Related papers: Quantum Trajectories for a Class of Continuous Mat…
The concept of stochastic matrix product states is introduced and a natural form for the states is derived. This allows to define the analogue of Schmidt coefficients for steady states of non-equilibrium stochastic processes. We discuss a…
In recent years, interest in expressing the success of neural networks to the quantum computing has increased significantly. Tensor network theory has become increasingly popular and widely used to simulate strongly entangled correlated…
We extend the recently introduced continuous matrix product state (cMPS) variational class to the setting of (1+1)-dimensional relativistic quantum field theories. This allows one to overcome the difficulties highlighted by Feynman…
Quantum stochastic master equations of jump type are formulated in a general way and connections with quantum/classical hybrid systems and quantum filtering theory are discussed. By introducing the notion of ``typical trajectory", we show…
We construct matrix product steady state for a class of interacting particle systems where particles do not obey hardcore exclusion, meaning each site can occupy any number of particles subjected to the global conservation of total number…
The purpose of this paper is to derive filters for an arbitrary open quantum system driven by a light wavepacket prepared in a continuous-mode multi-photon state. A continuous-mode multi-photon state is a state of a travelling light…
The time evolution of the one-point probability vector of stochastic processes and quantum processes for $N$-level systems have been unified. Hence, quantum states and quantum operations can be regarded as generalizations of the one-point…
We propose a new version of the matrix product (MP) states approach to the description of quantum spin chains, which allows one to construct MP states with certain total spin and its z-projection. We show that previously known MP…
Two level quantum system (Qubit) and non-classical states of light such as single photon and superposition of coherent state are under special attention in quantum technologies such as quantum computing, quantum communication and quantum…
The classical embeddability problem asks whether a given stochastic matrix $T$, describing transition probabilities of a $d$-level system, can arise from the underlying homogeneous continuous-time Markov process. Here, we investigate the…
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…
The matrix product state formalism is used to simulate Hamiltonian lattice gauge theories. To this end, we define matrix product state manifolds which are manifestly gauge invariant. As an application, we study 1+1 dimensional one flavour…
Improving the understanding of strongly correlated quantum many body systems such as gases of interacting atoms or electrons is one of the most important challenges in modern condensed matter physics, materials research and chemistry.…
Stationary states of stochastic models, which have $N$ states per site, in matrix product form are considered. First we give a necessary condition for the existence of a finite $M$-dimensional matrix product state for any ${N,M}$. Second,…
We obtain the finite-temperature unconditional master equation of the density matrix for two coupled quantum dots (CQD) when one dot is subjected to a measurement of its electron occupation number using a point contact (PC). To determine…
We introduce a functional matrix product state (FMPS) based method for simulating the real-space representation of continuous-variable (CV) quantum computation. This approach efficiently simulates non-Gaussian CV systems by leveraging their…
Quantum state tomography (QST) is the gold standard technique for obtaining an estimate for the state of small quantum systems in the laboratory. Its application to systems with more than a few constituents (e.g. particles) soon becomes…
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 present a framework for preparing quantum states from matrix product states (MPS) with open and periodic boundary conditions on quantum devices. The MPS tensors are mapped to unitary gates, which are subsequently decomposed into native…
In this work, we present a novel representation of matrix product states (MPS) within the framework of quasi-local algebras. By introducing an enhanced compatibility condition, we enable the extension of finite MPS to an infinite-volume…