Lattice folding mapping for quantum annealing.
(a) Step-by-step construction of the binary representation of lattice protein. Two qubits per bond are needed and the bond directions are denoted as “00” (downwards), “01” (rightwards), “10” (leftwards) and “11” (upwards). The example shows one of the possible folds of an arbitrary six-amino-acid sequence. Any possible N-amino-acid fold can be represented by a string of variables with . (b)Time-dependence of the A(τ) and B(τ) functions, where τ = t/trun with trun = 148 µs, (c) time-dependent spectrum obtained through numerical diagonalization and (d) Bloch-Redfield simulations showing the time-dependent population in the first eight instantaneous eigenstates of the experimentally implemented 8-qubit Hamiltonian (Eq. 3) with Hp from Eq. S18 in the Supplementary material. In panel (c), for each instantaneous eigenenergy curve we have subtracted the energy of the ground state, effectively plotting the gap of the seven-lowest-excited states with respect to the ground state (represented by the baseline at zero-energy). As a reference, we show the energy with the device temperature, which is comparable to the minimum gap between the ground and first excited state. In panel (d), populations are ordered in energy from top (ground state) to bottom. Although τ = t/trun runs from 0 to 1, we show the region where most of the population changes occur. As expected, this is in the proximity of the minimum gap between the ground and first excited state around τ ~ 0.4 [see panel(c)].