FIG. 1.

Schematic of the model. Spins in sublattice $\mathcal{A}$ (red, ${\widehat{\sigma }}_i$) are coupled to spins in sublattice $\mathcal{B}$ (blue, ${\widehat{\tau }}_j$) via Ising couplings ${\widehat{\sigma }}_i^x{\widehat{\tau }}_j^x$ and all of them start off in |↓〉. To lowest order in time, the matrix element of the time-evolution operator between an initial state with all spins initialized in |↓〉 and a final state with all qubits in |↑〉 receives contributions in which each spin is flipped precisely once (one such contributing term, between the spin on the second site of $\mathcal{A}$ and the spin on the first site of $\mathcal{B}$, is shown).