Fig. 5 | Nature Communications

Fig. 5

From: Finite temperature quantum annealing solving exponentially small gap problem with non-monotonic success probability

Fig. 5

Master equation results for the ground state population when restricting the excited states to single and two-fermion states. a The result of simulating the ASC problem with parameters (1,0.5,175) via the adiabatic Pauli master equation (8), restricted to the vacuum + single-fermion states, and vacuum + single-fermion + two-fermion states. Also shown is the dependence on the system-bath coupling parameter g in the two-fermion case; doubling it has little impact, whereas halving it increases the success probability somewhat for n < 14. The position of the minimum at n* = 5 matches the empirical result seen in Fig. 2a, except when g = 1/2, i.e., the position is robust to doubling g but not to halving it. Panels (b) and (c) show additional 2-fermion master equation results with g = 1. Note that for the (1,0.5,200) chain, these simulations exhibit better agreement with the DW2X data than the simple k* analysis plotted in Fig. 2d–f. This is because the simulations also keep track of the Boltzmann factor

Back to article page