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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

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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

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

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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

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

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Solutions ...

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