Quantum Monte Carlo
This course connects physical intuition, derivations, model boundaries and verifiable practice. Lessons state assumptions, work through examples and explain exercises; illustrations distinguish analytic models from simulation data.
1. Prerequisites and study method
Bring algebra, calculus and elementary probability. Quantum courses use complex numbers and linear algebra; sampling courses use partition functions. Read the overall roadmap, then follow the sequence below. For every formula, identify its variables, units, assumptions and failure conditions.
Recommended preparation: Quantum mechanics · Molecular methods · Monte Carlo
2. Numbered lessons
- The many-electron problem and QMC routes
- VMC and the local-energy estimator
- Slater–Jastrow states, cusps, and nodes
- Optimizing a trial state without optimizing noise
- Imaginary-time projection and branching
- Importance-sampled diffusion Monte Carlo
- Fermion signs, fixed nodes, and fixed phase
- Mixed estimators, timestep, and population bias
- Periodic cells, finite-size errors, and a validation project
- Thermal path integrals, ring polymers, and exchange
3. Core and advanced routes
Core route: complete the derivations and exercises in the first six lessons, then read the intuition and limitations of the remaining lessons. Advanced route: complete the full sequence, rederive the central equations independently, and connect them to numerical convergence or sampling design in the software tutorials. A shorter route does not waive the assumptions of advanced methods.
4. Completion task
Choose one target observable and separate its physical model, numerical approximation, statistical estimator and validation evidence. Supply one hand calculation, one convergence plan and one condition under which the interpretation fails. A proposed calculation must not be presented as an executed result.