Quantum computers, often heralded as the next technological revolution, exploit the laws of quantum mechanics to perform calculations that are supposedly more efficient than those performed by classical computers. Google and IBM, for example, have unveiled prototypes capable of solving specific problems designed to demonstrate the “quantum supremacy” of these machines. Impressive though they are, these machines have little practical use for the moment.
In the face of this breakthrough, conventional computers have been quick to strike back. Thanks to algorithms based on tensor networks, they have narrowed the supposed performance gap with quantum systems. As a result, quantum supremacy appears less obvious. The real question is which technology – quantum computers or tensor networks – will be able to solve concrete, truly useful problems. And on this front, the outcome remains uncertain.
The only problem where quantum computers seem to have a theoretical advantage is that of solving quantum mechanical equations applied to complex systems, notably the famous “N-body quantum problem”. Coincidentally, tensor networks were developed precisely for this type of challenge. To this day, they remain the most efficient way of dealing with this problem, although they have yet to fully elucidate all its facets.
In this article, Antoine Tilloy explains what the N-body quantum problem is, and why it represents a major challenge for science. He also traces the history of the various attempts to overcome this challenge, before discussing the contemporary solutions offered by quantum computers and tensor networks. In addition, it examines the development of tensor networks, explaining how they work and their potential impact, making these tools a valuable asset to classical computers in today’s technological competition.
Antoine Tilloy is a teacher-researcher specializing in theoretical physics at the Centre Automatique et Systèmes (CAS) at Mines Paris – PSL. After a post-doctorate at the Max Planck Institute in Germany, he returned to France to join CAS, where he joined the Quantic team, a collaboration of experimental physicists and applied mathematicians involving Mines Paris – PSL,Inria,ENS – PSL, Sorbonne Université and CNRS. The main objective of this interdisciplinary team is to develop both theoretical methods and experimental devices guaranteeing robust processing of quantum information.
Its research has been recognized by the award of a 1.21 million euro grant from theEuropean Research Council (ERC) Starting Grant 2021 for its “QFT.zip” project, developing a tensor network method applied to quantum field theory.
