Quantum annealing with Jarzynski equality

We show a practical application of the Jarzynski equality in quantum computation. Its implementation may open a way to solve combinatorial optimization problems, minimization of a real single-valued function, cost function, with many arguments. We consider to incorpolate the Jarzynski equality into quantum annealing, which is one of the generic algorithms to solve the combinatorial optimization problem. The ordinary quantum annealing suffers from non-adiabatic transitions whose rate is characterized by the minimum energy gap $\Delta_{\rm min.}$ of the quantum system under consideration. The quantum sweep speed is therefore restricted to be extremely slow for the achievement to obtain a solution without relevant errors. However, in our strategy shown in the present study, we find that such a difficulty would not matter.Comment: 4 pages, to appear in Phys. Rev. Let

Nonequilibrium work on spin glasses in longitudinal and transverse fields

We derive a number of exact relations between equilibrium and nonequilibrium quantities for spin glasses in external fields using the Jarzynski equality and gauge symmetry. For randomly-distributed longitudinal fields, a lower bound is established for the work done on the system in nonequilibrium processes, and identities are proven to relate equilibrium and nonequilibrium quantities. In the case of uniform transverse fields, identities are proven between physical quantities and exponentiated work done to the system at different parts of the phase diagram with the context of quantum annealing in mind. Additional relations are given, which relate the exponentiated work in quantum and simulated (classical) annealing. It is also suggested that the Jarzynski equality may serve as a guide to develop a method to perform quantum annealing under non-adiabatic conditions.Comment: 17 pages, 5 figures, submitted to JPS

Analytical evidence for the absence of spin glass transition on self-dual lattices

We show strong evidence for the absence of a finite-temperature spin glass transition for the random-bond Ising model on self-dual lattices. The analysis is performed by an application of duality relations, which enables us to derive a precise but approximate location of the multicritical point on the Nishimori line. This method can be systematically improved to presumably give the exact result asymptotically. The duality analysis, in conjunction with the relationship between the multicritical point and the spin glass transition point for the symmetric distribution function of randomness, leads to the conclusion of the absence of a finite-temperature spin glass transition for the case of symmetric distribution. The result is applicable to the random bond Ising model with $\pm J$ or Gaussian distribution and the Potts gauge glass on the square, triangular and hexagonal lattices as well as the random three-body Ising model on the triangular and the Union-Jack lattices and the four dimensional random plaquette gauge model. This conclusion is exact provided that the replica method is valid and the asymptotic limit of the duality analysis yields the exact location of the multicritical pointComment: 11 Pages, 4 figures, 1 table. submitted to J. Phys. A Math. Theo

Universality in phase boundary slopes for spin glasses on self dual lattices

We study the effects of disorder on the slope of the disorder--temperature phase boundary near the Onsager point (Tc = 2.269...) in spin-glass models. So far, studies have focused on marginal or irrelevant cases of disorder. Using duality arguments, as well as exact Pfaffian techniques we reproduce these analytical estimates. In addition, we obtain different estimates for spin-glass models on hierarchical lattices where the effects of disorder are relevant. We show that the phase-boundary slope near the Onsager point can be used to probe for the relevance of disorder effects.Comment: 8 pages, 6 figure

Multicritical Points of Potts Spin Glasses on the Triangular Lattice

We predict the locations of several multicritical points of the Potts spin glass model on the triangular lattice. In particular, continuous multicritical lines, which consist of multicritical points, are obtained for two types of two-state Potts (i.e., Ising) spin glasses with two- and three-body interactions on the triangular lattice. These results provide us with numerous examples to further verify the validity of the conjecture, which has succeeded in deriving highly precise locations of multicritical points for several spin glass models. The technique, called the direct triangular duality, a variant of the ordinary duality transformation, directly relates the triangular lattice with its dual triangular lattice in conjunction with the replica method.Comment: 18 pages, 2, figure

The nature of the different zero-temperature phases in discrete two-dimensional spin glasses: Entropy, universality, chaos and cascades in the renormalization group flow

The properties of discrete two-dimensional spin glasses depend strongly on the way the zero-temperature limit is taken. We discuss this phenomenon in the context of the Migdal-Kadanoff renormalization group. We see, in particular, how these properties are connected with the presence of a cascade of fixed points in the renormalization group flow. Of particular interest are two unstable fixed points that correspond to two different spin-glass phases at zero temperature. We discuss how these phenomena are related with the presence of entropy fluctuations and temperature chaos, and universality in this model.Comment: 14 pages, 5 figures, 2 table

CENP-C and CENP-I are key connecting factors for kinetochore and CENP-A assembly

Although it is generally accepted that chromatin containing the histone H3 variant CENP-A is an epigenetic mark maintaining centromere identity, the pathways leading to the formation and maintenance of centromere chromatin remain unclear. We previously generated human artificial chromosomes (HACs) whose centromeres contain a synthetic alpha-satellite (alphoid) DNA array containing the tetracycline operator (alphoid(tetO)). We also obtained cell lines bearing the alphoid(tetO) array at ectopic integration sites on chromosomal arms. Here, we have examined the regulation of CENP-A assembly at centromeres as well as de novo assembly on the ectopic arrays by tethering tetracycline repressor (tetR) fusions of substantial centromeric factors and chromatin modifiers. This analysis revealed four classes of factors that influence CENP-A assembly. Interestingly, many kinetochore structural components induced de novo CENP-A assembly at the ectopic site. We showed that these components work by recruiting CENP-C and subsequently recruiting M18BP1. Furthermore, we found that CENP-I can also recruit M18BP1 and, as a consequence, enhances M18BP1 assembly on centromeres in the downstream of CENP-C. Thus, we suggest that CENP-C and CENP-I are key factors connecting kinetochore to CENP-A assembly

Esperanto for histones : CENP-A, not CenH3, is the centromeric histone H3 variant

The first centromeric protein identified in any species was CENP-A, a divergent member of the histone H3 family that was recognised by autoantibodies from patients with scleroderma-spectrum disease. It has recently been suggested to rename this protein CenH3. Here, we argue that the original name should be maintained both because it is the basis of a long established nomenclature for centromere proteins and because it avoids confusion due to the presence of canonical histone H3 at centromeres

Salivary testosterone levels in preadolescent children

BACKGROUND: Saliva reflects the plasma free fraction of testosterone which is biologically active, and available for uptake by tissues. Testosterone concentration in saliva, though differing slightly from the concentration of unbound testosterone in serum, is in good correlation with the latter, indicating that salivary testosterone provides a reliable method for determination of serum free testosterone. The study aimed to investigate salivary testosterone levels and their changes in preadolescent children and to study sexual dimorphism. METHODS: Testosterone levels were determined in 203 healthy preadolescent children (77 girls and 126 boys) from saliva samples by radioimmunoassay. Sampling was performed once a year with respect to circadian and seasonal fluctuations of testosterone. Data were statistically analyzed by Statgraphic software. RESULTS: Mean salivary testosterone concentrations (± SD) were 0.038 ± 0.012 nmol/L and 0.046 ± 0.026 nmol/L for girls and boys, with the medians 0.035 nmol/L and 0.041 nmol/L, respectively. Statistical analysis did not prove changes in salivary testosterone concentrations in the preadolescent period of life, with an exception of the insignificant fall at the age of 7 years, and an insignificant rise at the age of 9 years in girls. CONCLUSIONS: Generally it can be concluded that salivary testosterone levels in our prepubertal subjects remained stable. There was no significant increase of salivary testosterone levels from the age of 6 until the age of 9 in both sexes. Sexual dimorphism in salivary testosterone levels was proved with significantly higher (p = 0.009) salivary testosterone levels in boys than in girls

Topological Color Codes and Two-Body Quantum Lattice Hamiltonians

Topological color codes are among the stabilizer codes with remarkable properties from quantum information perspective. In this paper we construct a four-valent lattice, the so called ruby lattice, governed by a 2-body Hamiltonian. In a particular regime of coupling constants, degenerate perturbation theory implies that the low energy spectrum of the model can be described by a many-body effective Hamiltonian, which encodes the color code as its ground state subspace. The gauge symmetry $\mathbf{Z}_{2}\times\mathbf{Z}_{2}$ of color code could already be realized by identifying three distinct plaquette operators on the lattice. Plaquettes are extended to closed strings or string-net structures. Non-contractible closed strings winding the space commute with Hamiltonian but not always with each other giving rise to exact topological degeneracy of the model. Connection to 2-colexes can be established at the non-perturbative level. The particular structure of the 2-body Hamiltonian provides a fruitful interpretation in terms of mapping to bosons coupled to effective spins. We show that high energy excitations of the model have fermionic statistics. They form three families of high energy excitations each of one color. Furthermore, we show that they belong to a particular family of topological charges. Also, we use Jordan-Wigner transformation in order to test the integrability of the model via introducing of Majorana fermions. The four-valent structure of the lattice prevents to reduce the fermionized Hamiltonian into a quadratic form due to interacting gauge fields. We also propose another construction for 2-body Hamiltonian based on the connection between color codes and cluster states. We discuss this latter approach along the construction based on the ruby lattice.Comment: 56 pages, 16 figures, published version