Related papers: Matrix Product States for Quantum Stochastic Model…
We present a method for quantum state tomography that enables the efficient estimation, with fixed precision, of any of the matrix elements of the density matrix of a state, provided that the states from the basis in which the matrix is…
It is known that exact traveling wave solutions exist for families of (n+1)-states stochastic one-dimensional non-equilibrium lattice models with open boundaries provided that some constraints on the reaction rates are fulfilled. These…
Predicting the quantum dynamics of promising solid-state and molecular quantum technology candidates remains a formidable challenge. Yet, accessing these dynamics is key to understanding and controlling decoherence mechanisms -- a…
Predictive State Representations (PSRs) are an expressive class of models for controlled stochastic processes. PSRs represent state as a set of predictions of future observable events. Because PSRs are defined entirely in terms of…
Quantum turbulence spans length scales from the system size $L$ to the healing length $\xi$, making direct numerical simulations (DNS) of the Gross-Pitaevskii (GP) equation computationally expensive when $L \gg \xi$. We present a matrix…
We introduce an efficient algorithm for the systematic design of shallow-depth quantum circuits capable of preparing many-body quantum states represented as Matrix Product States (MPS). The proposed method leverages Schmidt spectrum…
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…
Matrix product states (MPS), a tensor network designed for one-dimensional quantum systems, has been recently proposed for generative modeling of natural data (such as images) in terms of `Born machine'. However, the exponential decay of…
Matrix product states (MPS) have proven to be a very successful tool to study lattice systems with local degrees of freedom such as spins or bosons. Topologically ordered systems can support anyonic particles which are labeled by conserved…
To compute approximate solutions for combinatorial optimization problems, we describe variational methods based on the product state (PS) and matrix product state (MPS) ansatzes. We perform variational energy minimization with respect to a…
We find an efficient approach to approximately convert matrix product states (MPSs) into restricted Boltzmann machine wave functions consisting of a multinomial hidden unit through a canonical polyadic (CP) decomposition of the MPSs. This…
Bayesian analysis of state-space models includes computing the posterior distribution of the system's parameters as well as filtering, smoothing, and predicting the system's latent states. When the latent states wander around $\mathbb{R}^n$…
While general quantum many-body systems require exponential resources to be simulated on a classical computer, systems of non-interacting fermions can be simulated exactly using polynomially scaling resources. Such systems may be of…
We argue and demonstrate that projected entangled-pair states (PEPS) outperform matrix product states significantly for the task of generative modeling of datasets with an intrinsic two-dimensional structure such as images. Our approach…
Continuous-time stochastic processes pervade everyday experience, and the simulation of models of these processes is of great utility. Classical models of systems operating in continuous-time must typically track an unbounded amount of…
State preparation is a necessary component of many quantum algorithms. In this work, we combine a method for efficiently representing smooth differentiable probability distributions using matrix product states with recently discovered…
Tensor network methods have progressed from variational techniques based on matrix-product states able to compute properties of one-dimensional condensed-matter lattice models into methods rooted in more elaborate states such as projected…
We present a new variational method, based on the matrix product operator (MPO) ansatz, for finding the steady state of dissipative quantum chains governed by master equations of the Lindblad form. Instead of requiring an accurate…
We introduce a method based on matrix product states (MPS) for computing spectral functions of (quasi) one-dimensional spin chains, working directly in momentum space in the thermodynamic limit. We simulate the time evolution after applying…
Quantum many body physics simulations with Matrix Product States can often be accelerated if the quantum symmetries present in the system are explicitly taken into account. Conventionally, quantum symmetries have to be determined before…