All computer calculations are currently performed on computers constrained by the laws of Newtonian physics, also known as classical physics. However, as Richard Feynman suggested in the 1980s, a quantum computer could take advantage of the superposition and entanglement phenomena of quantum physics to speed up calculations. As limited prototypes of quantum computers gradually emerge, start-ups, major digital companies and even governments are gradually gearing their research, strategy and funding to harnessing the potential of this future computer.
Against this backdrop, this lecture at the Collège de France on Quantum Algorithms will attempt to meet a growing demand for information and training from a wide range of audiences. Through clear and scientifically rigorous explanations of the subject, this lecture will enable a varied audience to assimilate the notions and concepts of fundamental quantum algorithms, right up to the most recent, in order to better understand their applications and limitations. This lecture will be accessible to the widest possible audience, while providing the kind of training expected in the academic world. The target audience ranges from those curious to grasp the possibilities and limits of quantum computing, to those involved in computer science in the broadest sense: computer scientists, digital mathematicians and quantum physicists, whether students, researchers, developers, entrepreneurs or future users of quantum algorithms.
Starting with the first quantum paradoxes, we will study the foundations of quantum cryptography and communication. Next, we'll introduce the concepts of quantum computation through circuitry, which will enable us to present the main quantum algorithmic methods: the demonstration of algebraic properties enabling secret messages to be deciphered, and optimization opening the way to a vast field of algorithmic applications. We then turn to the limits of quantum computation, both theoretical and technological. Finally, we'll describe some of the current research into the short-term use of limited quantum computer prototypes, with potential applications in artificial intelligence and decentralized Internet applications.