3.2 Forward and Reverse Quantum Annealing
Having defined the QUBO problem, we now review how quantum annealing can act as an efficient solver.
3.2.1 Forward quantum annealing
The quantum annealing protocol, inspired by the adiabatic principle of quantum mechanics detailed in Chapter 2, dictates driving the system from an easy-to-prepare ground state of an initial Hamiltonian H0 to the unknown low-energy subspace of states of the problem Hamiltonian HF , ideally to the lowest energy state corresponding to the global minimum of the objective function. This forward quantum annealing procedure can be ideally described as attempting to drive the evolution of the time-dependent Hamiltonian
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starting from
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where H0 is a Hamiltonian describing an independent collection of local transverse fields for each spin of the system (σx is the Pauli X spin operator, or the quantum NOT gate, detailed in Section 6.3.3).
In expression (3.2...
