Spatial search by quantum walk

Grover's quantum search algorithm provides a way to speed up combinatorial search, but is not directly applicable to searching a physical database. Nevertheless, Aaronson and Ambainis showed that a database of N items laid out in d spatial dimensions can be searched in time of order sqrt(N) for d>2, and in time of order sqrt(N) poly(log N) for d=2. We consider an alternative search algorithm based on a continuous time quantum walk on a graph. The case of the complete graph gives the continuous time search algorithm of Farhi and Gutmann, and other previously known results can be used to show that sqrt(N) speedup can also be achieved on the hypercube. We show that full sqrt(N) speedup can be achieved on a d-dimensional periodic lattice for d>4. In d=4, the quantum walk search algorithm takes time of order sqrt(N) poly(log N), and in d<4, the algorithm does not provide substantial speedup.Comment: v2: 12 pages, 4 figures; published version, with improved arguments for the cases where the algorithm fail

Enhanced Peculiar Velocities in Brane-Induced Gravity

The mounting evidence for anomalously large peculiar velocities in our Universe presents a challenge for the LCDM paradigm. The recent estimates of the large scale bulk flow by Watkins et al. are inconsistent at the nearly 3 sigma level with LCDM predictions. Meanwhile, Lee and Komatsu have recently estimated that the occurrence of high-velocity merging systems such as the Bullet Cluster (1E0657-57) is unlikely at a 6.5-5.8 sigma level, with an estimated probability between 3.3x10^{-11} and 3.6x10^{-9} in LCDM cosmology. We show that these anomalies are alleviated in a broad class of infrared-modifed gravity theories, called brane-induced gravity, in which gravity becomes higher-dimensional at ultra large distances. These theories include additional scalar forces that enhance gravitational attraction and therefore speed up structure formation at late times and on sufficiently large scales. The peculiar velocities are enhanced by 24-34% compared to standard gravity, with the maximal enhancement nearly consistent at the 2 sigma level with bulk flow observations. The occurrence of the Bullet Cluster in these theories is 10^4 times more probable than in LCDM cosmology.Comment: 15 pages, 6 figures. v2: added reference

Further evidence of the involvement of the Wnt signaling pathway in Dupuytren's disease

Genetic background plays an important role in the development of Dupuytren's disease. A genome-wide association study (GWAS) showed that nine loci are associated with the disease, six of which contain genes that are involved in Wnt signaling (WNT2, WNT4, WNT7B, RSPO2, SFRP4, SULF1). To obtain insight in the role of these genes, we performed expression studies on affected and unaffected patient's tissues. Surgically obtained nodules and cords from eight Dupuytren's patients were compared to patient-matched control tissue (unaffected transverse palmar fascia). The Wnt-related genes found in the GWAS, the classical Wnt-downstream protein beta-catenin, as well as (myo) fibroblast markers were analyzed using real-time qPCR and immunohistochemical stainings for mRNA levels and protein levels, respectively. The collagen-coding genes COL1A1 and COL3A1 were highly upregulated on mRNA level, both in cords and nodules. Three Wnt-related genes were found to be differently regulated compared to control tissue: WNT2 was downregulated in nodules, WNT7B was upregulated in nodules, and SFRP4 was upregulated in nodules and cords. Immunohistochemistry revealed significantly less staining of Wnt2 in cords, but significantly more staining for Wnt7b in nodules. There was significantly more staining of alpha-SMA in nodules and cord and beta-catenin in nodules than in control tissue. We found differences in expression, both at mRNA and protein level, in several Wnt-related genes found earlier to be associated with Dupuytren's disease. Of these, Wnt7b was upregulated and found in close association with both alpha-SMA and beta-catenin expressing cells, making it a candidate pro-fibrotic mediator in Dupuytren's disease

Statistical Mechanics of the Quantum K-Satisfiability problem

We study the quantum version of the random $K$-Satisfiability problem in the presence of the external magnetic field $\Gamma$ applied in the transverse direction. We derive the replica-symmetric free energy functional within static approximation and the saddle-point equation for the order parameter: the distribution $P[h(m)]$ of functions of magnetizations. The order parameter is interpreted as the histogram of probability distributions of individual magnetizations. In the limit of zero temperature and small transverse fields, to leading order in $\Gamma$ magnetizations $m \approx 0$ become relevant in addition to purely classical values of $m \approx \pm 1$. Self-consistency equations for the order parameter are solved numerically using Quasi Monte Carlo method for K=3. It is shown that for an arbitrarily small $\Gamma$ quantum fluctuations destroy the phase transition present in the classical limit $\Gamma=0$, replacing it with a smooth crossover transition. The implications of this result with respect to the expected performance of quantum optimization algorithms via adiabatic evolution are discussed. The replica-symmetric solution of the classical random $K$-Satisfiability problem is briefly revisited. It is shown that the phase transition at T=0 predicted by the replica-symmetric theory is of continuous type with atypical critical exponents.Comment: 35 pages, 23 figures; changed abstract, improved discussion in the introduction, added references, corrected typo

Glimpses into the molecular pathogenesis of Peyronie's disease

Peyronie's disease (PD) is a fibroproliferative disease of the penis. Since little is known about the molecular pathogenesis of PD, we compared the biochemical make-up of PD plaques with normal tunica albuginea to clarify pathological processes in the scarred tissue. Protein and mRNA levels were measured in plaques and in unaffected pieces of the tunica albuginea. We investigated the presence of myofibroblasts, the deposition of collagens, and some key elements of Wnt and YAP1 signaling at protein level. The expression of 45 genes, all related to collagen homeostasis and extracellular matrix proteins, was quantified. In plaques, more myofibroblasts were present, and we observed an activation of Wnt signaling and YAP1 signaling. Increased levels of the collagens types I and III confirm the fibrotic nature of plaques. The mRNA ratio of collagen types III, IV, and VI to type I was increased. The expression of lysyl hydroxylase 3 was higher, whereas a decreased expression level was seen for fibronectin and cathepsin K. The biochemical composition of plaques was different from unaffected tunica albuginea: the relative and absolute abundance of various extracellular matrix proteins were changed, as well as the quality of collagen and the level of the collagen-degrading enzyme cathepsin K

Strong Pinning in High Temperature Superconductors

Detailed measurements of the critical current density jc of YBa2Cu3O7 films grown by pulsed laser deposition reveal the increase of jc as function of the filmthickness. Both this thickness dependence and the field dependence of the critical current are consistently described using a generalization of the theory of strong pinning of Ovchinnikov and Ivlev [Phys. Rev. B 43, 8024 (1991)]. From the model, we deduce values of the defect density (10^21 m^-3) and the elementary pinning force, which are in good agreement with the generally accepted values for Y2O3-inclusions. In the absence of clear evidence that the critical current is determined by linear defects or modulations of the film thickness, our model provides an alternative explanation for the rather universal field dependence of the critical current density found in YBa2Cu3O7 films deposited by different methods.Comment: 11 pages; 8 Figures; Published Phys. Rev. B 66, 024523 (2002

The Quantum Reverse Shannon Theorem based on One-Shot Information Theory

The Quantum Reverse Shannon Theorem states that any quantum channel can be simulated by an unlimited amount of shared entanglement and an amount of classical communication equal to the channel's entanglement assisted classical capacity. In this paper, we provide a new proof of this theorem, which has previously been proved by Bennett, Devetak, Harrow, Shor, and Winter. Our proof has a clear structure being based on two recent information-theoretic results: one-shot Quantum State Merging and the Post-Selection Technique for quantum channels.Comment: 30 pages, 4 figures, published versio

Relativistic field theories in a magnetic background as noncommutative field theories

We study the connection of the dynamics in relativistic field theories in a strong magnetic field with the dynamics of noncommutative field theories (NCFT). As an example, the Nambu-Jona-Lasinio models in spatial dimensions $d \geq 2$ are considered. We show that this connection is rather sophisticated. In fact, the corresponding NCFT are different from the conventional ones considered in the literature. In particular, the UV/IR mixing is absent in these theories. The reason of that is an inner structure (i.e., dynamical form-factors) of neutral composites which plays an important role in providing consistency of the NCFT. An especially interesting case is that for a magnetic field configuration with the maximal number of independent nonzero tensor components. In that case, we show that the NCFT are finite for even $d$ and their dynamics is quasi-(1+1)-dimensional for odd $d$. For even $d$, the NCFT describe a confinement dynamics of charged particles. The difference between the dynamics in strong magnetic backgrounds in field theories and that in string theories is briefly discussed.Comment: 19 pages, REVTeX4, clarifications added, references added, to appear in Phys. Rev.