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The interferometric power of a bipartite quantum state quantifies the precision, measured by quantum Fisher information, that such a state enables for the estimation of a parameter embedded in a unitary dynamics applied to one subsystem…
Infinite projected entangled pair states (iPEPS) have emerged as a powerful tool for studying interacting two-dimensional fermionic systems. In this review, we discuss the iPEPS construction and some basic properties of this tensor network…
Tensor networks offer a variational formalism to efficiently represent wave-functions of extended quantum many-body systems on a lattice. In a tensor network N, the dimension \chi of the bond indices that connect its tensors controls the…
We present a new class of tensor network states that are specifically designed to capture the electron correlation of a molecule of arbitrary structure. In this ansatz, the electronic wave function is represented by a Complete-Graph Tensor…
The study of topological band insulators has revealed fascinating phases characterized by band topology indices and anomalous boundary modes protected by global symmetries. In strongly correlated systems, where the traditional notion of…
The quantum efficiency in the transfer of an initial excitation in disordered finite networks, modeled by the $k$-body embedded Gaussian ensembles of random matrices, is studied for bosons and fermions. The influence of the presence or…
We present a new variational method for investigating the ground state and out of equilibrium dynamics of quantum many-body bosonic and fermionic systems. Our approach is based on constructing variational wavefunctions which extend Gaussian…
In this paper the entanglement of multi-qubit fermionic pseudo Hermitian coherent states (FPHCS) described by anticommutative Grassmann numbers is studied. The pseudo-Hermitian versions of the well known maximally entangled pure states such…
We use complex network theory to study a class of continuous-variable quantum states that present both multipartite entanglement and non-Gaussian statistics. We consider the intermediate scale of several dozens of components at which such…
Tensor networks are an efficient platform to represent interesting quantum states of matter as well as to compute physical observables and information-theoretic quantities. We present a general protocol to construct fixed-point tensor…
Trial wavefunctions that can be represented by summing over locally-coupled degrees of freedom are called tensor network states (TNSs); they have seemed difficult to construct for two-dimensional topological phases that possess protected…
Multimode Gaussian states are a versatile resource for quantum information technologies and have been realized across a wide range of physical platforms. Recent progress in the large-scale generation of such states provides a key ingredient…
Schr\"odinger equation belongs to the most fundamental differential equations in quantum physics. However, the exact solutions are extremely rare, and many analytical methods are applicable only to the cases with small perturbations or weak…
We investigate the low-energy physics of non-Hermitian quantum spin models with $PT$-symmetry. To this end we consider the one-dimensional Ising chain and the two-dimensional toric code in a non-Hermitian staggered field. For both systems…
We define two dual tensor network representations of the (3+1)d toric code ground state subspace. These two representations, which are obtained by initially imposing either family of stabilizer constraints, are characterized by different…
It was recently proposed to leverage the representational power of artificial neural networks, in particular Restricted Boltzmann Machines, in order to model complex quantum states of many-body systems [Science, 355(6325), 2017]. States…
We introduce the concept of concatenated tensor networks to efficiently describe quantum states. We show that the corresponding concatenated tensor network states can efficiently describe time evolution and possess arbitrary block-wise…
We show how to achieve perfect quantum state transfer and construct effective two-qubit gates between distant sites in engineered bosonic and fermionic networks. The Hamiltonian for the system can be determined by choosing an eigenvalue…
The entanglement negativity is a versatile measure of entanglement that has numerous applications in quantum information and in condensed matter theory. It can not only efficiently be computed in the Hilbert space dimension, but for…
This thesis develops advanced Tensor Network (TN) methods to address Hamiltonian Lattice Gauge Theories (LGTs), overcoming limitations in real-time dynamics and finite-density regimes. A novel dressed-site formalism is introduced, enabling…