The Hamiltonian is a concept in (unsurprisingly) Hamiltonian mechanics which represents an operator in a system. In many cases it corresponds to the total energy of a system and so I’ll continue to use it as analogous for the total energy although this is not always true. Just picture it as an equation with each term representing one of the kinds of energy a system contains. Now often you want to find the ground state, the lowest possible energy, for the system as this will provide useful information to solve it. But what if this Hamiltonian’s ground state is very complicated, if not impossible, to find algebraically? Well, this is the basis of an adapted form of quantum computing called adiabatic quantum computing.

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