The physical implementation of quantum annealing algorithm

Quantum annealing (QA) is a classical randomized algorithm … suggested by the behaviour of quantum systems.

Thus, there is no part of QA that necessarily “depends on quantum hardware.” In classical annealing (CA), a term analogous to temperature is the source of the random perturbations that allow the algorithm to explore a problem’s solution space. In QA, the temperature term is replaced by a term analogous to quantum tunneling field strength. Presumably, in a quantum implementation of QA, steps involving quantum tunneling would be carried out directly in hardware. A comparison of the two techniques can be found here, and D-Wave’s explanation here. EDIT: from D-Wave’s Processor operation documentation (emphasis added): Let there be an optimization problem of the form $E(vec{s})=-sumlimits_ih_is_i + sumlimits_{i,j>i}K_{ij}s_is_j$ where $-1leq h_i$, $K_{ij} leq +1$ and $s_i = pm1$. There exists an optimal solution $vec{s}_{gs}$ that minimizes the objective $E$. Map the problem onto a quantum Ising spin glass (QSG) Hamiltonian $frac{mathcal{H}_{QSG}(t)}{E_0(t)}=-sumlimits_ih_isigma_z^{(i)}+sumlimits_{i,j>i}K_{ij}sigma_z^{(i)}sigma_z^{(j)}-Gamma(t)sumlimits_isigma_x^{(i)}$ Use a physical system to find the $|vec{s_{gs}}rangle$ by evolving $Gamma(t)$ such that $Gamma(0) ll h_i,K_{ij}$ $Gamma(t_f) gg h_i,K_{ij}$