### Looking for hard quantum problems? Follow the **entangled** *sign* 😉

**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**:

- Lattice Methods:
- Exact Diagonalization (ED)
- Matrix Product State (MPS)
- Density Matrix Renormalization Group Optimization Algorithm (DMRG)

- Core Concepts:
- Markov Chain: Memory-less random walk on a graph
- “Metropolis”: Sample a distribution \(\pi \) by building a graph

- Continuum Methods
- Variational Monte Carlo (VMC)
- Diffusion Monte Carlo (DMC)
- Path Integral Monte Carlo (PIMC)