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Analytical solution of thermal magnetization on memory stabilizer structures

Publication ,  Journal Article
Tomita, Y; Viteri, CR; Brown, KR
Published in: Physical Review A - Atomic, Molecular, and Optical Physics
October 6, 2010

We return to the question of how the choice of stabilizer generators affects the preservation of information on structures whose degenerate ground state encodes a classical redundancy code. Controlled-not gates are used to transform the stabilizer Hamiltonian into a Hamiltonian consisting of uncoupled single spins and/or pairs of spins. This transformation allows us to obtain an analytical partition function and derive closed-form equations for the relative magnetization and susceptibility. These equations are in agreement with the numerical results presented in Viteri [Phys. Rev. APLRAAN1050-294710.1103/ PhysRevA.80.042313 80, 042313 (2009)] for finite size systems. Analytical solutions show that there is no finite critical temperature, Tc=0, for all of the memory structures in the thermodynamic limit. This is in contrast to the previously predicted finite critical temperatures based on extrapolation. The mismatch is a result of the infinite system being a poor approximation even for astronomically large finite-size systems, where spontaneous magnetization still arises below an apparent finite critical temperature. We extend our analysis to the canonical stabilizer Hamiltonian. Interestingly, Hamiltonians with two-body interactions have a higher apparent critical temperature than the many-body Hamiltonian. © 2010 The American Physical Society.

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Published In

Physical Review A - Atomic, Molecular, and Optical Physics

DOI

EISSN

1094-1622

ISSN

1050-2947

Publication Date

October 6, 2010

Volume

82

Issue

4

Related Subject Headings

  • General Physics
  • 03 Chemical Sciences
  • 02 Physical Sciences
  • 01 Mathematical Sciences
 

Citation

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Tomita, Y., Viteri, C. R., & Brown, K. R. (2010). Analytical solution of thermal magnetization on memory stabilizer structures. Physical Review A - Atomic, Molecular, and Optical Physics, 82(4). https://doi.org/10.1103/PhysRevA.82.042303
Tomita, Y., C. R. Viteri, and K. R. Brown. “Analytical solution of thermal magnetization on memory stabilizer structures.” Physical Review A - Atomic, Molecular, and Optical Physics 82, no. 4 (October 6, 2010). https://doi.org/10.1103/PhysRevA.82.042303.
Tomita Y, Viteri CR, Brown KR. Analytical solution of thermal magnetization on memory stabilizer structures. Physical Review A - Atomic, Molecular, and Optical Physics. 2010 Oct 6;82(4).
Tomita, Y., et al. “Analytical solution of thermal magnetization on memory stabilizer structures.” Physical Review A - Atomic, Molecular, and Optical Physics, vol. 82, no. 4, Oct. 2010. Scopus, doi:10.1103/PhysRevA.82.042303.
Tomita Y, Viteri CR, Brown KR. Analytical solution of thermal magnetization on memory stabilizer structures. Physical Review A - Atomic, Molecular, and Optical Physics. 2010 Oct 6;82(4).

Published In

Physical Review A - Atomic, Molecular, and Optical Physics

DOI

EISSN

1094-1622

ISSN

1050-2947

Publication Date

October 6, 2010

Volume

82

Issue

4

Related Subject Headings

  • General Physics
  • 03 Chemical Sciences
  • 02 Physical Sciences
  • 01 Mathematical Sciences