# PHYS 598 Algorithms on Strongly Correlated Systems

### Looking for hard quantum problems? Follow the entangledsign 😉

Themes:

1. Sign
If a quantum wave function is not allowed to have positive and negative parts, then a quantum computer is only as powerful as a classical computer. On the other hand, without complex numbers, quantum computers are still powerful. This may imply that a quantum problem without signs can be simulated on a classical computer.

2. Entanglement
A state that is not too entangled can also be simulated on a classical computer. This could be the motivation behind tensor network and DMRG.

Topics:

1. Lattice Methods:
1. Exact Diagonalization (ED)
2. Matrix Product State (MPS)
3. Density Matrix Renormalization Group Optimization Algorithm (DMRG)
2. Core Concepts:
1. Markov Chain: Memory-less random walk on a graph
2. Metropolis”: Sample a distribution $$\pi$$ by building a graph
3. Continuum Methods
1. Variational Monte Carlo (VMC)
2. Diffusion Monte Carlo (DMC)
3. Path Integral Monte Carlo (PIMC)