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

Modified glass ionomer and orthodontic band: An interim alternative for the treatment of molar incisor hypomineralization. A case report

Introduction: Molar incisor hypomineralization (MIH) is a developmental condition resulting in defects in the enamel characterized by demarcated opacities mainly affecting first permanent molars and occasionally permanent incisors in 1 of every 6 children worldwide. Affected molars have greater susceptibility to post eruptive breakdown, extensive caries and, in severe cases, are difficult to restore. When the MIH-affected molar presents severe crown destruction, it is necessary to perform an intermediate restoration to preserve the remaining dental structure in order to maintain occlusion, proper hygiene and periodontal health. The case of an 11-year-old patient with severe MIH is reported. The patient had extensive crown destruction by caries in tooth 1.6 without clinical or radiographic signs of pulp pathology. After an initial preventive intervention, enamel without dentin support and carious dentin were removed from tooth 1.6. Subsequently, crown restoration was performed with resin modified glass ionomer, followed by the cementation of an orthodontic band. After 18 months of follow-up, the patient reported no pain or discomfort. The restoration was preserved intact, maintaining occlusal functionality, pulp and gingival health. Conclusion: The interim treatment, cementing an orthodontic band over a tooth restored with glass ionomer seems to favor retention and compressive strength, keeping the MIH-affected molar asymptomatic for at least 18 months. Further studies evaluating this treatment option in similar clinical situations are recommended

Infinite boundary conditions for matrix product state calculations

We propose a formalism to study dynamical properties of a quantum many-body system in the thermodynamic limit by studying a finite system with infinite boundary conditions (IBC) where both finite size effects and boundary effects have been eliminated. For one-dimensional systems, infinite boundary conditions are obtained by attaching two boundary sites to a finite system, where each of these two sites effectively represents a semi-infinite extension of the system. One can then use standard finite-size matrix product state techniques to study a region of the system while avoiding many of the complications normally associated with finite-size calculations such as boundary Friedel oscillations. We illustrate the technique with an example of time evolution of a local perturbation applied to an infinite (translationally invariant) ground state, and use this to calculate the spectral function of the S=1 Heisenberg spin chain. This approach is more efficient and more accurate than conventional simulations based on finite-size matrix product state and density-matrix renormalization-group approaches.Comment: 10 page

Dynamical windows for real-time evolution with matrix product states

We propose the use of a dynamical window to investigate the real-time evolution of quantum many-body systems in a one-dimensional lattice. In a recent paper [H. Phien et al, arxiv:????.????], we introduced infinite boundary conditions (IBC) in order to investigate real-time evolution of an infinite system under a local perturbation. This was accomplished by restricting the update of the tensors in the matrix product state to a finite window, with left and right boundaries held at fixed positions. Here we consider instead the use of a dynamical window, namely a window where the positions of left and right boundaries are allowed to change in time. In this way, all simulation efforts can be devoted to the space-time region of interest, which leads to a remarkable reduction in computational costs. For illustrative purposes, we consider two applications in the context of the spin-1 antiferromagnetic Heisenberg model in an infinite spin chain: one is an expanding window, with boundaries that are adjusted to capture the expansion in time of a local perturbation of the system; the other is a moving window of fixed size, where the position of the window follows the front of a propagating wave

Larvae of Illex argentinus from five surveys on the continental shelf of southern Brazil

Three types of rhynchoteuthion larvae and one of small juvenile ommastrephid were collected in 116 of 371 samples obtained in five surveys on the shelf of southern Brazil. The cruises were between Santa Marta Grande Cape (28°30'S) and Chui (34°40'S); one cruise in autumn 1980-1982, one in winter, and three in spring. Samples were collected with a bongo net of 0.33-mm mesh in oblique hauls from bottom to surface between the coast and approximately the 200-m isobath line. Juveniles and the type of larvae that accounted for over 90% of the total were identified as Illex argentinus. They were found mostly in winter and spring in association with the western boundary of the Brazil Current and Subtropical Waters and rarely with Coastal and Subantarctic Waters. Their abundance in southern Brazil may be explained by spawning in the region and northward transport of egg masses

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

Computer Based Production of Saffron (Crocus Sativus L.): From Mechanical Design to Electronic Control

[EN] The article describes the design and implementation of a computer based industrial system for production of saffron. The proposal is based on an automated greenhouse with temperature, light and irrigation control together with harvesting and stigma separation devices. The harvesting device has been specifically developed using scalability properties and computer vision. The greenhouse is designed to increase the crop density if required generating a more sustainable and continuous production. The main advantages of the proposed method are as follows: the harvesting of the saffron flower and the procedure to get the stigmas are carried out in the same process; the greenhouse allows to significantly extend the flowering time of the saffron plant; and higher productivity per worker and per planting area is achieved. In order to show the feasibility and applicability of the proposed approach, real experimentation has been carried out for the extension of the flowering time and for the harvesting and stigma separation devices and successful results have been obtained.This work has been partially supported by the European Commission under Grant No. 683987. The authors thank Enrique Gil Botella for helping with the machine design and drawings and Angel Flores Pérez for helping to generate the program for the cutting system.Perez-Vidal, C.; Gracia Calandin, LI. (2020). Computer Based Production of Saffron (Crocus Sativus L.): From Mechanical Design to Electronic Control. Computers and Electronics in Agriculture. 169:1-11. https://doi.org/10.1016/j.compag.2019.105198S11116