Hamiltonian simulation refers to the use of algorithms to efficiently approximate the time evolution of quantum systems governed by a Hamiltonian, which is a mathematical operator that describes the total energy of a system in quantum mechanics. In simpler terms, a Hamiltonian defines how a quantum system evolves in time.
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Hamiltonian simulation constructs a quantum circuit approximating the time-evolution operator generated by a Hamiltonian operator , with cost controlled by the evolution time, requested precision, and structure of .