Quantum Computing Explained

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ADIABATIC QUANTUMCOMPUTATION

Adiabatic quantum computation is an alternative approach to quantum computation based on the time evolution of a quantum system. Before describing adiabatic processes, let’s quickly review the dynamics of a quantum system. The time evolution of a quantum state |ψ(t)〉 is described by the Schrödinger equation

where H is the Hamiltonian operator. This operator is the total energy of the system and can be expressed in terms of kinetic and potential energies

where ∇² is the Laplacian operator and V is the potential energy function. In one dimension (14.2) becomes

In many cases of interest, the potential V is time-independent. Where this is the case, then solutions of (14.1) are products of a function that depends only on the spatial coordinates and a function that depends only on time. In one dimension the solution can be written in the form

By inserting (14.4) into (14.1) and using (14.3), its not too hard to show that the solution can be written as

Solutions ...