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Cited by 19Quantum Computing Algorithms and ArchitectureComputability, Logic, AI AlgorithmsQuantum Information and Cryptography

Necessary and Sufficient Conditions for Quantum Computation

Lloyd, Seth·1994·Journal of Modern Optics
DOI 10.1080/09500349414552341
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Abstract

Necessary and sufficient conditions are given for a quantummechanical system to possess a coordinate system with respect to which its behaviour at discrete times is that of a universal digital computer. The form of the diagonal representation for the unitary time evolution operator for quantum universal computers is derived; aspects of the transformation between the diagonal representation and the computational representation are shown to be uncomputable. A quantum-mechanical treatment of macroscopic, dissipative computers is given.

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Crossref · 10.1080/09500349414552341

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  • A wide variety of physical systems-ranging from nearest neighbor Ising models to quantum electrodynamics and conformal field theories-are known to be computationally universal.

    “Although computational universality might at first seem to be a stringent demand on a physical system, a wide variety of physical systems - ranging from nearest neighbor Ising models 52 to quantum electrodynamics 84 and conformal field theories 86 - are known to be computationally universal 51 -53 , 55 -65 .”

    From Ultimate physical limits to computation (2000) · cites this paper as [53]

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Authors
Lloyd, S.
Affiliations
Los Alamos National Laboratory (US)
Corresponding author
Lloyd, Seth
ORCID
Lloyd, Seth
Venue
Journal of Modern Optics
Publisher
Informa UK Limited
Published
1994-12
Volume
41
Issue
12
Pages
2503-2520
ISSN
  • 0950-0340 (ISSN-L)
  • 1362-3044
DOI
10.1080/09500349414552341
OpenAlex
W2004230505
Cited by
19
References
30
Citations by year
2025: 2 · 2024: 1 · 2022: 2 · 2020: 1 · 2018: 1 · 2013: 1 · 2012: 1
FWCI
2.57
Type
journal article
Language
en
Open access
closed
Locations
Journal of Modern Optics (publishedVersion)
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
  • Physical Sciences › Computer Science › Computational Theory and Mathematics › Computability, Logic, AI Algorithms
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
Keywords
quantum computing, universal quantum computer, necessary and sufficient conditions, uncomputability

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