Adiabatic Quantum Computation: From Adiabatic Theorem to D-Wave Computer

In this paper we describe the fundamentals of the adiabatic quantum computing, which consists of the interpolation of different Hamiltonians, from an initial Hamiltonian, with known eigenstates and eigenenergies, to a final Hamiltonian, in which the solution to a given problem is encoded. In particular, we discuss the quantum annealing method, which is used by the Canadian company D-Wave, a pioneer in this area. Firstly, we present the proof of the quantum adiabatic theorem and an adiabaticity condition for the evolution of quantum systems. To exemplify, we describe the implementation of the Grover algorithm via adiabatic quantum computing, discussing the impacts of the choice of the interpolation form of the initial and final Hamiltonians on the complexity of the algorithm. In the following, we show an algorithm for the travelling salesman problem executable on the D-Wave platform. Finally, we present important physical aspects of D-Wave’s quantum computer technology, exposing its advantages and disadvantages, in addition to qualitatively describing the engineering of its quantum processor.