Fast convergence of imaginary time evolution tensor network algorithms by recycling the environment

We propose an environment recycling scheme to speed up a class of tensor network algorithms that produce an approximation to the ground state of a local Hamiltonian by simulating an evolution in imaginary time. Specifically, we consider the time-evolving block decimation (TEBD) algorithm applied to infinite systems in 1D and 2D, where the ground state is encoded, respectively, in a matrix product state (MPS) and in a projected entangled-pair state (PEPS). An important ingredient of the TEBD algorithm (and a main computational bottleneck, especially with PEPS in 2D) is the computation of the so-called environment, which is used to determine how to optimally truncate the bond indices of the tensor network so that their dimension is kept constant. In current algorithms, the environment is computed at each step of the imaginary time evolution, to account for the changes that the time evolution introduces in the many-body state represented by the tensor network. Our key insight is that close to convergence, most of the changes in the environment are due to a change in the choice of gauge in the bond indices of the tensor network, and not in the many-body state. Indeed, a consistent choice of gauge in the bond indices confirms that the environment is essentially the same over many time steps and can thus be re-used, leading to very substantial computational savings. We demonstrate the resulting approach in 1D and 2D by computing the ground state of the quantum Ising model in a transverse magnetic field.Comment: 17 pages, 28 figure

Analytical and numerical Ku−BK_u - B phase diagrams for cobalt nanostructures: stability region for a Bloch skyrmion

In this letter we calculate the energies corresponding to the different magnetic phases present in a ferromagnetic cylinder by means of analytical calculations. From the comparison of these energies, it is possible to construct magnetic phase diagrams as a function of the uniaxial anisotropy of the sample and the external magnetic field applied. As proof of concept, we analyzed the magnetic phase diagrams for a cobalt dot of 240 nm in diameter and 70 nm in length, with an easy axis parallel to the dot axis, and with a magnetic field applied towards or perpendicular to this axis. From these diagrams we have obtained the stability regions for a Bloch skyrmion (Sk), a vortex core (VC) and a ferromagnetic (F) configuration, which can point in any $\psi$ direction. Our results provide a pathway to engineer the formation and controllability of a skyrmion in a ferromagnetic dot to different anisotropy constants and magnetic fields.Comment: 5 pages, 4 figure

Optimal distillation of a GHZ state

We present the optimal local protocol to distill a Greenberger-Horne-Zeilinger (GHZ) state from a single copy of any pure state of three qubits.Comment: RevTex, 4 pages, 2 figures. Published version, some references adde

Electrochemical and photo-electrochemical processes of Methylene blue oxidation by Ti/TiO2 electrodes modified with Fe-allophane

Indexación: Scopus.This work reports the degradation of methylene blue (MB) on Ti/TiO2 and Ti/TiO2/Fe-allophane electrodes in a pH 3 using 0.1 M Na2SO4 as support electrolyte. SEM micrographs show a homogeneous distribution of TiO2 over the whole electrode surface forming nanotubes and nanopores. Fe-allophane modified electrode shows the formation of large-grains agglomerate on the electrode surface due to allophane, which provides a greater surface area to the electrode due to meso and micropore structures. Preliminary cyclic voltammetry show that Ti/TiO2 has the typical voltammetric response due to Ti(III)/Ti(IV) pair. Diffusional problems were observed through of the film when the electrode is modified with Fe-allophane modifying the quasi-reversible process Ti(III)/Ti(IV). Different kind of methodologies in the degradation process were used: Electrochemistry (EC), Photochemistry (PC), Photoelectrochemistry (PEC) and Adsorption (Ads). These methods were developing to discard any reaction or interaction that is not of interest. On Ti/TiO2 with PC and Ads methodologies was not observed any activity to MB degradation showing that is not photosensitive and that the interaction between this and surface electrode is low. But with EC and PEC degradation to 55% is reached after 3 hours of electrolysis. With Ti/TiO2-Fe-allophane electrodes are observed a higher activity for all methodologies. The PC and Ads methods show that the MB degradation reaches to ∼20 % of the initial concentration. As mentioned above, the PC and Ads processes no show degradation on Ti/TiO2, therefore the degradation it only due to the adsorption of MB in/on allophane coat behaving as concentrator matrix. A lower improvement is observed with EC process when is incorporated Ti/TiO2-Fe-allophane is due to the barrier of the electrode surface by oxidation products. With PEC is reached the higher degradation value of ∼88 %, showing an improvement of the degradation with the presence of Fe-allophane. The results indicate that the main role of Fe-allophane on the electrode is similar to a concentrator matrix.http://ref.scielo.org/shz7t

Matrix product states for anyonic systems and efficient simulation of dynamics

Matrix product states (MPS) have proven to be a very successful tool to study lattice systems with local degrees of freedom such as spins or bosons. Topologically ordered systems can support anyonic particles which are labeled by conserved topological charges and collectively carry non-local degrees of freedom. In this paper we extend the formalism of MPS to lattice systems of anyons. The anyonic MPS is constructed from tensors that explicitly conserve topological charge. We describe how to adapt the time-evolving block decimation (TEBD) algorithm to the anyonic MPS in order to simulate dynamics under a local and charge-conserving Hamiltonian. To demonstrate the effectiveness of anyonic TEBD algorithm, we used it to simulate (i) the ground state (using imaginary time evolution) of an infinite 1D critical system of (a) Ising anyons and (b) Fibonacci anyons both of which are well studied, and (ii) the real time dynamics of an anyonic Hubbard-like model of a single Ising anyon hopping on a ladder geometry with an anyonic flux threading each island of the ladder. Our results pertaining to (ii) give insight into the transport properties of anyons. The anyonic MPS formalism can be readily adapted to study systems with conserved symmetry charges, as this is equivalent to a specialization of the more general anyonic case.Comment: 18 pages, 15 figue

Three qubits can be entangled in two inequivalent ways

Invertible local transformations of a multipartite system are used to define equivalence classes in the set of entangled states. This classification concerns the entanglement properties of a single copy of the state. Accordingly, we say that two states have the same kind of entanglement if both of them can be obtained from the other by means of local operations and classical communcication (LOCC) with nonzero probability. When applied to pure states of a three-qubit system, this approach reveals the existence of two inequivalent kinds of genuine tripartite entanglement, for which the GHZ state and a W state appear as remarkable representatives. In particular, we show that the W state retains maximally bipartite entanglement when any one of the three qubits is traced out. We generalize our results both to the case of higher dimensional subsystems and also to more than three subsystems, for all of which we show that, typically, two randomly chosen pure states cannot be converted into each other by means of LOCC, not even with a small probability of success.Comment: 12 pages, 1 figure; replaced with revised version; terminology adapted to earlier work; reference added; results unchange

Modelling the spinning dust emission from LDN 1780

We study the anomalous microwave emission (AME) in the Lynds Dark Nebula (LDN) 1780 on two angular scales. Using available ancillary data at an angular resolution of 1 degree, we construct an SED between 0.408 GHz to 2997 GHz. We show that there is a significant amount of AME at these angular scales and the excess is compatible with a physical spinning dust model. We find that LDN 1780 is one of the clearest examples of AME on 1 degree scales. We detected AME with a significance > 20$\sigma$. We also find at these angular scales that the location of the peak of the emission at frequencies between 23-70 GHz differs from the one on the 90-3000 GHz map. In order to investigate the origin of the AME in this cloud, we use data obtained with the Combined Array for Research in Millimeter-wave Astronomy (CARMA) that provides 2 arcmin resolution at 30 GHz. We study the connection between the radio and IR emissions using morphological correlations. The best correlation is found to be with MIPS 70$\mu$m, which traces warm dust (T$\sim$50K). Finally, we study the difference in radio emissivity between two locations within the cloud. We measured a factor $\approx 6$ of difference in 30 GHz emissivity. We show that this variation can be explained, using the spinning dust model, by a variation on the dust grain size distribution across the cloud, particularly changing the carbon fraction and hence the amount of PAHs.Comment: 14 pages, 11 figures, submitted to MNRA

Characterization of non-local gates

A non-local unitary transformation of two qubits occurs when some Hamiltonian interaction couples them. Here we characterize the amount, as measured by time, of interaction required to perform two--qubit gates, when also arbitrarily fast, local unitary transformations can be applied on each qubit. The minimal required time of interaction, or interaction cost, defines an operational notion of the degree of non--locality of gates. We characterize a partial order structure based on this notion. We also investigate the interaction cost of several communication tasks, and determine which gates are able to accomplish them. This classifies two--qubit gates into four categories, differing in their capability to transmit classical, as well as quantum, bits of information.Comment: revtex, 14 pages, no pictures; proof of result 1 simplified significantl

Electromagnetic dipole moments of charged baryons with bent crystals at the LHC

We propose a unique program of measurements of electric and magnetic dipole moments of charm, beauty and strange charged baryons at the LHC, based on the phenomenon of spin precession of channeled particles in bent crystals. Studies of crystal channeling and spin precession of positively- and negatively-charged particles are presented, along with feasibility studies and expected sensitivities for the proposed experiment using a layout based on the LHCb detector.Comment: 19 pages, 13 figure

Interaction cost of non-local gates

We introduce the interaction cost of a non-local gate as the minimal time of interaction required to perform the gate when assisting the process with fast local unitaries. This cost, of interest both in the areas of quantum control and quantum information, depends on the specific interaction, and allows to compare in an operationally meaningful manner any two non-local gates. In the case of a two-qubit system, an analytical expression for the interaction cost of any unitary operation given any coupling Hamiltonian is obtained. One gate may be more time-consuming than another for any possible interaction. This defines a partial order structure in the set of non-local gates, that compares their degree of non-locality. We analytically characterize this partial order in a region of the set of two-qubit gates.Comment: revtex, 4 pages, no pictures, typos corrected, small changes in nomenclatur