Related papers: Matrix Product States in Quantum Spin Chains
We study frustration-free Hamiltonians of fractional quantum Hall (FQH) states from the point of view of the matrix product state (MPS) representation of their ground and excited states. There is a wealth of solvable models relating to FQH…
Correlator product states (CPS) are a powerful and very broad class of states for quantum lattice systems whose amplitudes can be sampled exactly and efficiently. They work by gluing together states of overlapping clusters of sites on the…
Finance, especially option pricing, is a promising industrial field that might benefit from quantum computing. While quantum algorithms for option pricing have been proposed, it is desired to devise more efficient implementations of costly…
In this work we introduce an ansatz for continuous matrix product operators for quantum field theory. We show that (i) they admit a closed-form expression in terms of finite number of matrix-valued functions without reference to any lattice…
In this study, we introduce a novel family of tensor networks, termed constrained matrix product states (MPS), designed to incorporate exactly arbitrary discrete linear constraints, including inequalities, into sparse block structures.…
Towards the efficient simulation of near-term quantum devices using tensor network states, we introduce an improved real-space parallelizable matrix-product state (MPS) compression method. This method enables efficient compression of all…
We report on a systematic implementation of su(2) invariance for matrix product states (MPS) with concrete computations cast in a diagrammatic language. As an application we present a variational MPS study of $su(2)$ invariant quantum spin…
Preparing arbitrary quantum states requires exponential resources. Matrix Product States (MPS) admit more efficient constructions, particularly when accuracy is traded for circuit complexity. Existing approaches to MPS preparation mostly…
We study thermal states of strongly interacting quantum spin chains and prove that those can be represented in terms of convex combinations of matrix product states. Apart from revealing new features of the entanglement structure of Gibbs…
In recent years, a close connection between the description of open quantum systems, the input-output formalism of quantum optics, and continuous matrix product states in quantum field theory has been established. So far, however, this…
In quantum physics, multiparticle systems are described by quantum states acting on tensor products of Hilbert spaces. This product structure leads to the distinction between product states and entangled states; moreover, one can quantify…
Cluster states are multi-particle entangled states with special entanglement properties particularly suitable for quantum computation. It has been shown that cluster states can exhibit Greenberger-Horne-Zeilinger (GHZ)-type non-locality…
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…
We develop in full detail the formalism of tangent states to the manifold of matrix product states, and show how they naturally appear in studying time-evolution, excitations and spectral functions. We focus on the case of systems with…
We introduce a new class of continuous matrix product (CMP) states and establish the stochastic master equations (quantum filters) for an arbitrary quantum system probed by a bosonic input field in this class of states. We show that this…
Preparing matrix product states (MPSs) on quantum computers is an essential routine in the simulation of many-body physics. However, widely-used schemes based on staircase circuits are often too deep to execute on current hardware. Here we…
Efficient encoding of classical information plays a fundamental role in numerous practical quantum algorithms. However, the preparation of an arbitrary amplitude-encoded state has been proven to be time-consuming, and its deployment on…
Generalized symmetries have emerged as a powerful organizing principle for exotic quantum phases. However, their role in open quantum systems, especially for non-invertible cases, remains largely unexplored. We address this by applying a…
The set of two-body reduced states of translation invariant, infinite quantum spin chains can be approximated from inside and outside using matrix product states and marginals of finite systems, respectively. These lead to hierarchies of…
We present several improvements of the infinite matrix product state (iMPS) algorithm for finding ground states of one-dimensional quantum systems with long-range interactions. As a main new ingredient we introduce the superposed…