MPS-based Method Research Articles

Chebyshev Matrix Product States with Canonical Orthogonalization for Spectral Functions of Many-Body Systems.

We propose a method to calculate the spectral functions of many-body systems by Chebyshev expansion in the framework of matrix product states coupled with canonical orthogonalization (coCheMPS). The canonical orthogonalization can improve the accuracy and efficiency significantly because the orthogonalized Chebyshev vectors can provide an ideal basis for constructing the effective Hamiltonian in which the exact recurrence relation can be retained. In addition, not only the spectral function but also the excited states and eigenenergies can be directly calculated, which is usually impossible for other MPS-based methods such as time-dependent formalism or correction vector. The remarkable accuracy and efficiency of coCheMPS over other methods are demonstrated by calculating the spectral functions of spin chain and ab initio hydrogen chain. For the first time we demonstrate that Chebyshev MPS can be used to deal with ab initio electronic Hamiltonian effectively. We emphasize the strength of coCheMPS to calculate the low excited states of systems with sparse discrete spectrum. We also caution the application for electron-phonon systems with dense density of states.

Influence Matrix Approach to Many-Body Floquet Dynamics

In this work, we introduce an approach to study quantum many-body dynamics, inspired by the Feynman-Vernon influence functional. Focusing on a family of interacting, Floquet spin chains, we consider a Keldysh path-integral description of the dynamics. The central object in our approach is the influence matrix (IM), which describes the effect of the system on the dynamics of a local subsystem. For translationally invariant models, we formulate a self-consistency equation for the influence matrix. For certain special values of the model parameters, we obtain an exact solution which represents a perfect dephaser (PD). Physically, a PD corresponds to a many-body system that acts as a perfectly Markovian bath on itself: at each period, it measures every spin. For the models considered here, we establish that PD points include dual-unitary circuits investigated in recent works. In the vicinity of PD points, the system is not perfectly Markovian, but rather acts as a bath with a short memory time. In this case, we demonstrate that the self-consistency equation can be solved using matrix-product states (MPS) methods, as the IM temporal entanglement is low. A combination of analytical insights and MPS computations allows us to characterize the structure of the influence matrix in terms of an effective "statistical-mechanics" description. We finally illustrate the predictive power of this description by analytically computing how quickly an embedded impurity spin thermalizes. The influence matrix approach formulated here provides an intuitive view of the quantum many-body dynamics problem, opening a path to constructing models of thermalizing dynamics that are solvable or can be efficiently treated by MPS-based methods, and to further characterizing quantum ergodicity or lack thereof.

Local matrix product operators: Canonical form, compression, and control theory

We present a new method for compressing matrix product operators (MPOs) which represent sums of local terms, such as Hamiltonians. Just as with area law states, such local operators may be fully specified with a small amount of information per site. Standard matrix product state (MPS) tools are ill-suited to this case, due to extensive Schmidt values that coexist with intensive ones, and Jordan blocks in the transfer matrix. We ameliorate these issues by introducing an "almost Schmidt decomposition" that respects locality. Our method is "$\varepsilon$-close" to the accuracy of MPS-based methods for finite MPOs, and extends seamlessly to the thermodynamic limit, where MPS techniques are inapplicable. In the framework of control theory, our method generalizes Kung's algorithm for model order reduction. Several examples are provided, including an all-MPO version of the operator recursion method (Lanczos algorithm) directly in the thermodynamic limit. All results are accompanied by practical algorithms, well-suited for the large MPOs that arise in DMRG for long-range or quasi-2D models.

Анализ спектра мутаций в генах COL1A1 и COL1A2 с использованием массового параллельного секвенирования у больных несовершенным остеогенезом в Томской области

Using massively parallel sequencing, the COL1A1 and COL1A2 genes were analyzed in 16 patients from 10 families with osteogenesis imperfecta types I, III, and IV. To analyze the mutations in these genes, a panel of primers was developed for sequencing the complete gene sequence. As a result of the work, 10 mutations were revealed: six of them are in the COL1A1 gene, four mutations in the COL1A2 gene. All mutations, except one, were previously described in the literature and were found in patients with various types of osteogenesis imperfecta. Missense mutations were identified in five families, nonsense mutations in two families, splice site mutations in two cases, and a frameshift mutation in one patient. Unique mutations that were not repeated in unrelated patients were found in all families. The revealed high heterogeneity of the spectrum of mutations in the COL1A1 and COL1A2 genes in osteogenesis imperfecta indicates the effectiveness of using MPS-based methods for the diagnosis of this pathology.

In-house validation of MPS-based methods in a forensic laboratory

Massively parallel sequencing (MPS) methods are increasingly applied in forensic casework. However, adequate validation guidelines are lacking. In this work, we describe our in-house validation of the ForenSeq DNA Signature Prep Kit (Verogen) for analysis of ancestry- and phenotype-informative SNPs. We also discuss in-house validation of MPS assays in general terms. When validating the SNP assay, we focused on the reliability of SNP genotype calls and the compatibility with commonly analysed sample types. Other issues, for example analytical thresholds and accuracy of the data prediction model were considered to be covered by the developmental validation of the kit. Our study included determination of (1) concordance, (2) limit of detection, (3) matrix effects, (4) repeatability, and (5) contamination risk. In conclusion, the MPS-based SNP assay showed overall adequate performance for single-source samples, with correct genotype calls. We welcome a broad discussion on how to perform in-house validation of MPS-based methods, as this is vital to ensure timely implementation of reliable assays in forensic laboratories.

Improved MPS method and its variations for simulating incompressible fluids on GPU

Meshless methods to simulate fluid flows have been increasingly evolving through the years since they are a great alternative to deal with large deformations, which is where meshbased methods fail to perform efficiently. A well known meshless method is the Moving Particle Semi-implicit (MPS) method, which was designed to simulate free-surface truly incompressible fluid flows. Many variations and refinements of the method’s accuracy and precision have been proposed through the years and, in this paper, a reasonably wide literature review was performed together with their theoretical and mathematical explanations. Due to these works, it has proved to be very useful in a wide range of naval and mechanical engineering problems. However, one of its drawbacks is a high computational load and some quite time-consuming functions, which prevents it to be more used in Computer Graphics and Virtual Reality applications. Graphics Processing Units (GPU) provide unprecedented capabilities for scientific computations. To promote the GPU-acceleration, the solution of the Poisson Pressure equation was brought into focus. This work benefits from some of the techniques presented in the related work and also from the CUDA language in order to get a stable, accurate and GPU-accelerated MPS-based method, which is this work’s main contribution. It is shown that the GPU version of the method developed can perform from, approximately, 6 to 10 times faster with the same reliability as the CPU version, both extended to three dimensions. Lastly, a simulation containing a total of 62,600 particles is fully rendered in 3D.

Accelerating multi-point statistics reconstruction method for porous media via deep learning

Reconstruction of three-dimensional (3D) porous media from a single two-dimensional (2D) image or limited morphological information has been an outstanding problem. Specifically, multi-point statistics (MPS)-based methods have been proved to be effective and promising to address this problem. Besides, recently sampling-based MPS methods that reconstruct 3D microstructure layer by layer have attracted increasing attention, for its relatively lower computational cost and memory demand. However, due to the nature that one has to search and match multi-point information in a data structure like binary tree or list for each simulation, it is very time-consuming, especially for large template used to reconstruct geometrically complex media. In this paper, to overcome this challenge, for the first time to the best of our knowledge, an accelerating reconstruction method based on deep learning is proposed. Specially, conditional generative adversarial networks (CGAN) is leveraged to model and characterize the relation between the sampling image which contains conditioning data and the target void-solid image. Unlike conventional MPS-based method generally performing simulation point by point, our method is able to directly translate the sampling image to the target one instantaneously, thus leading to a significant speedup factor (∼760 for 2D reconstruction and ∼25 for 3D reconstruction on CPU). Meanwhile, to assess the performance of our method, we test it on sandstone samples, and two-point correlation function, lineal-path function and two-point cluster function, as well as local porosity distribution are quantitatively compared with those of the target microstructure. The comparison indicates that our method is of high efficiency while preserving good agreement of statistical functions with that of the target system. We remark that our approach opens the door to a new methodology that incorporating machine learning/deep learning techniques into conventional methods to address CPU- or memory-demanding issues in a wide range of related fields.

Variational principle for quantum impurity systems in and out of equilibrium: Application to Kondo problems

We provide a detailed formulation of the recently proposed variational approach [Y. Ashida et al., Phys. Rev. Lett. 121, 026805 (2018)] to study ground-state properties and out-of-equilibrium dynamics for generic quantum spin-impurity systems. Motivated by the original ideas by Tomonaga, Lee, Low, and Pines, we construct a canonical transformation that completely decouples the impurity from the bath degrees of freedom. By combining this transformation with a Gaussian ansatz for the fermionic bath, we obtain a family of variational many-body states that can efficiently encode the strong entanglement between the impurity and fermions of the bath. We give a detailed derivation of equations of motions in the imaginary- and real-time evolutions on the variational manifold. We benchmark our approach by applying it to investigate ground-state and dynamical properties of the anisotropic Kondo model and compare results with those obtained using matrix-product state (MPS) ansatz. We show that our approach can achieve an accuracy comparable to MPS-based methods with several orders of magnitude fewer variational parameters than the corresponding MPS ansatz. Comparisons to the Yosida ansatz and the exact solution from the Bethe ansatz are also discussed. We use our approach to investigate the two-lead Kondo model and analyze its long-time spatiotemporal behavior and the conductance behavior at finite bias and magnetic fields. The obtained results are consistent with the previous findings in the Anderson model and the exact solutions at the Toulouse point.

Digital Elevation Data Fusion Using Multiple-Point Geostatistical Simulation

This paper proposes advanced methods based on multiple-point geostatistical simulations (MPSs) for data fusion in digital elevation models (DEMs). MPS-based methods can capture similar patterns using the spatial correlation residing in the training images and then reproduce the area of interest in terms of spatial patterning through conditional simulation. For this, the FILTERSIM algorithm, which is based on MPS, can be applied to augment the prediction results from traditional geostatistical approaches to derive fused datasets from complementary sources. However, the FILTERSIM algorithm discerns similar patterns based on a filter-based prototyping process and does not account for nonstationarity of spatial structures. Thus, an enhanced data fusion method based on a modified FILTERSIM algorithm was proposed, in which new strategies for forming prototypes were incorporated. An experiment was carried out in a study area in Northwest China to test the proposed methods. The aim is to produce fused DEM datasets at fine spatial resolution by integrating fine-resolution but sparsely sampled SRTM data and regularly gridded coarse-resolution GMTED2010 data, and then to test three data fusion methods: 1) the traditional geostatistical interpolation, which provides baseline results for comparison; 2) the conventional FILTERSIM algorithm; and 3) a modified FILTERSIM algorithm. For both the first and second methods, three different kriging approaches were used; for the third method, three new schemes for building prototypes were tested for an improvement in performance. The results show that the improved FILTERSIM method can achieve greater accuracy and retain more spatial structure than the other two methods.

Prenatal Detection of Aneuploidy and Imbalanced Chromosomal Arrangements by Massively Parallel Sequencing

Fetal chromosomal abnormalities are the most common reasons for invasive prenatal testing. Currently, G-band karyotyping and several molecular genetic methods have been established for diagnosis of chromosomal abnormalities. Although these testing methods are highly reliable, the major limitation remains restricted resolutions or can only achieve limited coverage on the human genome at one time. The massively parallel sequencing (MPS) technologies which can reach single base pair resolution allows detection of genome-wide intragenic deletions and duplication challenging karyotyping and microarrays as the tool for prenatal diagnosis. Here we reported a novel and robust MPS-based method to detect aneuploidy and imbalanced chromosomal arrangements in amniotic fluid (AF) samples. We sequenced 62 AF samples on Illumina GAIIx platform and with averagely 0.01× whole genome sequencing data we detected 13 samples with numerical chromosomal abnormalities by z-test. With up to 2× whole genome sequencing data we were able to detect microdeletion/microduplication (ranged from 1.4 Mb to 37.3 Mb of 5 samples from chorionic villus sampling (CVS) using SeqSeq algorithm. Our work demonstrated MPS is a robust and accurate approach to detect aneuploidy and imbalanced chromosomal arrangements in prenatal samples.

On entropy growth and the hardness of simulating time evolution

The simulation of quantum systems is a task for which quantum computers are believed to give an exponential speed up as compared with classical ones. While ground states of one-dimensional systems can be efficiently approximated using matrix product states (MPS), their time evolution can encode quantum computations, so that simulating the latter should be hard classically. However, one might believe that for systems with high enough symmetry, and thus insufficient parameters to encode a quantum computation, efficient classical simulation is possible. We discuss supporting evidence to the contrary: we provide a rigorous proof of the observation that a time-independent local Hamiltonian can yield a linear increase of the entropy when acting on a product state in a translational invariant framework. This criterion has to be met by any classical simulation method, which in particular implies that every global approximation of the evolution requires exponential resources for any MPS-based method.