non-frustrated interacting boson systems, while providing an approximate description of interacting fermion systems. Most methods aim at computing the ground state wavefunction of the system, with the exception of path integral Monte Carlo and finite-temperature auxiliary-field Monte Carlo, which calculate the density matrix. In addition to static properties, the time-dependent Schrödinger equation can also be solved, albeit only approximately, restricting the functional form of the time-evolved wave function, as done in the time-dependent variational Monte Carlo. From a probabilistic point of view, the computation of the top eigenvalues and the corresponding ground state eigenfunctions associated with the Schrödinger equation relies on the numerical solving of Feynman–Kac path integration problems. Quantum Monte Carlo methods There are several quantum Monte Carlo methods, each of which uses Monte Carlo in different ways to solve the many-body problem. Zero-temperature (only ground state) Variational Monte Carlo: A good place to start; it is commonly used in many sorts of quantum problems. Diffusion Monte Carlo: The most common high-accuracy method for electrons (that is, chemical problems), since it comes quite close to the exact ground-state energy fairly efficiently. Also used for simulating the quantum behavior of atoms, etc. Reptation Monte Carlo: Recent zero-temperature method related to path integral Monte Carlo, with applications similar to diffusion Monte Carlo but with some different tradeoffs. Gaussian quantum Monte Carlo Path integral ground state: Mainly used for boson systems; for those it allows calculation of physical observables exactly, i.e. with arbitrary accuracy Finite-temperature (thermodynamic) Auxiliary-field Monte Carlo: Usually applied to lattice problems, although there has been recent work on applying it to electrons in chemical systems. Continuous-time quantum Monte Carlo Determinant quantum Monte Carlo or Hirsch–Fye quantum Monte Carlo Hybrid quantum Monte Carlo Path integral Monte Carlo: Finite-temperature technique mostly applied to bosons where temperature is very important, especially superfluid helium. Stochastic Green function algorithm: An algorithm designed for bosons that can simulate any complicated lattice Hamiltonian that does not have a sign problem. World-line quantum Monte Carlo Real-time dynamics (closed quantum systems) Time-dependent variational Monte Carlo: An extension of the variational Monte Carlo to study the dynamics of pure quantum states. See also Monte Carlo method QMC@Home Quantum chemistry Quantum Markov chain Density matrix renormalization group Time-evolving block decimation Metropolis–Hastings algorithm Wavefunction optimization Monte Carlo molecular modeling Quantum chemistry computer programs Numerical analytic continuation Notes References External links QMC in Cambridge and around the world Large amount of general