相关论文: Matrix Product State Representations

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…

Continuous Matrix Product States (cMPS) are powerful variational ansatz states for ground states of continuous quantum field theories in (1+1) dimension. In this paper we introduce a novel parametrization of the cMPS wave function based on…

Matrix product purifications (MPPs) are a very efficient tool for the simulation of strongly correlated quantum many-body systems at finite temperatures. When a system features symmetries, these can be used to reduce computation costs…

In this note, we describe a method for reconstructing matrix product states from a small number of efficiently-implementable measurements. Our method is exponentially faster than standard tomography, and it can also be used to certify that…

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…

Classical simulation of quantum physics is a central approach to investigating physical phenomena. Quantum computers enhance computational capabilities beyond those of classical resources, but it remains unclear to what extent existing…

The continuous matrix product state (cMPS) ansatz is a promising numerical tool for studying quantum many-body systems in continuous space. Although it provides a clean framework that allows one to directly simulate continuous systems, the…

We derive an exact formula for a matrix product state (MPS) representation (or a PEPS in higher number of dimensions) of the ground state of translationally invariant bosonic lattice systems in terms of a single one-dimensional Euclidean…

Common wisdom says that the entanglement of fermionic systems can be low in the second quantization formalism but is extremely large in the first quantization. Hence Matrix Product State (MPS) methods based on moderate entanglement have…

Using truncated conformal field theory (CFT), we present the formalism necessary to obtain exact matrix product state (MPS) representations for any fractional quantum hall model state which can be written as an expectation value of primary…

In this work, we investigate the universal representation capacity of the Matrix Product States (MPS) from the perspective of boolean functions and continuous functions. We show that MPS can accurately realize arbitrary boolean functions by…

For every Matrix Product State (MPS) one can always construct a so-called parent Hamiltonian. This is a local, frustration free, Hamiltonian which has the MPS as ground state and is gapped. Whenever that parent Hamiltonian has a degenerate…

We study the set of random matrix product states (RMPS) introduced in arXiv:0908.3877 as a tool to explore foundational aspects of quantum statistical mechanics. In the present work, we provide an accurate numerical and analytical…

Matrix Product States (MPS) and Operators (MPO) have been proven to be a powerful tool to study quantum many-body systems but are restricted to moderately entangled states as the number of parameters scales exponentially with the…

Quantum computing is finding promising applications in optimization, machine learning and physics, leading to the development of various models for representing quantum information. Because these representations are often studied in…

We propose a framework to design concurrently a frustration-free quantum many-body Hamiltonian and its numerically exact ground states on a sufficiently large finite-size cluster in one and two dimensions using an elementary matrix product…

The density-matrix renormalization group method has become a standard computational approach to the low-energy physics as well as dynamics of low-dimensional quantum systems. In this paper, we present a new set of applications, available as…

Data representation in quantum state space offers an alternative function space for machine learning tasks. However, benchmarking these algorithms at a practical scale has been limited by ineffective simulation methods. We develop a quantum…

The study of frustration-free Hamiltonians and their relation to finite bond-dimension matrix product states (MPS) has a long tradition. However, fractional quantum Hall (FQH) states do not quite fit into this theme since the known MPS…

This paper introduces matrix product state (MPS) decomposition as a new and systematic method to compress multidimensional data represented by higher-order tensors. It solves two major bottlenecks in tensor compression: computation and…