nLab
quantum computation

Contents

Context

Constructivism, Realizability, Computability

Quantum Field Theory

algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)

Introduction

Concepts

field theory:

Lagrangian field theory

quantization

quantum mechanical system, quantum probability

free field quantization

gauge theories

interacting field quantization

renormalization

Theorems

States and observables

Operator algebra

Local QFT

Perturbative QFT

Contents

Idea

Quantum computation is computation in terms of quantum information theory, possibly implemented on quantum computers, hence on physical systems for which phenomena of quantum mechanics are not negligible. In terms of computational trinitarianism quantum computation is the computation corresponding to (some kind of) quantum logic.

Specifically, topological quantum computation is (or is meant to be) quantum computation implemented on physical systems governed by topological quantum field theory, such as Chern-Simons theory. A prominent example of this is the (fractional) quantum Hall effect in solid state physics.

There are arguments that a good formal context for quantum computing is (via computational trinitarianism) linear logic/linear type theory (e.g. Lago-Faffian 12). See also at quantum logic.

Programing languages

References

General

General discussions include

  • Michael A. Nielsen, Isaac L. Chuang, Quantum computation and quantum information, Cambridge University Press 2000 (pdf)

  • Jens Eisert, M. M. Wolf, Quantum computing, In: Handbook of Nature-Inspired and Innovative Computing, Springer 2006 (arXiv:quant-ph/0401019)

  • Greg Kuperberg, A concise introduction to quantum probability, quantum mechanics, and quantum computation, 2005 (pdf)

  • Michael Loceff, A course in quantum computing, 2013 (pdf)

  • Wikipedia, Quantum computation

  • Scott Aaronson, Lecture notes Quantum Computing Since Democritus 2006 (web)

  • National Academies of Sciences, Engineering, and Medicine, Quantum Computing: Progress and Prospects, The National Academies Press 2019 (doi:10.17226/25196)

In terms of dagger-compact categories

Discussion in terms of finite quantum mechanics in terms of dagger-compact categories:

  • Jamie Vicary, Section 3 of: The Topology of Quantum Algorithms, (LICS 2013) Proceedings of 28th Annual ACM/IEEE Symposium on Logic in Computer Science, pages 93-102 (arXiv:1209.3917)

As linear logic

Discussion of quantum computation as the internal linear logic/linear type theory of compact closed categories is in

An exposition along these lines is in

  • John Baez, Mike Stay, Physics, topology, logic and computation: a rosetta stone, arxiv/0903.0340; in “New Structures for Physics”, ed. Bob Coecke, Lecture Notes in Physics 813, Springer, Berlin, 2011, pp. 95-174

In terms of monads

Discussion of aspects of quantum computing in terms of monads in functional programming are in

Topological quantum computing

topological quantum computation is discussed in

Relation to tensor networks

Relation to tensor networks, specifically matrix product states:

  • Yiqing Zhou, E. Miles Stoudenmire, Xavier Waintal, What limits the simulation of quantum computers? (arXiv:2002.07730)

Last revised on February 21, 2020 at 08:35:04. See the history of this page for a list of all contributions to it.