**Quantum Monte Carlo** is a large class of computer algorithms that simulate

quantum systems with the idea of solving the quantum

many-body problem. They use, in one way or another, the

Monte Carlo method to handle the many-dimensional integrals that arise. Quantum Monte Carlo allows a direct representation of many-body effects in the

wave function, at the cost of statistical uncertainty that can be reduced with more simulation time. For

bosons, there exist numerically exact and

polynomial-scaling

algorithms. For

fermions, there exist very good approximations and numerically exact exponentially scaling quantum Monte Carlo algorithms, but none that are both.

## Background

In principle, any physical system can be described by the many-body

Schrödinger equation as long as the constituent particles are not moving "too" fast; that is, they are not moving near the speed of light. This includes the electrons in almost every material in the world, so if we could solve the Schrödinger equation, we could predict the behavior of any electronic system, which has important applications in fields from computers to biology. This also includes the

nuclei in

Bose–Einstein condensate and

superfluids such as

liquid helium. The difficulty is that the Schrödinger equation involves a function of three times the number of particles and is difficult to solve even using

parallel computing technology in a reasonable amount of time. Traditionally, theorists have approximated the...

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