Application of Polynomial Algorithms to a Random Elastic Medium

A randomly pinned elastic medium in two dimensions is modeled by a disordered fully-packed loop model. The energetics of disorder-induced dislocations is studied using exact and polynomial algorithms from combinatorial optimization. Dislocations are found to become unbound at large scale, and the elastic phase is thus unstable giving evidence for the absence of a Bragg glass in two dimensions.Comment: 8 pages. Invited talk at the CCP1998 - Computational Physics (Granada

A multi-party correlation measure based on cumulant

We propose a genuine multi-party correlation measure for a multi-party quantum system as the trace norm of the cumulant of the state. The legitimacy of our multi-party correlation measure is explicitly demonstrated by proving it satisfies the five basic conditions required for a correlation measure. As an application we construct an efficient algorithm for the calculation of our measures for all stabilizer states.Comment: 9 pages, 1 figure, to be published in Phys. Rev.

Non-adiabatic effects of superconductor silane under high pressure

Investigations of non-adiabatic effects by including vertex corrections in the standard Eliashberg theory show that high phonon frequency is unfavorable to superconductivity in regime of strong vertex correction. This means that it is hard to find high-transition-temperature superconductors in the compounds with light elements if the non-adiabatic effects are strong. The interplay interaction between non-adiabatic effect and Coulomb interaction makes the transition temperature of silane superconductor not so high as predicted by the standard Eliashberg theory

Dissipation in Josephson tunneling junctions at low temperatures

It is important to know the decoherence mechanism of a qubit based on Josephson junctions. At low temperatures, as quasiparticle concentration becomes exponentially small, one needs to consider energy transfer from tunneling electrons to other degrees of freedom to find dissipation in Josephson junctions and decoherence in qubits. Here we discuss the energy transfer to two-level systems, i.e. the transitions between two different configurations of ions inside insulating layer separated by a potential barrier. We derive a general equation of motion for the phase difference between two superconducting electrodes and we find a retarded dissipation term due to electromagnetic mechanism and also contribution due to electron tunneling mechanism. Using the equation of motion we calculate the decay of Rabi oscillations and frequency shift in qubits due to the presence of the two-level systems. In the long time limit our results coincide with those obtained by Martinis et al. [J. M. Martinis et al.. Phys. Rev. Lett. 95, 210503 (2005)] within the Fermi's Golden rule approach up to a numerical factor.Comment: 4.5 pages and no figure; submitted to PRB on 22 Jul. 2014, accepted on Aug. 4 2014, published on Aug. 14 201

Tc map and superconductivity of simple metals at high pressure

We calculate Tc map in region of weak electron-phonon coupling based on simple phonon spectrum. By using linear-response method and density functional theory, we calculate phonon spectra and Eliashberg functions of simple metals under pressure. Based on the evolutions of superconducting parameters of simple metals on the Tc map with increasing pressure, we find that there are two different responses to pressure for simple metals: (1) enhancing electron-phonon interaction $\lambda$ such as for La and Li, (2) increasing phonon frequency such as for Pb, Pt. The $\lambda$ threshold effect is found, which origins from the competition between electron-phonon interaction and electron-electron Coulomb interaction and is the reason why Tc of most superconductors of simple metals are higher than 0.1K

A criterion for testing multi-particle NPT entanglement

We revisit the criterion of multi-particle entanglement based on the overlaps of a given quantum state $\rho$ with maximally entangled states. For a system of $m$ particles, each with $N$ distinct states, we prove that $\rho$ is $m$-particle negative partial transpose (NPT) entangled, if there exists a maximally entangled state $|{\rm MES}>$, such that $<{\rm MES}|\rho|{\rm MES}>>{1}/{N}$. While this sufficiency condition is weaker than the Peres-Horodecki criterion in all cases, it applies to multi-particle systems, and becomes especially useful when the number of particles ($m$) is large. We also consider the converse of this criterion and illustrate its invalidity with counter examples.Comment: 4 page

Operator representations for a class of quantum entanglement measures and criterions

We find that a class of entanglement measures for bipartite pure state can be expressed by the average values of quantum operators, which are related to any complete basis of one partite operator space. Two specific examples are given based on two different ways to generalize Pauli matrices to $d$ dimensional Hilbert space and the case for identical particle system is also considered. In addition, applying our measure to mixed state case will give a sufficient condition for entanglement.Comment: 9 pages, no figure

Irreducible many-body correlations in topologically ordered systems

Topologically ordered systems exhibit large-scale correlation in their ground states, which may be characterized by quantities such as topological entanglement entropy. We propose that the concept of irreducible many-body correlation, the correlation that cannot be implied by all local correlations, may also be used as a signature of topological order. In a topologically ordered system, we demonstrate that for a part of the system with holes, the reduced density matrix exhibits irreducible many-body correlation which becomes reducible when the holes are removed. The appearance of these irreducible correlations then represents a key feature of topological phase. We analyze the many-body correlation structures in the ground state of the toric code model in an external magnetic field, and show that the topological phase transition is signaled by the irreducible many-body correlations

Phylogeny-based tumor subclone identification using a Bayesian feature allocation model

Tumor cells acquire different genetic alterations during the course of evolution in cancer patients. As a result of competition and selection, only a few subgroups of cells with distinct genotypes survive. These subgroups of cells are often referred to as subclones. In recent years, many statistical and computational methods have been developed to identify tumor subclones, leading to biologically significant discoveries and shedding light on tumor progression, metastasis, drug resistance and other processes. However, most existing methods are either not able to infer the phylogenetic structure among subclones, or not able to incorporate copy number variations (CNV). In this article, we propose SIFA (tumor Subclone Identification by Feature Allocation), a Bayesian model which takes into account both CNV and tumor phylogeny structure to infer tumor subclones. We compare the performance of SIFA with two other commonly used methods using simulation studies with varying sequencing depth, evolutionary tree size, and tree complexity. SIFA consistently yields better results in terms of Rand Index and cellularity estimation accuracy. The usefulness of SIFA is also demonstrated through its application to whole genome sequencing (WGS) samples from four patients in a breast cancer study.Comment: 35 pages, 11 figure

Semi-Clifford operations, structure of Ck\mathcal{C}_k hierarchy, and gate complexity for fault-tolerant quantum computation

Teleportation is a crucial element in fault-tolerant quantum computation and a complete understanding of its capacity is very important for the practical implementation of optimal fault-tolerant architectures. It is known that stabilizer codes support a natural set of gates that can be more easily implemented by teleportation than any other gates. These gates belong to the so called $\mathcal{C}_k$ hierarchy introduced by Gottesman and Chuang (Nature \textbf{402}, 390). Moreover, a subset of $\mathcal{C}_k$ gates, called semi-Clifford operations, can be implemented by an even simpler architecture than the traditional teleportation setup (Phys. Rev. \textbf{A62}, 052316). However, the precise set of gates in $\mathcal{C}_k$ remains unknown, even for a fixed number of qubits $n$, which prevents us from knowing exactly what teleportation is capable of. In this paper we study the structure of $\mathcal{C}_k$ in terms of semi-Clifford operations, which send by conjugation at least one maximal abelian subgroup of the $n$-qubit Pauli group into another one. We show that for $n=1,2$, all the $\mathcal{C}_k$ gates are semi-Clifford, which is also true for $\{n=3,k=3\}$. However, this is no longer true for $\{n>2,k>3\}$. To measure the capability of this teleportation primitive, we introduce a quantity called `teleportation depth', which characterizes how many teleportation steps are necessary, on average, to implement a given gate. We calculate upper bounds for teleportation depth by decomposing gates into both semi-Clifford $\mathcal{C}_k$ gates and those $\mathcal{C}_k$ gates beyond semi-Clifford operations, and compare their efficiency.Comment: 13 pages, 10 figure