Completeness of the Classical 2D Ising Model and Universal Quantum Computation

Completeness of classical spin models and universal quantum computation

We study mappings between distinct classical spin systems that leave the partition function invariant. As recently shown in [Phys. Rev. Lett. 10

Classical Ising model test for quantum circuits

We exploit a recently constructed mapping between quantum circuits and graphs in order to prove that circuits corresponding to certain planar graphs can be efficiently simulated classically. The proof uses an expression for the Ising model partition function in terms of quadratically signed weight enumerators (QWGTs), which are polynomials that arise naturally in an expansion of quantum circuit...

Universal ratios in the 2D tricritical ising model

We consider the universality class of the two-dimensional tricritical Ising model. The scaling form of the free energy leads to the definition of universal ratios of critical amplitudes which may have experimental relevance. We compute these universal ratios by a combined use of results coming from perturbed conformal field theory, integrable quantum field theory, and numerical methods.

Quantum Computation and NP-Completeness

Structure-Function Relationship of the Brain: A comparison between the 2D Classical Ising model and the Generalized Ising model

There is evidence that the functional patterns of the brain observed at rest using fMRI are sustained by a structural architecture of axonal fiber bundles. As neuroimaging techniques advance with time, the relationship between structure and function has become the object of many studies in neuroscience. As recently suggested, the well-defined connectivity structure found in the brain can be use...