In this seminar we review the quantum science approaches to the solution of the many-body quantum problem. In particular, we introduce the tensor network methods, a class of classical algorithms developed to simulate many-body quantum systems, and review some of their applications, such as the benchmarking of quantum simulators, quantum annealing and the quantum version of Conway's game of life.
The simulation of many-body quantum systems is one of the most challenging problems in computational physics, since a quantum system of N elements is described by an N-body wave function and the dynamical equations form a system of coupled partial differential equations with a number of variables that grows exponentially with N. Indeed, the original idea of quantum computers has been first put forward by R. Feynman to solve this class of problems.
Some of the most exciting instances of the equilibrium and out-of-equilibrium quantum many-body problem are the simulation of condensed matter models, of lattice gauge theories and of quantum annealing, that can be applied to attack classical hard problems. Nowadays, the quantum many-body problem can be attacked either via classical numerical methods such as tensor networks, or via the first generation of quantum simulations.
Tensor network methods provide a compressed but faithful description of many-body quantum systems in a wide range of scenarios by means of a decomposition of the N-rank tensor into a network of low-rank tensors. Quantum simulators are dedicated quantum hardware tailored to reproduce the physics of another system in a controlled environment. They are the equivalent for many-body quantum systems of the wind tunnel for hydrodynamics.
Eventually, it is expected that quantum simulators will overcome the predictive power of classical methods. However, to benchmark and build trust in the first generations of quantum simulators, detailed classical numerical simulations are required.
Contact Person: Alessandra Di Pierro