Related papers: Matrix Product States for Quantum Stochastic Model…
We show that any matrix product state (MPS) can be exactly represented by a recurrent neural network (RNN) with a linear memory update. We generalize this RNN architecture to 2D lattices using a multilinear memory update. It supports…
Matrix Product States can be defined as the family of quantum states that can be sequentially generated in a one-dimensional system. We introduce a new family of states which extends this definition to two dimensions. Like in Matrix Product…
We quantify how well matrix product states approximate exact ground states of 1-D quantum spin systems as a function of the number of spins and the entropy of blocks of spins. We also investigate the convex set of local reduced density…
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…
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…
Generative modeling, which learns joint probability distribution from data and generates samples according to it, is an important task in machine learning and artificial intelligence. Inspired by probabilistic interpretation of quantum…
We show that the model wave functions used to describe the fractional quantum Hall effect have exact representations as matrix product states (MPS). These MPS can be implemented numerically in the orbital basis of both finite and infinite…
Stochastic model-predictive control (SMPC) has evolved to a powerful framework for the control of stochastic dynamical systems. SMPC utilizes a probabilistic uncertainty description to provide a systematic trade-off between the control…
The canonical form of Matrix Product States (MPS) and the associated fundamental theorem, which relates different MPS representations of a state, are the theoretical framework underlying many of the analytical results derived through MPS,…
We reconstruct a matrix product state (MPS) in reduced spaces using density matrix. This scheme applies to a MPS built on a blocked quantum lattice. Each block contains $N$ physical sites that have a local space of rank $R$. The simulation…
Matrix-product state (MPS) skeletons are connected networks of Hamiltonians with exact MPS ground states that underlie a phase diagram. Such skeletons have previously been found in classes of free-fermion models. For the…
(Please refer to arXiv:1810.08050, which has completely different aims but contains all the main contents of this paper) In this work, we propose to access the information of criticality and excitations of one-dimensional quantum systems by…
We present an implementation of an efficient algorithm for the calculation of the spectrum of one-dimensional quantum systems with periodic boundary conditions. This algorithm is based on a matrix product representation for quantum states…
Relativistic continuous matrix product states (RCMPS) are a powerful variational ansatz for quantum field theories of a single field. However, they inherit a property of their non-relativistic counterpart that makes them divergent for…
Models whose ground states can be written as an exact matrix product state (MPS) provide valuable insights into phases of matter. While MPS-solvable models are typically studied as isolated points in a phase diagram, they can belong to a…
Tensor network, which originates from quantum physics, is emerging as an efficient tool for classical and quantum machine learning. Nevertheless, there still exists a considerable accuracy gap between tensor network and the sophisticated…
We investigate chains of 'd' dimensional quantum spins (qudits) on a line with generic nearest neighbor interactions without translational invariance. We find the conditions under which these systems are not frustrated, i.e. when the ground…
Using random matrix techniques and the theory of Matrix Product States we show that reduced density matrices of quantum spin chains have generically maximum entropy.
Bosonic Gaussian states are ubiquitous in quantum optics and condensed matter physics. While they are efficiently handled within the Gaussian formalism, sampling requires calculating amplitudes in the boson occupation basis. This step,…
A state-space model is a time-series model that has an unobserved latent process from which we take noisy measurements over time. The observations are conditionally independent given the latent process and the latent process itself is…