Related papers: Matrix Product States as Observations of Entangled…
We quantify the representational power of matrix product states (MPS) for entangled qubit systems by giving polynomial expressions in a pure quantum state's amplitudes which hold if and only if the state is a translation invariant matrix…
Matrix Product States (MPS) are a particular type of one dimensional tensor network states, that have been applied to the study of numerous quantum many body problems. One of their key features is the possibility to describe and encode…
The matrix product state (MPS) is utilized to study the ground state properties and quantum phase transitions (QPTs) of the one-dimensional quantum compass model (QCM). The MPS wavefunctions are argued to be very efficient descriptions of…
This paper introduces a Heisenberg picture approach to Matrix Product States (MPS), offering a rigorous yet intuitive framework to explore their structure and classification. MPS efficiently represent ground states of quantum many-body…
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…
We investigate ensembles of Matrix Product States (MPSs) generated by quantum circuit evolution followed by projection onto MPSs with a fixed bond dimension $\chi$. Specifically, we consider ensembles produced by: (i) random sequential…
We introduce Gaussian Matrix Product States (GMPS), a generalization of Matrix Product States (MPS) to lattices of harmonic oscillators. Our definition resembles the interpretation of MPS in terms of projected maximally entangled pairs,…
Matrix Product States (MPS) and Projected Entangled Pair States (PEPS) are powerful analytical and numerical tools to assess quantum many-body systems in one and higher dimensions, respectively. While MPS are comprehensively understood, in…
The theory of entanglement provides a fundamentally new language for describing interactions and correlations in many body systems. Its vocabulary consists of qubits and entangled pairs, and the syntax is provided by tensor networks. We…
Numerical simulations are a powerful tool to study quantum systems beyond exactly solvable systems lacking an analytic expression. For one-dimensional entangled quantum systems, tensor network methods, amongst them Matrix Product States…
In stochastic modeling, there has been a significant effort towards finding predictive models that predict a stochastic process' future using minimal information from its past. Meanwhile, in condensed matter physics, matrix product states…
The matrix product state (MPS) belongs to the most important mathematical models in, for example, condensed matter physics and quantum information sciences. However, to realize an $N$-qubit MPS with large $N$ and large entanglement on a…
This is a partly non-technical introduction to selected topics on tensor network methods, based on several lectures and introductory seminars given on the subject. It should be a good place for newcomers to get familiarized with some of the…
Multipartite entanglement offers a powerful framework for understanding the complex collective phenomena in quantum many-body systems that are often beyond the description of conventional bipartite entanglement measures. Here, we propose a…
Quantum machine learning (QML) is a rapidly expanding field that merges the principles of quantum computing with the techniques of machine learning. One of the powerful mathematical frameworks in this domain is tensor networks. These…
We extend the formalism of Matrix Product States (MPS) to describe one-dimensional gapped systems of fermions with both unitary and anti-unitary symmetries. Additionally, systems with orientation-reversing spatial symmetries are considered.…
Matrix Product States (MPS), also known as Tensor Train (TT) decomposition in mathematics, has been proposed originally for describing an (especially one-dimensional) quantum system, and recently has found applications in various…
The relation between entanglement entropy and the computational difficulty of classically simulating Quantum Mechanics is briefly reviewed. Matrix product states are proven to provide an efficient representation of one-dimensional quantum…
Matrix product states (MPS) illustrate the suitability of tensor networks for the description of interacting many-body systems: ground states of gapped $1$-D systems are approximable by MPS as shown by Hastings [J. Stat. Mech. Theor. Exp.,…
Matrix product states are useful representations for a large variety of naturally occurring quantum states. Studying their typical properties is important for understanding universal behavior, including quantum chaos and thermalization, as…