Related papers: On tensor network representations of the (3+1)d to…

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…

Ground-state phase diagram of the toric code model in a parallel magnetic field has three distinct phases: topological, charge-condensed, and vortex-condensed states. To study it we consider an implicit local order parameter characterizing…

We have discussed the tensor-network representation of classical statistical or interacting quantum lattice models, and given a comprehensive introduction to the numerical methods we recently proposed for studying the tensor-network…

We propose a single-layer tensor network framework for the variational determination of ground states in two-dimensional quantum lattice models. By combining the nested tensor network method [Phys. Rev. B 96, 045128 (2017)] with the…

We describe the use of tensor networks to numerically determine wave functions of interacting two-dimensional fermionic models in the continuum limit. We use two different tensor network states: one based on the numerical continuum limit of…

The fields of entanglement theory and tensor networks have recently emerged as central tools for characterising quantum phases of matter. In this article, we determine the entanglement structure of ground states of gapped symmetric quantum…

In many cases, Neural networks can be mapped into tensor networks with an exponentially large bond dimension. Here, we compare different sub-classes of neural network states, with their mapped tensor network counterpart for studying the…

Parallel tensor network contraction algorithms have emerged as the pivotal benchmarks for assessing the classical limits of computation, exemplified by Google's demonstration of quantum supremacy through random circuit sampling. However,…

We introduce a holographic framework for analyzing the steady states of repeated quantum channels with strong symmetries. Using channel-state duality, we show that the steady state of a $d$-dimensional quantum channel is holographically…

Conventional holographic tensor networks can be described as toy holographic maps constructed from many small linear maps acting in a spatially local way, all connected together with ``background entanglement'', i.e. links of a fixed state,…

We introduce a novel tensor network structure augmenting the well-established Tree Tensor Network representation of a quantum many-body wave function. The new structure satisfies the area law in high dimensions remaining efficiently…

This thesis contributes to the understanding of symmetry-enriched topological phases focusing on their descriptions in terms of tensor network states. The Projected Entangled Pair State (PEPS) formalism allows us to locally encode the main…

We present bulk tensor networks that exactly represent the ground states of a continuous family of one-dimensional frustration-free Hamiltonians. These states, which are known as area-deformed Motzkin and Fredkin states, exhibit a novel…

We consider various aspects of Kitaev's toric code model on a plane in the C^*-algebraic approach to quantum spin systems on a lattice. In particular, we show that elementary excitations of the ground state can be described by localized…

Given a microscopic lattice Hamiltonian for a topologically ordered phase, we describe a tensor network approach to characterize its emergent anyon model and, in a chiral phase, also its gapless edge theory. First, a tensor network…

We provide a detailed study of the general structure of two-dimensional topological stabilizer quantum error correcting codes, including subsystem codes. Under the sole assumption of translational invariance, we show that all such codes can…

We apply the recently suggested strategy to lift state spaces and operators for (2+1)-dimensional topological quantum field theories to state spaces and operators for a (3+1)-dimensional TQFT with defects. We start from the…

We investigate topological insulating states in both two and three dimensions with the harmonic potential and strong spin-orbit couplings breaking the inversion symmetry. Landau-level like quantizations appear with the full 2D and 3D…

We devise an all-optical scheme for the generation of entangled multimode photonic states encoded in temporal modes of light. The scheme employs a nonlinear down-conversion process in an optical loop to generate one- and higher-dimensional…

The S-matrix invariant is known to be complete for translation invariant topological stabilizer models in two spatial dimensions, as such models are phase equivalent to some number of copies of toric code. In three dimensions, much less is…