Abstract-The error threshold for fault-tolerant quantum computation with concatenated encoding of qubits is penalized by internal communication overhead. Many quantum computation proposals rely on nearest neighbor communication, which requires excess gate operations. For a qubit stripe with a width of + 1 physical qubits implementing levels of concatenation, we find that the error threshold of 2.1 10 5 without any communication burden is reduced to 1.2 10 7 when gate errors are the dominant source of error. This 175 penalty in error threshold translates to an 13 penalty in the amplitude and timing of gate operation control pulses.

We introduce a general approach to calculating the morphological consequences of coherent strain relaxation in heteroepitaxial thin films based on lattice statics using linear elasticity. The substrate and film are described by a simple cubic lattice of atoms with localized interactions. The boundary conditions at concave and convex corners that appear as a result of this construction, those along straight interfacial segments, and the governing equations are obtained from a variational calculation applied to a discretized form of the total elastic energy. The continuum limit of the equations and the boundary conditions along straight boundaries reproduces standard results of elasticity theory, but the boundary conditions at corners have no such analog. Our method enables us to calculate quantities such as the local strain energy density for any surface morphology once the lattice misfit and the elastic constants of the constituent materials are specified. The methodology is illustrated by examining the strain, displacement, and energies of one-dimensional strained vicinal surfaces. We discuss the effects of epilayer thickness on the energy of various step configurations and suggest that coupling between surface and substrate steps should affect the equilibration of the surface toward the bunched state.

Landau theory of domain walls for one-dimensional asymmetric potentials Am. J. Phys. 71, 1005 (2003) Watching a drunkard for 10 nights: A study of distributions of variances Am.

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