TY - JOUR
T1 - Undecidability in tensor network states
AU - Morton, Jason
AU - Biamonte, Jacob
N1 - Copyright:
Copyright 2012 Elsevier B.V., All rights reserved.
PY - 2012/9/10
Y1 - 2012/9/10
N2 - Recent work has examined how undecidable problems can arise in quantum-information science. We augment this by introducing three undecidable problems stated in terms of tensor networks. These relate to ideas of Penrose about the physicality of a spin network representing a physical process, closed timelike curves, and Boolean relation theory. Seemingly slight modifications of the constraints on the topology or the tensor families generating the networks lead to problems that transition from decidable to undecidable to even always satisfiable.
AB - Recent work has examined how undecidable problems can arise in quantum-information science. We augment this by introducing three undecidable problems stated in terms of tensor networks. These relate to ideas of Penrose about the physicality of a spin network representing a physical process, closed timelike curves, and Boolean relation theory. Seemingly slight modifications of the constraints on the topology or the tensor families generating the networks lead to problems that transition from decidable to undecidable to even always satisfiable.
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U2 - 10.1103/PhysRevA.86.030301
DO - 10.1103/PhysRevA.86.030301
M3 - Article
AN - SCOPUS:84866084321
SN - 1050-2947
VL - 86
JO - Physical Review A - Atomic, Molecular, and Optical Physics
JF - Physical Review A - Atomic, Molecular, and Optical Physics
IS - 3
M1 - 030301
ER -