Related papers: Continuum tensor network field states, path integr…

Tensors with finite correlation afford very compact tensor network representations. A novel tensor network-based decomposition of real-time path integral simulations involving Feynman-Vernon influence functional is introduced. In this…

An extension of the projected entangled-pair states (PEPS) algorithm to infinite systems, known as the iPEPS algorithm, was recently proposed to compute the ground state of quantum systems on an infinite two-dimensional lattice. Here we…

Isometric tensor product states (isoTPS) generalize the isometric form of the one-dimensional matrix product states (MPS) to tensor networks in two and higher dimensions. Here, we introduce an alternative isometric form for isoTPS by…

Quantum physics, despite its observables being intrinsically of a probabilistic nature, does not have a quantum entropy assigned to them. We propose a quantum entropy that quantify the randomness of a pure quantum state via a conjugate pair…

In this thesis we extend the formalism of tensor network algorithms to incorporate global internal symmetries. We describe how to both numerically protect the symmetry and exploit it for computational gain in tensor network simulations. Our…

We characterize the conditions under which a translationally invariant matrix product state (MPS) is invariant under local transformations. This allows us to relate the symmetry group of a given state to the symmetry group of a simple…

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…

We consider (2+1)-dimensional topological quantum states which possess edge states described by a chiral (1+1)-dimensional Conformal Field Theory (CFT), such as e.g. a general quantum Hall state. We demonstrate that for such states the…

We describe a class of spin chains with new physical and computational properties. On the physical side, the spin chains give examples of symmetry-protected topological phases that are defined by non-onsite symmetries, i.e. symmetries that…

We introduce the concept of embedding quantum simulators, a paradigm allowing the efficient quantum computation of a class of bipartite and multipartite entanglement monotones. It consists in the suitable encoding of a simulated quantum…

Symmetric quantum states are fascinating objects. They correspond to multipartite systems that remain invariant under particle permutations. This symmetry is reflected in their compact mathematical characterisation but also in their unique…

Approaching the long-time dynamics of non-Markovian open quantum systems presents a challenging task if the bath is strongly coupled. Recent proposals address this problem through a representation of the so-called process tensor in terms of…

We introduce configuration space path integrals for quantum fields interacting with classical fields. We show that this can be done consistently by proving that the dynamics are completely positive directly, without resorting to master…

Modern approaches to generative modeling of continuous data using tensor networks incorporate compression layers to capture the most meaningful features of high-dimensional inputs. These methods, however, rely on traditional Matrix Product…

The experimental realisation of large scale many-body systems has seen immense progress in recent years, rendering full tomography tools for state identification inefficient, especially for continuous systems. In order to work with these…

We propose an efficient numerical method, which combines the advantages of recently developed tensor-network based methods and standard trial wave functions, to study the ground state properties of quantum many-body systems. In this…

We consider the problem of quantum behavior in the finite background. Introduction of continuum or other infinities into physics leads only to technical complications without any need for them in description of empirical observations. The…

The quantum $5$-state Potts model is known to possess a perturbative description using complex conformal field theory (CCFT), the analytic continuation of ``theory space" to a complex plane. To study the corresponding complex fixed point on…

The quantum mechanics formalism introduced new revolutionary concepts challenging our everyday perceptions. Arguably, quantum entanglement, which explains correlations that cannot be reproduced classically, is the most notable of them.…

We demonstrate that projected entangled-pair states (PEPS) are able to represent ground states of critical, fermionic systems exhibiting both 1d and 0d Fermi surfaces on a 2D lattice with an efficient scaling of the bond dimension.…