scholarly journals Quantum-inspired event reconstruction with Tensor Networks: Matrix Product States

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Jack Y. Araz ◽  
Michael Spannowsky
Keyword(s):  
Top Quark ◽  
Entanglement Entropy ◽  
Feature Space ◽  
Machine Learning Techniques ◽  
Stochastic Gradient Descent ◽  
Matrix Product ◽  
Density Matrix Renormalization ◽  
Matrix Product State ◽  
Tensor Networks ◽  
Many Body Systems

Abstract Tensor Networks are non-trivial representations of high-dimensional tensors, originally designed to describe quantum many-body systems. We show that Tensor Networks are ideal vehicles to connect quantum mechanical concepts to machine learning techniques, thereby facilitating an improved interpretability of neural networks. This study presents the discrimination of top quark signal over QCD background processes using a Matrix Product State classifier. We show that entanglement entropy can be used to interpret what a network learns, which can be used to reduce the complexity of the network and feature space without loss of generality or performance. For the optimisation of the network, we compare the Density Matrix Renormalization Group (DMRG) algorithm to stochastic gradient descent (SGD) and propose a joined training algorithm to harness the explainability of DMRG with the efficiency of SGD.

scholarly journals Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy)

2018 ◽  
Author(s):  
Johannes Hauschild ◽  
Frank Pollmann
Keyword(s):  
Matrix Product ◽  
Many Body ◽  
Density Matrix Renormalization ◽  
Tensor Networks ◽  
Condensed Matter Theory ◽  
Tensor Network ◽  
Matter Theory ◽  
Particle Number Conservation ◽  
Many Body Systems ◽  
The One

Tensor product state (TPS) based methods are powerful tools to efficiently simulate quantum many-body systems in and out of equilibrium. In particular, the one-dimensional matrix-product (MPS) formalism is by now an established tool in condensed matter theory and quantum chemistry. In these lecture notes, we combine a compact review of basic TPS concepts with the introduction of a versatile tensor library for Python (TeNPy) [1]. As concrete examples, we consider the MPS based time-evolving block decimation and the density matrix renormalization group algorithm. Moreover, we provide a practical guide on how to implement abelian symmetries (e.g., a particle number conservation) to accelerate tensor operations.

scholarly journals Area law of noncritical ground states in 1D long-range interacting systems

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Tomotaka Kuwahara ◽  
Keiji Saito
Keyword(s):  
Long Range ◽  
Ground States ◽  
Matrix Product ◽  
Range Interaction ◽  
Density Matrix Renormalization ◽  
Matrix Product State ◽  
The Matrix ◽  
Interacting Systems ◽  
Critical Phases ◽  
Area Law

Abstract The area law for entanglement provides one of the most important connections between information theory and quantum many-body physics. It is not only related to the universality of quantum phases, but also to efficient numerical simulations in the ground state. Various numerical observations have led to a strong belief that the area law is true for every non-critical phase in short-range interacting systems. However, the area law for long-range interacting systems is still elusive, as the long-range interaction results in correlation patterns similar to those in critical phases. Here, we show that for generic non-critical one-dimensional ground states with locally bounded Hamiltonians, the area law robustly holds without any corrections, even under long-range interactions. Our result guarantees an efficient description of ground states by the matrix-product state in experimentally relevant long-range systems, which justifies the density-matrix renormalization algorithm.

scholarly journals Efficient variational contraction of two-dimensional tensor networks with a non-trivial unit cell

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 328
Author(s):  
A. Nietner ◽  
B. Vanhecke ◽  
F. Verstraete ◽  
J. Eisert ◽  
L. Vanderstraeten
Keyword(s):  
Variational Principles ◽  
Valence Bond ◽  
Computational Effort ◽  
Unit Cell ◽  
Square Lattice ◽  
Partition Functions ◽  
Matrix Product ◽  
Two Dimensional ◽  
Matrix Product State ◽  
Tensor Networks

Tensor network states provide an efficient class of states that faithfully capture strongly correlated quantum models and systems in classical statistical mechanics. While tensor networks can now be seen as becoming standard tools in the description of such complex many-body systems, close to optimal variational principles based on such states are less obvious to come by. In this work, we generalize a recently proposed variational uniform matrix product state algorithm for capturing one-dimensional quantum lattices in the thermodynamic limit, to the study of regular two-dimensional tensor networks with a non-trivial unit cell. A key property of the algorithm is a computational effort that scales linearly rather than exponentially in the size of the unit cell. We demonstrate the performance of our approach on the computation of the classical partition functions of the antiferromagnetic Ising model and interacting dimers on the square lattice, as well as of a quantum doped resonating valence bond state.

Entangled spin chain

2017 ◽  
Vol 29 (10) ◽  
pp. 1750031 ◽  
Author(s):  
Olof Salberger ◽  
Vladimir Korepin
Keyword(s):  
Entanglement Entropy ◽  
Square Lattice ◽  
Symmetric Model ◽  
Matrix Product ◽  
Reversible Computing ◽  
Half Integer ◽  
Matrix Product State ◽  
Fredkin Gate ◽  
Leading Term ◽  
Higher Spins

We introduce a new model of interacting spin 1/2. It describes interactions of three nearest neighbors. The Hamiltonian can be expressed in terms of Fredkin gates. The Fredkin gate (also known as the controlled swap gate) is a computational circuit suitable for reversible computing. Our construction generalizes the model presented by Peter Shor and Ramis Movassagh to half-integer spins. Our model can be solved by means of Catalan combinatorics in the form of random walks on the upper half plane of a square lattice (Dyck walks). Each Dyck path can be mapped on a wave function of spins. The ground state is an equally weighted superposition of Dyck walks (instead of Motzkin walks). We can also express it as a matrix product state. We further construct a model of interacting spins 3/2 and greater half-integer spins. The models with higher spins require coloring of Dyck walks. We construct a [Formula: see text] symmetric model (where [Formula: see text] is the number of colors). The leading term of the entanglement entropy is then proportional to the square root of the length of the lattice (like in the Shor–Movassagh model). The gap closes as a high power of the length of the lattice [5, 11].

scholarly journals Parallel quantum simulation of large systems on small NISQ computers

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
F. Barratt ◽  
James Dborin ◽  
Matthias Bal ◽  
Vid Stojevic ◽  
Frank Pollmann ◽  
...  
Keyword(s):  
Finite Depth ◽  
Quantum Circuit ◽  
Quantum Simulation ◽  
Quantum Spin ◽  
Matrix Product ◽  
One Dimensional ◽  
Matrix Product State ◽  
Tensor Networks ◽  
Large Systems ◽  
Invariant Quantum

AbstractTensor networks permit computational and entanglement resources to be concentrated in interesting regions of Hilbert space. Implemented on NISQ machines they allow simulation of quantum systems that are much larger than the computational machine itself. This is achieved by parallelising the quantum simulation. Here, we demonstrate this in the simplest case; an infinite, translationally invariant quantum spin chain. We provide Cirq and Qiskit code that translates infinite, translationally invariant matrix product state (iMPS) algorithms to finite-depth quantum circuit machines, allowing the representation, optimisation and evolution of arbitrary one-dimensional systems. The illustrative simulated output of these codes for achievable circuit sizes is given.

scholarly journals bCNN-Methylpred: Feature-Based Prediction of RNA Sequence Modification Using Branch Convolutional Neural Network

Genes ◽  
2021 ◽  
Vol 12 (8) ◽  
pp. 1155
Author(s):  
Naeem Islam ◽  
Jaebyung Park
Keyword(s):  
Neural Network ◽  
Convolutional Neural Network ◽  
Domain Knowledge ◽  
Feature Space ◽  
Experimental Methods ◽  
Machine Learning Techniques ◽  
Rna Modification ◽  
Biological Processes ◽  
Rna Sequence ◽  
Functional Mechanisms

RNA modification is vital to various cellular and biological processes. Among the existing RNA modifications, N6-methyladenosine (m6A) is considered the most important modification owing to its involvement in many biological processes. The prediction of m6A sites is crucial because it can provide a better understanding of their functional mechanisms. In this regard, although experimental methods are useful, they are time consuming. Previously, researchers have attempted to predict m6A sites using computational methods to overcome the limitations of experimental methods. Some of these approaches are based on classical machine-learning techniques that rely on handcrafted features and require domain knowledge, whereas other methods are based on deep learning. However, both methods lack robustness and yield low accuracy. Hence, we develop a branch-based convolutional neural network and a novel RNA sequence representation. The proposed network automatically extracts features from each branch of the designated inputs. Subsequently, these features are concatenated in the feature space to predict the m6A sites. Finally, we conduct experiments using four different species. The proposed approach outperforms existing state-of-the-art methods, achieving accuracies of 94.91%, 94.28%, 88.46%, and 94.8% for the H. sapiens, M. musculus, S. cerevisiae, and A. thaliana datasets, respectively.

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