Local stabilizer codes in three dimensions without string logical operators

Journal Article · Fri Apr 15 00:00:00 EDT 2011 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.83.042330· OSTI ID:21544597

Haah, Jeongwan ^[1]

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

We suggest concrete models for self-correcting quantum memory by reporting examples of local stabilizer codes in 3D that have no string logical operators. Previously known local stabilizer codes in 3D all have stringlike logical operators, which make the codes non-self-correcting. We introduce a notion of ''logical string segments'' to avoid difficulties in defining one-dimensional objects in discrete lattices. We prove that every stringlike logical operator of our code can be deformed to a disjoint union of short segments, each of which is in the stabilizer group. The code has surfacelike logical operators whose partial implementation has unsatisfied stabilizers along its boundary.

• OSTI ID: 21544597
• Journal Information: Physical Review. A, Vol. 83, Issue 4; Other Information: DOI: 10.1103/PhysRevA.83.042330; (c) 2011 American Institute of Physics; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COMPUTER CODES
MATHEMATICAL LOGIC
MATHEMATICAL OPERATORS
MEMORY DEVICES
ONE-DIMENSIONAL CALCULATIONS
QUANTUM INFORMATION
INFORMATION