2.2 Principles of Adiabatic Quantum Computing
Adiabatic quantum optimisation is a promising approach to solving NP-complete and NP-hard problems [97]. Assume that a solution to the optimisation problem is encoded in the ground state (i.e., the quantum state corresponding to the lowest eigenvalue) of a quantum Hamiltonian HF . By the second postulate of quantum mechanics (Section 1.2.2), the dynamics of a quantum system is fully specified by its Hamiltonian. If we know how to encode the objective function that we want to minimise in the Hamiltonian of a quantum system, then finding the ground state of the Hamiltonian is equivalent to finding the set of decision variables that minimises the objective function.
As a simple example of equivalence between the minimum of a function and the ground state of a Hamiltonian, consider a function f : {0,1}n →ℝ that needs to be minimised and take the Hamiltonian
Clearly, for any z0 ∈{0,1}n,
since the computational...
