Hamiltonian

In quantum computing, a Hamiltonian is the operator (think “energy rulebook”) that determines how a quantum system evolves over time and which states are energetically favored. Practically, you define or engineer a Hamiltonian so that evolving the system (or finding its lowest-energy state) performs a computation—e.g., simulating molecules/materials or solving optimization problems by encoding the answer in the ground state. Quantum algorithms like Hamiltonian simulation and variational/annealing methods use the Hamiltonian as the central object to implement and control the computation.