Feasibility of self-correcting quantum memory and thermal stability of topological order

Journal Article · Sat Oct 15 00:00:00 EDT 2011 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2011.06.001· OSTI ID:21583284

Yoshida, Beni

Recently, it has become apparent that the thermal stability of topologically ordered systems at finite temperature, as discussed in condensed matter physics, can be studied by addressing the feasibility of self-correcting quantum memory, as discussed in quantum information science. Here, with this correspondence in mind, we propose a model of quantum codes that may cover a large class of physically realizable quantum memory. The model is supported by a certain class of gapped spin Hamiltonians, called stabilizer Hamiltonians, with translation symmetries and a small number of ground states that does not grow with the system size. We show that the model does not work as self-correcting quantum memory due to a certain topological constraint on geometric shapes of its logical operators. This quantum coding theoretical result implies that systems covered or approximated by the model cannot have thermally stable topological order, meaning that systems cannot be stable against both thermal fluctuations and local perturbations simultaneously in two and three spatial dimensions. - Highlights: > We define a class of physically realizable quantum codes. > We determine their coding and physical properties completely. > We establish the connection between topological order and self-correcting memory. > We find they do not work as self-correcting quantum memory. > We find they do not have thermally stable topological order.

• OSTI ID: 21583284
• Journal Information: Annals of Physics (New York), Vol. 326, Issue 10; Other Information: DOI: 10.1016/j.aop.2011.06.001; PII: S0003-4916(11)00102-3; Copyright (c) 2011 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DISTURBANCES
FLUCTUATIONS
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GROUND STATES
HAMILTONIANS
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PERTURBATION THEORY
PHYSICAL PROPERTIES
QUANTUM FIELD THEORY
QUANTUM INFORMATION
SPIN
STABILITY
SYMMETRY
TOPOLOGY
ANGULAR MOMENTUM
ENERGY LEVELS
FIELD THEORIES
INFORMATION
MATHEMATICAL OPERATORS
MATHEMATICS
PARTICLE PROPERTIES
QUANTUM OPERATORS
VARIATIONS