Related papers: Modeling Sequences with Quantum States: A Look Und…
We demonstrate that a tensor product structure could be obtained by introducing pseudorandom phase sequences into classical fields with two orthogonal modes. Using classical fields modulated with pseudorandom phase sequences, we discuss…
Coalgebras generalize various kinds of dynamical systems occuring in mathematics and computer science. Examples of systems that can be modeled as coalgebras include automata and Markov chains. We will present a coalgebraic representation of…
Continuous-variable quantum systems are foundational to quantum computation, communication, and sensing. While traditional representations using wave functions or density matrices are often impractical, the tomographic picture of quantum…
Distributed quantum networks are not merely information conduits but intricate systems that embody the principles of quantum mechanics. In our study, we examine the underlying mechanisms of quantum connectivity within a distributed…
Quantum systems are the ultimate touchstone for the production of random sequences of numbers. Spatially spread entangled systems allow the generation of identical random sequences in remote locations. The impossibility of observing a…
A quantum system's state is identified with a density matrix. Though their probabilistic interpretation is rooted in ensemble theory, density matrices embody a known shortcoming. They do not completely express an ensemble's physical…
In the discussion about the quantumness of NMR computation a conclusion is done that computational states are separable and therefore can not be entangled. This conclusion is based on the assumption that the initial density matrix of an…
Quantum magnetism in low dimensions has been one of the central areas of theoretical research for many decades now. One of the key reasons for the long standing interest in this field has been the existence of simplified models, which serve…
We introduce a class of variational states to describe quantum many-body systems. This class generalizes matrix product states which underly the density-matrix renormalization group approach by combining them with weighted graph states.…
Quantum Recurrent Neural Networks (QRNNs) are robust candidates for modelling and predicting future values in multivariate time series. However, the effective implementation of some QRNN models is limited by the need for mid-circuit…
We demonstrate how to parallelize the density matrix renormalization group (DMRG) algorithm in real space through a straightforward modification of serial DMRG. This makes it possible to apply at least an order of magnitude more…
It is known that quantum correlations exhibited by a maximally entangled qubit pair can be simulated with the help of shared randomness, supplemented with additional resources, such as communication, post-selection or non-local boxes. For…
The Categorical Compositional Distributional (DisCoCat) framework models meaning in natural language using the mathematical framework of quantum theory, expressed as formal diagrams. DisCoCat diagrams can be associated with tensor networks…
The density matrix renormalization group (DMRG) is a numerical method that optimizes a variational state expressed by a tensor product. We show that the ground state is not fully optimized as far as we use the standard finite system…
Hidden Quantum Markov Models (HQMMs) can be thought of as quantum probabilistic graphical models that can model sequential data. We extend previous work on HQMMs with three contributions: (1) we show how classical hidden Markov models…
The frame of classical probability theory can be generalized by enlarging the usual family of random variables in order to encompass nondeterministic ones: this leads to a frame in which two kinds of correlations emerge: the classical…
We propose a tensor network algorithm for the efficient sampling of quantum pure states belonging to a generalized microcanonical ensemble. The algorithm consists in an adaptation of the power method to a recently introduced ensemble of…
Quantum Extreme Learning Machine (QELM) is an emerging hybrid quantum machine learning framework that leverages quantum system dynamics to enhance classical models. However, QELM can suffer from the exponential concentration problem, where…
This is an introductory course to the Lanczos Method and Density Matrix Renormalization Group Algorithms(DMRG), two among the leading numerical techniques applied in studies of low-dimensional quantum models. The idea of studying the models…
We present an efficient algorithm for twirling a multi-qudit quantum state. The algorithm can be used for approximating the twirling operation in an ensemble of physical systems in which the systems cannot be individually accessed. It can…