 4: Faulty implementations of the BV algorithm.
From: Solving the Bernstein-Vazirani problem using Majorana-based topological quantum algorithms
Time-dependent transition probabilities for s=111 and a a detuned generalized Hadamard gate (scenario I), and b a non-adiabatic implementation with a significantly reduced execution time of the BV algorithm (scenario II). Δρ(r) after completion of the fusion process for s = 100 and c scenario I, and d scenario II. Energy-resolved non-equilibrium local density of states at the site marked by the yellow dot in c for e scenario I and f scenario II, showing the movement of one of the Majorana zero modes through this site. Parameters are (μ, α, Δ, JS) = (−3.93, 0.45, 1.2, 2.6)te, Γ = 0.01te and execution times of 36800τe (640.0τe) for the generalized Hadamard gate, 2460τe (496τe) for the oracle, and 4800τe(960τe) for the initialization and fusion processes for scenario I (II). For scenario I, the detuning was achieved by choosing TR, ΔTR = (1600, 320)τe, in contrast to the perfect generalized Hadamard gate used for the results shown in Fig.3 with TR, ΔTR = (1000, 20)τe.
