Quantum implicit computational complexity

We introduce a quantum lambda calculus inspired by Lafont’s Soft Linear Logic and capturing the polynomial quantum complexity classes EQP, BQP and ZQP. The calculus is based on the “classical control and quantum data” paradigm. This is the first example of a formal system capturing quantum complexit...

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Bibliographic Details
Published in:Theoretical computer science Vol. 411; no. 2; pp. 377 - 409
Main Authors: Dal Lago, Ugo, Masini, Andrea, Zorzi, Margherita
Format: Journal Article
Language:English
Published: Oxford Elsevier B.V 02.01.2010
Elsevier
Subjects:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Computer science; control theory; systems
Exact sciences and technology
General logic
Implicit computational complexity
Lambda calculus
Logic and foundations
Mathematical logic, foundations, set theory
Mathematics
Miscellaneous
Programming theory
Quantum computation
Sciences and techniques of general use
Theoretical computing
Quantum computation
Lambda calculus
Implicit computational complexity
Polynomial
Complexity class
Linear logic
Paradigm
Computer theory
Syntax
Computational complexity
ISSN:0304-3975, 1879-2294
Online Access:Get full text
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Summary:We introduce a quantum lambda calculus inspired by Lafont’s Soft Linear Logic and capturing the polynomial quantum complexity classes EQP, BQP and ZQP. The calculus is based on the “classical control and quantum data” paradigm. This is the first example of a formal system capturing quantum complexity classes in the spirit of implicit computational complexity — it is machine-free and no explicit bound (e.g., polynomials) appears in its syntax.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2009.07.045