Quantum Monte Carlo

Quantum Monte Carlo is a family of stochastic methods that uses random sampling to solve or approximate quantum many-body problems.

Variational Monte Carlo: A quantum Monte Carlo method that estimates observables by sampling a trial wavefunction and optimizes its parameters. It evaluates a chosen wavefunction directly, making it a basic variational approach.
Quantum sign problem: A cancellation problem in stochastic calculations where positive and negative contributions make averages exponentially noisy. It is the main obstacle to efficient sampling in many fermionic and frustrated systems.
Quantum chemistry: The application of quantum mechanics to molecular structure, bonding, and chemical properties. Quantum Monte Carlo estimates molecular energies and electron correlations.
Monte Carlo method: A computational method that uses random sampling to estimate quantities that may be difficult to calculate directly. Quantum Monte Carlo adapts this general strategy to quantum states and observables.
Nicholas Metropolis: A Greek-American physicist and computer scientist who helped develop the Metropolis sampling algorithm. His algorithm became a foundational sampling tool used in quantum simulations.
Diffusion Monte Carlo: A projector method that uses stochastic walkers to approach a quantum system’s ground state. It improves on a trial state by projecting toward lower-energy states in imaginary time.
Fixed-node approximation: A constraint in diffusion Monte Carlo that fixes the nodes of the trial wavefunction to control fermionic errors. It reduces sign instability but introduces bias tied to the trial state's nodal surface.
Electronic structure theory: The theoretical and computational study of electrons in atoms, molecules, and materials. Quantum Monte Carlo is one family of tools for predicting electronic properties.
Many-body problem: The problem of predicting the collective behavior of a system containing many interacting constituents. Quantum Monte Carlo targets many-body quantities that grow difficult to compute exactly.
Arianna Rosenbluth: A physicist who co-developed the Metropolis algorithm and implemented its early computational form. Her work helped establish the practical random-walk method behind Monte Carlo sampling.

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