Perfect Sampling with Unitary Tensor Networks

Tensor network states are powerful variational ans\"atze for many-body ground states of quantum lattice models. The use of Monte Carlo sampling techniques in tensor network approaches significantly reduces the cost of tensor contractions, potentially leading to a substantial increase in computational efficiency. Previous proposals are based on a Markov chain Monte Carlo scheme generated by locally updating configurations and, as such, must deal with equilibration and autocorrelation times, which result in a reduction of efficiency. Here we propose a perfect sampling scheme, with vanishing equilibration and autocorrelation times, for unitary tensor networks -- namely tensor networks based on efficiently contractible, unitary quantum circuits, such as unitary versions of the matrix product state (MPS) and tree tensor network (TTN), and the multi-scale entanglement renormalization ansatz (MERA). Configurations are directly sampled according to their probabilities in the wavefunction, without resorting to a Markov chain process. We also describe a partial sampling scheme that can result in a dramatic (basis-dependent) reduction of sampling error.Comment: 11 pages, 9 figures, renamed partial sampling to incomplete sampling for clarity, extra references, plus a variety of minor change

Tensor network states and algorithms in the presence of a global SU(2) symmetry

The benefits of exploiting the presence of symmetries in tensor network algorithms have been extensively demonstrated in the context of matrix product states (MPSs). These include the ability to select a specific symmetry sector (e.g. with a given particle number or spin), to ensure the exact preservation of total charge, and to significantly reduce computational costs. Compared to the case of a generic tensor network, the practical implementation of symmetries in the MPS is simplified by the fact that tensors only have three indices (they are trivalent, just as the Clebsch-Gordan coefficients of the symmetry group) and are organized as a one-dimensional array of tensors, without closed loops. Instead, a more complex tensor network, one where tensors have a larger number of indices and/or a more elaborate network structure, requires a more general treatment. In two recent papers, namely (i) [Phys. Rev. A 82, 050301 (2010)] and (ii) [Phys. Rev. B 83, 115125 (2011)], we described how to incorporate a global internal symmetry into a generic tensor network algorithm based on decomposing and manipulating tensors that are invariant under the symmetry. In (i) we considered a generic symmetry group G that is compact, completely reducible and multiplicity free, acting as a global internal symmetry. Then in (ii) we described the practical implementation of Abelian group symmetries. In this paper we describe the implementation of non-Abelian group symmetries in great detail and for concreteness consider an SU(2) symmetry. Our formalism can be readily extended to more exotic symmetries associated with conservation of total fermionic or anyonic charge. As a practical demonstration, we describe the SU(2)-invariant version of the multi-scale entanglement renormalization ansatz and apply it to study the low energy spectrum of a quantum spin chain with a global SU(2) symmetry.Comment: 32 pages, 37 figure

Multi-wavelength differential astrometry of the S5 polar cap sample

We report on the status of our S5 polar cap astrometry program. Since 1997 we have observed all the 13 radio sources of the complete S5 polar cap sample at the wavelengths of 3.6 cm, 2 cm and 7 mm. Images of the radio sources at 3.6 and 2 cm have already been published reporting morphological changes. Preliminary astrometric analyses have been carried out at three frequencies with precisions in the relative position determination ranging from 80 to 20 microarcseconds. We report also on the combination of our phase-delay global astrometry results with the microarcsecond-precise optical astrometry that will be provided by future space-based instruments.Comment: 2 pages. 1 figure. Proceedings of the 7th European VLBI Network Symposium held in Toledo, Spain on October 12-15, 2004. Editors: R. Bachiller, F. Colomer, J.-F. Desmurs, P. de Vicente (Observatorio Astronomico Nacional), p. 323-324. Needs evn2004.cl

Matrix product decomposition and classical simulation of quantum dynamics in the presence of a symmetry

We propose a refined matrix product state representation for many-body quantum states that are invariant under SU(2) transformations, and indicate how to extend the time-evolving block decimation (TEBD) algorithm in order to simulate time evolution in an SU(2) invariant system. The resulting algorithm is tested in a critical quantum spin chain and shown to be significantly more efficient than the standard TEBD.Comment: 5 pages, 4 figure

Ground state fidelity from tensor network representations

For any D-dimensional quantum lattice system, the fidelity between two ground state many-body wave functions is mapped onto the partition function of a D-dimensional classical statistical vertex lattice model with the same lattice geometry. The fidelity per lattice site, analogous to the free energy per site, is well-defined in the thermodynamic limit and can be used to characterize the phase diagram of the model. We explain how to compute the fidelity per site in the context of tensor network algorithms, and demonstrate the approach by analyzing the two-dimensional quantum Ising model with transverse and parallel magnetic fields.Comment: 4 pages, 2 figures. Published version in Physical Review Letter

1.6 GHz VLBI Observations of SN 1979C: almost-free expansion

We report on 1.6 GHz Very-Long-Baseline-Interferometry (VLBI) observations of supernova SN 1979C made on 18 November 2002. We derive a model-dependent supernova size. We also present a reanalysis of VLBI observations made by us on June 1999 and by other authors on February 2005. We conclude that, contrary to our earlier claim of strong deceleration in the expansion, SN 1979C has been undergoing almost-free expansion ($m = 0.91\pm0.09$; $R \propto t^m$) for over 25 years.Comment: 4 pages, 4 figures; submitted to A&A on 14 May 2009. Accepted on 7 Jul 200

Robust and Cooperative Image-Based Visual Servoing System Using a Redundant Architecture

The reliability and robustness of image-based visual servoing systems is still unsolved by the moment. In order to address this issue, a redundant and cooperative 2D visual servoing system based on the information provided by two cameras in eye-in-hand/eye-to-hand configurations is proposed. Its control law has been defined to assure that the whole system is stable if each subsystem is stable and to allow avoiding typical problems of image-based visual servoing systems like task singularities, features extraction errors, disappearance of image features, local minima, etc. Experimental results with an industrial robot manipulator based on Schunk modular motors to demonstrate the stability, performance and robustness of the proposed system are presented

A Sliding Mode Control Architecture for Human-Manipulator Cooperative Surface Treatment Tasks

© 2018 IEEE. This paper presents a control architecture readily suitable for surface treatment tasks such as polishing, grinding, finishing or deburring as carried out by a human operator, with the added benefit of accuracy, recurrence and physical strength as administered by a robotic manipulator partner. The shared strategy effectively couples the human operator propioceptive abilities and fine skills through his interactions with the autonomous physical agent. The novel proposed control scheme is based on task prioritization and a non-conventional sliding mode control, which is considered to benefit from its inherent robustness and low computational cost. The system relies on two force sensors, one located between the last link of the robot and the surface treatment tool, and the other located in some place of the robot end-effector: the former is used to suitably accomplish the conditioning task, while the latter is used by the operator to manually guide the robotic tool. When the operator chooses to cease guiding the tool, the robot motion safely switches back to an automatic reference tracking. The paper presents the theories for the novel collaborative controller, whilst its effectiveness for robotic surface treatment is substantiated by experimental results using a redundant 7R manipulator and a mock-up conditioning tool

The iTEBD algorithm beyond unitary evolution

The infinite time-evolving block decimation (iTEBD) algorithm [Phys. Rev. Lett. 98, 070201 (2007)] allows to simulate unitary evolution and to compute the ground state of one-dimensional quantum lattice systems in the thermodynamic limit. Here we extend the algorithm to tackle a much broader class of problems, namely the simulation of arbitrary one-dimensional evolution operators that can be expressed as a (translationally invariant) tensor network. Relatedly, we also address the problem of finding the dominant eigenvalue and eigenvector of a one-dimensional transfer matrix that can be expressed in the same way. New applications include the simulation, in the thermodynamic limit, of open (i.e. master equation) dynamics and thermal states in 1D quantum systems, as well as calculations with partition functions in 2D classical systems, on which we elaborate. The present extension of the algorithm also plays a prominent role in the infinite projected entangled-pair states (iPEPS) approach to infinite 2D quantum lattice systems.Comment: 11 pages, 16 figures, 1 appendix with algorithms for specific types of evolution. A typo in the appendix figures has been corrected. Accepted in PR

Protection Strategies for the Connection of Diode Rectifier-Based Wind Power Plants to HVdc Interconnectors

The connection of diode rectifier (DR)-based wind power plants (WPPs) to existing or planned high-voltage dc (HVdc) interconnectors can lead to important savings on cost and system robustness. Since the DR station usually operates in a bipolar configuration, its connection to symmetric monopoles is particularly challenging. However, there are no published detailed studies on the protection of DR connection WPPs to symmetric monopole interconnectors or even to bipolar interconnectors. This article includes the comparative study of five different protection strategies for such systems, including both solid and resistive DR station grounding and strategies with and without the use of dc-circuit breakers (dcCBs). An analytical study allows for the calculation of fault current during fault onset for both half-bridge and hybrid modular multilevel converter (MMC) stations. Using detailed electromagnetic transient (EMT) simulation studies, the different protection strategies are evaluated in terms of current, voltage, and isolation requirements of each element, as well as the need for dcCBs, fast communication, or larger surge arresters. Moreover, a distance fault detection algorithm is included for the wind turbine converters to distinguish between local ac-grid and dc-cable faults. From the simulation results, it is possible to conclude that DR high-impedance grounding, together with wind turbine distance protection, can be used for the protection of DR-based offshore WPPs connected to symmetric monopole interconnectors without requiring dcCBs