相关论文: Anticoncentration and state design of random tenso…

We explore a class of random tensor network models with "stabilizer" local tensors which we name Random Stabilizer Tensor Networks (RSTNs). For RSTNs defined on a two-dimensional square lattice, we perform extensive numerical studies of…

Quantum machine learning (QML) is a rapidly expanding field that merges the principles of quantum computing with the techniques of machine learning. One of the powerful mathematical frameworks in this domain is tensor networks. These…

Tensor network states are an indispensable tool for the simulation of strongly correlated quantum many-body systems. In recent years, tree tensor network states (TTNS) have been successfully used for two-dimensional systems and to benchmark…

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…

Random tensor networks provide useful models that incorporate various important features of holographic duality. A tensor network is usually defined for a fixed graph geometry specified by the connection of tensors. In this paper, we…

Classical simulation of a programmable quantum processor is crucial in identifying the threshold of a quantum advantage. We demonstrate the simple update of projected entangled-pair states (PEPSs) in the Vidal gauge that represent random…

This paper presents a generalization of the random dot product model for networks whose edge weights are drawn from a parametrized probability distribution. We focus on the case of integer weight edges and show that many previously studied…

We discuss how to analytically obtain an -- essentially infinite -- Matrix Product State (MPS) representation of the ground state of the XY model. On the one hand this allows to illustrate how the Ornstein-Zernike form of the correlation…

Tensor network methods have proved to be highly effective in addressing a wide variety of physical scenarios, including those lacking an intrinsic one-dimensional geometry. In such contexts, it is possible for the problem to exhibit a weak…

Real-space renormalization approaches for quantum lattice systems generate certain hierarchical classes of states that are subsumed by the multi-scale entanglement renormalization ansatz (MERA). It is shown that, with the exception of one…

Projected Entangled Pair States (PEPS) provide a framework for the construction of models where a single tensor gives rise to both Hamiltonian and ground state wavefunction on the same footing. A key problem is to characterize the behavior…

The reconstruction of quantum states from experimental measurements, often achieved using quantum state tomography (QST), is crucial for the verification and benchmarking of quantum devices. However, performing QST for a generic…

We establish a direct connection between general tensor networks and deep feed-forward artificial neural networks. The core of our results is the construction of neural-network layers that efficiently perform tensor contractions, and that…

We introduce a novel breakthrough approach to evaluate the nonstabilizerness of an $N$-qubits Matrix Product State (MPS) with bond dimension $\chi$. In particular, we consider the recently introduced Stabilizer R\'enyi Entropies (SREs). We…

We study the statistical and dynamic properties of the systems characterized by an ultrametric space of states and translationary non-invariant symmetric transition matrices of the Parisi type subjected to "locally constant" randomization.…

We investigate quantum-inspired tensor networks (QTNs) for approximating flow maps of hydrodynamic partial differential equations (PDEs). Motivated by the effective low-rank structure that emerges after tensorization of discretized…

A generalization of matrix product states (MPS) is introduced which is suitable for describing interacting quantum systems in two and three dimensions. These scale-renormalized matrix-product states (SR-MPS) are based on a course-graining…

We present an improved version of the algorithm contracting and optimizing finite projected entangled pair states (fPEPS) in conjunction with projected entangled pair operators (PEPOs). Our work has two components to it. First, we explain…

Strongly correlated layered 2D systems are of central importance in condensed matter physics, but their numerical study is very challenging. Motivated by the enormous successes of tensor networks for 1D and 2D systems, we develop an…

We quantify the representational power of matrix product states (MPS) for entangled qubit systems by giving polynomial expressions in a pure quantum state's amplitudes which hold if and only if the state is a translation invariant matrix…