Related papers: Capturing long-range memory structures with tree-g…
We present a tree-tensor-network-based method to study strongly correlated systems with nonlocal interactions in higher dimensions. Although the momentum-space and quantum-chemistry versions of the density matrix renormalization group…
We introduce complex-valued tensor network models for sequence processing motivated by correspondence to probabilistic graphical models, interpretability and resource compression. Inductive bias is introduced to our models via network…
In the path integral formulation of the evolution of an open quantum system coupled to a Gaussian, non-interacting environment, the dynamical contribution of the latter is encoded in an object called the influence functional. Here, we…
In the domain of sequence modelling, Recurrent Neural Networks (RNN) have been capable of achieving impressive results in a variety of application areas including visual question answering, part-of-speech tagging and machine translation.…
Every year, substantial theoretical and experimental progress is made towards the realisation of a genuinely new computational paradigm in the construction of a quantum computer. But progress is fractal; to make headway is to unearth the…
Many complex systems exhibit interactions that depend not only on pairwise connections, but also group structures and memory effects. To capture such effects, we develop a unified tensor framework for modeling higher-order Markov chains…
While several numerical techniques are available for predicting the dynamics of non-Markovian open quantum systems, most struggle with simulations for very long memory and propagation times, e.g., due to superlinear scaling with the number…
Many scientific areas, from computer science to the environmental sciences and finance, give rise to multivariate time series which exhibit long memory, or loosely put, a slow decay in their autocorrelation structure. Efficient modelling…
Tensors are a natural way to express correlations among many physical variables, but storing tensors in a computer naively requires memory which scales exponentially in the rank of the tensor. This is not optimal, as the required memory is…
We show how to learn structures of generic, non-Markovian, quantum stochastic processes using a tensor network based machine learning algorithm. We do this by representing the process as a matrix product operator (MPO) and train it with a…
In recent years, tree tensor network methods have proven capable of simulating quantum many-body and other high-dimensional systems. This work is a user guide to our Python library PyTreeNet. It includes code examples and exercises to…
Open quantum systems provide a conceptually simple setting for the exploration of collective behavior stemming from the competition between quantum effects, many-body interactions, and dissipative processes. They may display dynamics…
This paper is concerned with the approximation of high-dimensional functions in a statistical learning setting, by empirical risk minimization over model classes of functions in tree-based tensor format. These are particular classes of…
The process tensor framework to open quantum systems provides the most general description of multi-time correlations in non-Markovian quantum dynamics. A compressed representation of a process tensor in terms of matrix product operators…
We describe a quantum-assisted machine learning (QAML) method in which multivariate data is encoded into quantum states in a Hilbert space whose dimension is exponentially large in the length of the data vector. Learning in this space…
We develop and analyze a method for simulating quantum circuits on classical computers by representing quantum states as rooted tree tensor networks. Our algorithm first determines a suitable, fixed tree structure adapted to the expected…
The complexity of quantum many-body systems is manifested in the vast diversity of their correlations, making it challenging to distinguish the generic from the atypical features. This can be addressed by analyzing correlations through…
Tensor-power (TP) recurrent model is a family of non-linear dynamical systems, of which the recurrence relation consists of a p-fold (a.k.a., degree-p) tensor product. Despite such the model frequently appears in the advanced recurrent…
Many real-world complex systems are characterized by interactions in groups that change in time. Current temporal network approaches, however, are unable to describe group dynamics, as they are based on pairwise interactions only. Here, we…
Temporal networks are widely used models for describing the architecture of complex systems. Network memory -- that is the dependence of a temporal network's structure on its past -- has been shown to play a prominent role in diffusion,…