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 .
A local Hamiltonian is a sum of terms, each acting nontrivially on only a bounded number of subsystems.
A -local Hamiltonian is a sum of terms that each act nontrivially on at most subsystems. The integer remains fixed as the system size grows.
Product-formula Hamiltonian simulation approximates by alternating exponentials of and , which are assumed easier to implement separately.
The symmetric second-order formula, also called Strang splitting, isfor bounded operators, with the constant controlled by nested commutators.
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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.