Quantum computational complexity in the presence of closed timelike curves

Journal Article · Wed Sep 01 04:00:00 EDT 2004 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.70.032309· OSTI ID:20646014

Bacon, Dave ^[1]

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1. Institute for Quantum Information, California Institute of Technology, Pasadena, California 91125 (United States)

Quantum computation with quantum data that can traverse closed timelike curves represents a new physical model of computation. We argue that a model of quantum computation in the presence of closed timelike curves can be formulated which represents a valid quantification of resources given the ability to construct compact regions of closed timelike curves. The notion of self-consistent evolution for quantum computers whose components follow closed timelike curves, as pointed out by Deutsch [Phys. Rev. D 44, 3197 (1991)], implies that the evolution of the chronology respecting components which interact with the closed timelike curve components is nonlinear. We demonstrate that this nonlinearity can be used to efficiently solve computational problems which are generally thought to be intractable. In particular we demonstrate that a quantum computer which has access to closed timelike curve qubits can solve NP-complete problems with only a polynomial number of quantum gates.

• OSTI ID: 20646014
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 3 Vol. 70; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
EVOLUTION
INFORMATION THEORY
NONLINEAR PROBLEMS
POLYNOMIALS
QUANTUM MECHANICS