Analytical solution of thermal magnetization on memory stabilizer structures

作者：Tomita Yu^*; Viteri C Ricardo; Brown Kenneth R

来源：Physical Review A, 2010, 82(4): 042303.

DOI：10.1103/PhysRevA.82.042303

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 et al. [Phys. Rev. A 80, 042313 (2009)] for finite size systems. Analytical solutions show that there is no finite critical temperature, T(c) = 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.

• 出版日期2010-10-6