Related papers: Local Matrix Product Operators: Canonical Form, Co…
This work gives a detailed investigation of matrix product state (MPS) representations for pure multipartite quantum states. We determine the freedom in representations with and without translation symmetry, derive respective canonical…
Matrix product density operator (MPDO) provides an efficient tensor network representation of mixed states on one-dimensional quantum many-body systems. We study a real-space renormalization group transformation of MPDOs represented by a…
Given a set of matrices, modeled as samples of a matrix-valued function, we suggest a method to approximate the underline function using a product approximation operator. This operator extends known approximation methods by exploiting the…
The dynamics of one-dimensional quantum many-body systems is often numerically simulated with matrix-product states (MPSs). The computational complexity of MPS methods is known to be related to the growth of entropies of reduced density…
We present a new wavefunction ansatz that combines the strengths of spin projection with the language of matrix product states (MPS) and matrix product operators (MPO) as used in the density matrix renormalization group (DMRG).…
We introduce a matrix product state (MPS) with an incommensurate periodicity by applying the spin-rotation operator of each site to a uniform MPS in the thermodynamic limit. The spin rotations decrease the variational energy with…
Through a reformulation of the local limit theorem and law of small numbers, which is obtained by working in the spaces naturally associated to the limiting distributions, we discover a general and abstract framework for the investigation…
We propose an approach to represent the second-quantized electronic Hamiltonian in a compact sum-of-products (SOP) form. The approach is based on the canonical polyadic decomposition (CPD) of the original Hamiltonian projected onto the…
Product measures of dimension $n$ are known to be concentrated in Hamming distance: for any set $S$ in the product space of probability $\epsilon$, a random point in the space, with probability $1-\delta$, has a neighbor in $S$ that is…
We introduce the Markovian matrix product density operator, which is a special subclass of the matrix product density operator. We show that the von Neumann entropy of such ansatz can be computed efficiently on a classical computer. This is…
Matrix product states (MPS) provide a powerful framework for characterizing one-dimensional symmetry-protected topological (SPT) phases of matter and for formulating Lieb-Schultz-Mattis (LSM)-type constraints. Here we generalize the MPS…
Machine-learning interatomic potentials (MLIPs) have become a mainstay in computationally-guided materials science, surpassing traditional force fields due to their flexible functional form and superior accuracy in reproducing physical…
Due to the substantial scale of Large Language Models (LLMs), the direct application of conventional compression methodologies proves impractical. The computational demands associated with even minimal gradient updates present challenges,…
We introduce a general model of stochastically generated matrix product states (MPS) in which the local tensors share a common distribution and form a strictly stationary sequence, without requiring spatial independence. Under natural…
Encoding classical data in a quantum state is a key prerequisite of many quantum algorithms. Recently matrix product state (MPS) methods emerged as the most promising approach for constructing shallow quantum circuits approximating input…
The Robbins-Monro algorithm is a recursive, simulation-based stochastic procedure to approximate the zeros of a function that can be written as an expectation. It is known that under some technical assumptions, Gaussian limit distributions…
The Lov\'{a}sz Local Lemma is a very powerful tool in probabilistic combinatorics, that is often used to prove existence of combinatorial objects satisfying certain constraints. Moser and Tardos have shown that the LLL gives more than just…
Simulating quantum many-body systems (QMBS) is one of the long-standing, highly non-trivial challenges in condensed matter physics and quantum information due to the exponentially growing size of the system's Hilbert space. To date, tensor…
Quantum computers are believed to have the ability to process huge data sizes which can be seen in machine learning applications. In these applications, the data in general is classical. Therefore, to process them on a quantum computer,…
We present a method of extracting information about topological order from the ground state of a strongly correlated two-dimensional system represented by an infinite projected entangled pair state (iPEPS). As in Phys. Rev. B 101, 041108…