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Pauli Center for Theoretical Studies

The Swiss National Science Foundation

ETH Zurich (Computer Science and Physics Department)

Quantum Science and Technology

CQT Singapore

QAP European Project

Sandia National Laboratories

Institute for Quantum Computing

id Quantique

Classical simulation of many-body quantum systems

Ignacio Cirac, MPQ, Garching

Many body quantum systems are very hard to describe due to the exponential increase of the number of parameters with the number of particles. During the last years different methods have been envisioned in order to find efficient descriptions of certain many-body quantum states. Those methods are based on families of states which can be expressed in terms of few tensors. The corresponding families include Matrix Product States, Projected Entangled-Pair States, Multi-Scale Renormalization Ansatz, or Tensor-Tree states. In this lecture I will introduce those families of states, describe their properties, and show how they can be used in order to efficiently describe many-body quantum systems; in particular, those occuring in certain condensed matter problems.