Related papers: Using matrix-product states for time-series machin…
In audio signal processing, probabilistic time-frequency models have many benefits over their non-probabilistic counterparts. They adapt to the incoming signal, quantify uncertainty, and measure correlation between the signal's amplitude…
It is a fundamental, but still elusive question whether the schemes based on quantum mechanics, in particular on quantum entanglement, can be used for classical information processing and machine learning. Even partial answer to this…
Recent rapid development of sensor technology has allowed massive fine-grained time series (TS) data to be collected and set the foundation for the development of data-driven services and applications. During the process, data sharing is…
We investigate the relation between static correlation functions in the ground state of local quantum many-body Hamiltonians and the dispersion relations of the corresponding low energy excitations using the formalism of tensor network…
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…
Multivariate time series (MTS) data are becoming increasingly ubiquitous in diverse domains, e.g., IoT systems, health informatics, and 5G networks. To obtain an effective representation of MTS data, it is not only essential to consider…
The multiple-try Metropolis (MTM) algorithm is an extension of the Metropolis-Hastings (MH) algorithm by selecting the proposed state among multiple trials according to some weight function. Although MTM has gained great popularity owing to…
Modeling the joint distribution of high-dimensional data is a central task in unsupervised machine learning. In recent years, many interests have been attracted to developing learning models based on tensor networks, which have the…
This work is devoted to the study Translation-Invariant (TI) Matrix Product State (MPS) representations of quantum states with periodic boundary conditions (PBC). We pursue two directions: we introduce new methods for constructing TI MPS…
We develop and demonstrate a trainable temporal post-processor (TPP) harnessing a simple but versatile machine learning algorithm to provide optimal processing of quantum measurement data subject to arbitrary noise processes, for the…
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…
We compare the efficiency of different matrix product state (MPS) based methods for the calculation of two-time correlation functions in open quantum systems. The methods are the purification approach [1] and two approaches [2,3] based on…
We present a method to apply the well-known matrix product state (MPS) formalism to partially separable states in solid state systems. The computational effort of our method is equal to the effort of the standard density matrix…
Correlation functions of quantum systems -- central objects in quantum field theories -- are defined in high-dimensional space-time domains. Their numerical treatment thus suffers from the curse of dimensionality, which hinders the…
Time-series forecasting has gained significant attention in machine learning due to its crucial role in various domains. However, most existing forecasting models rely heavily on point-wise loss functions like Mean Square Error, which treat…
Tensor network states, especially Matrix Product States (MPS), are crucial tools for studying how particles in large quantum systems are entangled with each other. MPS are particularly effective for modeling systems in one-dimensional…
Accurate and efficient prediction of multicomponent adsorption equilibria across pressures, temperatures, and compositions remain a central challenge for designing energy-efficient adsorption-based separation processes. Traditional…
Gaussian Process state-space models capture complex temporal dependencies in a principled manner by placing a Gaussian Process prior on the transition function. These models have a natural interpretation as discretized stochastic…
We present and test a protocol to learn the matrix-product operator (MPO) representation of an experimentally prepared quantum state. The protocol takes as an input classical shadows corresponding to local randomized measurements, and…
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…