The suitability of tensor network ansatzes for the description of physically relevant states in one dimensional lattice gauge theories (LGT) has been demonstrated in the last years by a large amount of systematic studies, including abelian and non-abelian LGTs, and including scenarios where traditional Monte Carlo approaches fail due to a sign problem. While this establishes a solid motivation...

Quantum Cellular Automata are unitary maps that preserve locality and respect causality. I will show that in one spatial dimension they correspond to matrix product unitary operators, and that one can classify them in the presence of symmetries, giving rise to phenomenon analogous to symmetry protection. I will then show that in higher dimensions, they correspond to other tensor networks that...

We examine holographic complexity in the doubly holographic model to study quantum extremal islands. We focus on the holographic complexity=volume (CV) proposal for boundary subregions in the island phase. Exploiting the Fefferman-Graham expansion of the metric and other geometric quantities near the brane, we derive the leading contributions to the complexity and interpret these in terms of...

In contrast to the 4D case, there are well understood theories of quantum gravity for the 3D case. Indeed, 3D general relativity constitutes a topological field theory (of BF or equivalently Chern-Simons type) and can be quantized as such. The resulting quantum theory of gravity offers many interesting lessons for the 4D case.

In this talk I will discuss the quantum theory which...

"Besides tensor networks, quantum computations (QC) as well use a Hamiltonian formulation to solve physical problems. Although QC are presently very limited, since only small number of qubits are available, they have the principal advantage that they straightforwardly scale to higher dimensions. A standard tool in the QC approach are Variational Quantum Simulations (VQS) which form a class of...

In this talk, we report on our studies of the Thirring model using MPS techniques. The Thirring model is a quantum field theory describing self-interactions of the Dirac field in 1+1 dimensions. It evinces a non-trivial zero-temperature phase structure in the mass-interaction plane, with gapless (critical) and gapped (massive) phases separated by a Berezinskii-Kosterlitz-Thousless-type...

In this talk I will speak about the meeting point of two models that have raised interest in the community in the last years. From one side, we looked at measurement-based quantum computing (MBQC), which is an alternative to circuit-based quantum computing. Instead of modifying a state via gates, MBQC achieves the same result by measuring auxiliary qubits in a graph. From the other side, we...

We explain how periodic uniform matrix product states (puMPS) can be used to extract universal data of critical quantum spin chains. We show that puMPS and puMPS Bloch states accurately capture the ground state and low-energy excited states of critical quantum spin chains up to several hundreds of spins. This enables us to extract (i) scaling dimensions, conformal spins of scaling operators,...

In this talk we will start with a review of path-integraloptimization, which provides a useful description of non-unitary tensor networks for Euclidean path-integrals in CFTs. We will explain an emergence of AdS geometry in this method and an interpretation as a computational complexity. Next we will give its application to analytical calculations of entanglement of purification, which was...

We present some recent results on the development of efficient unconstrained tree tensor networks algorithms and their application to high-dimensional many-body quantum systems. In particular, we present our results on topological two-dimensional systems, two-dimensional Rydberg atom systems, and two- and three-dimensional lattice gauge theories in presence of fermonic matter. Finally, we...

The use of wavelet-based constructions has led to significant progress in the analytic understanding of holographic tensor networks, such as the multi-scale entanglement renormalization ansatz (MERA). In this talk I will give an overview of the (past and more recently established) connections between wavelets and MERA, and the discuss the important results that have followed. I will also...