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In computational physics, variational Monte Carlo is a quantum Monte Carlo method that applies the variational method to approximate the ground state of a quantum system.
The basic building block is a generic wave function | Ψ ⟩ {\displaystyle |\Psi \rangle } depending on some parameters a {\displaystyle a}. The optimal values of the parameters a {\displaystyle a} is then found upon minimizing the total energy of the system.
In particular, given the Hamiltonian H {\displaystyle {\mathcal {H}}} , and denoting with X {\displaystyle X} a many-body configuration, the expectation value of the energy can be written as: