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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…
Tensor networks states allow to find the low energy states of local lattice Hamiltonians through variational optimization. Recently, a construction of such states in the continuum was put forward, providing a first step towards the goal of…
The determination of genuine entanglement is a central problem in quantum information processing. We investigate the tripartite state as the tensor product of two bipartite entangled states by merging two systems. We show that the…
Matrix-product states and their continuous analogues are variational classes of states that capture quantum many-body systems or quantum fields with low entanglement; they are at the basis of the density-matrix renormalization group method…
Tensor network states form a variational ansatz class widely used, both analytically and numerically, in the study of quantum many-body systems. It is known that if the underlying graph contains a cycle, e.g. as in projected entangled pair…
Quantum mechanics of composite systems, gives rise to certain special states called entangled states. A physical system, that is in an entangled state displays an intricate correlation between its subsystems. There are also some composite…
Tensor networks establish an adaptable framework for the emulation of quantum circuits. By partitioning exponentially large registers and gates into smaller tensors, this unlocks fast transformations through tensor algebra, and grants fine…
The rank of a tensor is analyzed in context of quantum entanglement. A pure quantum state $\bf v$ of a composite system consisting of $d$ subsystems with $n$ levels each is viewed as a vector in the $d$-fold tensor product of…
We study Projected Entangled Pair States (PEPS) with continuous virtual symmetries, i.e., symmetries in the virtual degrees of freedom, through an elementary class of models with SU(2) symmetry. Discrete symmetries of that kind have…
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…
Thermal pure state algorithms, which employ pure quantum states representing thermal equilibrium states instead of statistical ensembles, are useful both for numerical simulations and for theoretical analysis of thermal states. However,…
We present experimentally and numerically accessible quantities that can be used to differentiate among various families of random entangled states. To this end, we analyze the entanglement properties of bipartite reduced states of a…
Symmetry-resolved entanglement is a useful tool for characterizing symmetry-protected topological states. In two dimensions, their entanglement spectra are described by conformal field theories but the symmetry resolution is largely…
Tensor networks are a powerful modeling framework developed for computational many-body physics, which have only recently been applied within machine learning. In this work we utilize a uniform matrix product state (u-MPS) model for…
We discuss the data-pattern tomography for reconstruction of entangled states of light. We show that for a moderate number of probe coherent states it is possible to achieve high accuracy of representation not only for single-mode states…
Determining the relationship between composite systems and their subsystems is a fundamental problem in quantum physics. In this paper we consider the spectra of a bipartite quantum state and its two marginal states. To each spectrum we can…
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…
The $\star_M$-family of tensor-tensor products is a framework which generalizes many properties from linear algebra to third order tensors. Here, we investigate positive semidefiniteness and semidefinite programming under the…
We construct parametrized isometric tensor network states -- referred to as skeletons -- that allow us to explore phases of abelian topological order and can be efficiently implemented on quantum processors. We obtain stable finite…
Identifying variational wave functions that efficiently parametrize the physically relevant states in the exponentially large Hilbert space is one of the key tasks towards solving the quantum many-body problem. Powerful tools in this…