Quantum complexity theory

Quantum complexity theory is the subfield of computational complexity theory that deals with complexity classes defined using quantum computers, a computational model based on quantum mechanics. It studies the hardness of computational problems in relation to these complexity classes, as well as the relationship between quantum complexity classes and classical (i.e., non-quantum) complexity classes. Two important quantum complexity classes are BQP and QMA. Computational complexity and Complexity class A complexity class is a collection of computational problems that can be solved by a computational model under certain resource constraints. For instance, the complexity class P is defined as the set of problems solvable by a Turing machine in polynomial time. Similarly, quantum complexity classes may be defined using quantum models of computation, such as the quantum circuit model or the equivalent quantum Turing machine. One of the main aims of quantum complexity theory is to find out how these classes relate to classical complexity classes such as P, NP, BPP, and PSPACE. One of the reasons quantum complexity theory is studied are the implications of quantum computing for the modern Church-Turing thesis. In short the modern Church-Turing thesis states that any computational model can be simulated in polynomial time with a probabilistic Turing machine. However, questions around the Church-Turing thesis arise in the context of quantum computing. It is unclear whether the Church-Turing thesis holds for the quantum computation model. There is much evidence that the thesis does not hold. It may not be possible for a probabilistic Turing machine to simulate quantum computation models in polynomial time. Both quantum computational complexity of functions and classical computational complexity of functions are often expressed with asymptotic notation. Some common forms of asymptotic notion of functions are , , and .

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Concepts associés (8)

Cours associés (24)

Séances de cours associées (221)

CS-308: Introduction to quantum computation

The course introduces the paradigm of quantum computation in an axiomatic way. We introduce the notion of quantum bit, gates, circuits and we treat the most important quantum algorithms. We also touch

CS-251: Theory of computation

This course constitutes an introduction to theory of computation. It discusses the basic theoretical models of computing (finite automata, Turing machine), as well as, provides a solid and mathematica

CS-630: Fault-tolerant quantum computing

The course explains how to execute scalable algorithms on fault-tolerant quantum computers. It describes error correction used to build reliable logical operations from noisy physical operations, and

Quantum complexity theory

Problème algorithmique

Un problème algorithmique est, en informatique théorique, un objet mathématique qui représente une question ou un ensemble de questions auxquelles un ordinateur devrait être en mesure de répondre. Le plus souvent, ces problèmes sont de la forme : étant donné un objet (l'instance), effectuer une certaine action ou répondre à telle question. Par exemple, le problème de la factorisation est le problème suivant : étant donné un nombre entier, trouver un facteur premier de cet entier.

Computational complexity

In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus is given to computation time (generally measured by the number of needed elementary operations) and memory storage requirements. The complexity of a problem is the complexity of the best algorithms that allow solving the problem. The study of the complexity of explicitly given algorithms is called analysis of algorithms, while the study of the complexity of problems is called computational complexity theory.

Délégation quantique de calcul

Couvre le concept de délégation quantique du calcul et la relation entre MIP et RE, en abordant les questions fréquentes et en discutant des matériaux utiles et des interactions avec les appareils quantiques.

Apprendre des modèles probabilistes

Défis posés par l'apprentissage des modèles probabilistes, couvrant la complexité des calculs, la reconstruction des données et les lacunes statistiques.

Simplification de la propagation des croyances PHYS-512: Statistical physics of computation

Explore la simplification des équations de propagation des croyances pour les modèles par paires, réduisant la complexité de calcul de l'ordre n cube à l'ordre n.