4.2 Quantum annealing

Although we have just seen that adiabatic quantum computing is, theoretically, a perfectly viable alternative to the quantum circuit model, in its practical incarnation it is usually implemented in a restricted version called quantum annealing.

Quantum annealing relies on the same core idea as adiabatic quantum computing: it takes an initial Hamiltonian , a final Hamiltonian whose ground state encodes the solution to the problem of interest, and it gradually changes the acting Hamiltonian from the initial to the final one by using some functions and (as described in the previous section) to decrease the action of and to increase the action of . However, quantum annealing deviates from full adiabatic quantum computing in two ways. First of all, in practical implementations of quantum annealing, the final Hamiltonian that can be realized cannot be chosen completely at will, but has to be selected from a certain, restricted class. A typical option is an Ising...