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The large deviation (LD) statistics of dynamical observables is encoded in the spectral properties of deformed Markov generators. Recent works have shown that tensor network methods are well suited to compute the relevant leading…
The generalization of matrix product states (MPS) to continuous systems, as proposed in the breakthrough paper [F. Verstraete, J.I. Cirac, Phys. Rev. Lett. 104, 190405(2010)], provides a powerful variational ansatz for the ground state of…
This paper examines the use of tensor networks, which can efficiently represent high-dimensional quantum states, in language modeling. It is a distillation and continuation of the work done in (van der Poel, 2023). To do so, we will…
Towards the efficient simulation of near-term quantum devices using tensor network states, we introduce an improved real-space parallelizable matrix-product state (MPS) compression method. This method enables efficient compression of all…
Simulation of quantum systems is challenging due to the exponential size of the state space. Tensor networks provide a systematically improvable approximation for quantum states. 2D tensor networks such as Projected Entangled Pair States…
Tensor networks (TNs) are one of the best available tools to study many-body quantum systems. TNs are particularly suitable for one-dimensional local Hamiltonians, while their performance for generic geometries is mainly limited by two…
We investigate ensembles of Matrix Product States (MPSs) generated by quantum circuit evolution followed by projection onto MPSs with a fixed bond dimension $\chi$. Specifically, we consider ensembles produced by: (i) random sequential…
Over the last decade tensor network states (TNS) have emerged as a powerful tool for the study of quantum many body systems. The matrix product states (MPS) are one particular class of TNS and are used for the simulation of…
Mean-field models are a popular tool in a variety of fields. They provide an understanding of the impact of interactions among a large number of particles or people or other "self-interested agents", and are an increasingly popular tool in…
We investigate the relation between the scaling of block entropies and the efficient simulability by Matrix Product States (MPS), and clarify the connection both for von Neumann and Renyi entropies (see Table I). Most notably, even states…
We study a matrix product state (MPS) algorithm to approximate excited states of translationally invariant quantum spin systems with periodic boundary conditions. By means of a momentum eigenstate ansatz generalizing the one of \"Ostlund…
Matrix Product State (MPS) is a versatile tensor network representation widely applied in quantum physics, quantum chemistry, and machine learning, etc. MPS sampling serves as a critical fundamental operation in these fields. As the…
We investigate quantum random tensor network states where the bond dimensions scale polynomially with the system size, $N$. Specifically, we examine the delocalization properties of random Matrix Product States (RMPS) in the computational…
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…
This paper introduces a Heisenberg picture approach to Matrix Product States (MPS), offering a rigorous yet intuitive framework to explore their structure and classification. MPS efficiently represent ground states of quantum many-body…
Multipartite entanglement offers a powerful framework for understanding the complex collective phenomena in quantum many-body systems that are often beyond the description of conventional bipartite entanglement measures. Here, we propose a…
We study finite state random dynamical systems (RDS) and their induced Markov chains (MC) as stochastic models for complex dynamics. The linear representation of deterministic maps in RDS are matrix-valued random variables whose…
Preparing long-range entangled states poses significant challenges for near-term quantum devices. It is known that measurement and feedback (MF) can aid this task by allowing the preparation of certain paradigmatic long-range entangled…
Efficient methods to access the entanglement of a quantum many-body state, where the complexity generally scales exponentially with the system size $N$, have long a concern. Here we propose the Schmidt tensor network state (Schmidt TNS)…
Because failures in distribution systems caused by extreme weather events directly result in consumers' outages, this paper proposes a state-based decision-making model with the objective of mitigating loss of load to improve the…