nLab
quantum computation

Contents

Context

Constructivism, Realizability, Computability

Quantum systems

quantum logic


quantum probability theoryobservables and states


quantum information


quantum computation

quantum algorithms:


quantum physics

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.

References

General

The idea of quantum computation was first expressed in:

  • Paul Benioff, The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines, J Stat Phys 22, 563–591 (1980) (doi:10.1007/BF01011339)

  • Richard Feynman, Simulating physics with computers, Int J Theor Phys 21, 467–488 (1982) (doi:10.1007/BF02650179)

It became a plausible practical possibility with the understanding of quantum error correction in

Introduction and survey:

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

  • John Preskill, Quantum Computation lecture notes, since 2004 (web)

  • 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)

Quantum programming languages

On quantum programming languages (programming languages for quantum computation):

General:

Survey:

functional programming languages for quantum computation:

QPL:

Quipper:

QML:

Quantum programming via dependent linear type theory/indexed monoidal (∞,1)-categories:

specifically with Quipper:

On quantum software verification:

with Quipper:

  • Linda Anticoli, Carla Piazza, Leonardo Taglialegne, Paolo Zuliani, Towards Quantum Programs Verification: From Quipper Circuits to QPMC, In: Devitt S., Lanese I. (eds) Reversible Computation. RC 2016. Lecture Notes in Computer Science, vol 9720. Springer, Cham (doi:10.1007/978-3-319-40578-0_16)

Quantum programming via monads

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

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 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)

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

Experimental realization

  • Han-Shen Zhong et al. Quantum computational advantage using photons, Science 370, n. 6523 (2020) 1460-1463 doi

Last revised on May 7, 2021 at 11:43:48. See the history of this page for a list of all contributions to it.