Related papers: Fermionic topological quantum states as tensor net…
The spin network simulator model represents a bridge between (generalised) circuit schemes for standard quantum computation and approaches based on notions from Topological Quantum Field Theories (TQFTs). The key tool is provided by the…
In this paper, we propose a novel framework for modeling topological phases of matter using code-based Narain conformal field theories (NCFTs). We show that the algebraic structure of the NCFTs naturally embeds into critical lattice quantum…
We study a tensor network formulation of the two dimensional lattice $\mathcal{N}=1$ Wess-Zumino model with Wilson derivatives for both fermions and bosons. The tensor renormalization group allows us to compute the partition function…
Solving the Schr\"{o}dinger equation for interacting many-body quantum systems faces computational challenges due to exponential scaling with system size. This complexity limits the study of important phenomena in materials science and…
In recent years, a close connection between the description of open quantum systems, the input-output formalism of quantum optics, and continuous matrix product states in quantum field theory has been established. So far, however, this…
The spin network simulator model represents a bridge between (generalized) circuit schemes for standard quantum computation and approaches based on notions from Topological Quantum Field Theories (TQFT). More precisely, when working with…
Classical artificial neural networks have witnessed widespread successes in machine-learning applications. Here, we propose fermion neural networks (FNNs) whose physical properties, such as local density of states or conditional…
We prove the conjectured classification of topological phases in two spatial dimensions with gappable boundary, in a simplified setting. Two gapped ground states of lattice Hamiltonians are in the same quantum phase of matter, or…
In this thesis, we study quantum phase transitions and topological phases in low dimensional fermionic systems. In the first part, we study quantum phase transitions and the nature of currents in one-dimensional systems, using field…
Neural networks have shown to be a powerful tool to represent the ground state of quantum many-body systems, including fermionic systems. However, efficiently integrating lattice symmetries into neural representations remains a significant…
The observation, design and analysis of mesh-like networks in bionics, polymer physics and biological systems has brought forward an extensive catalog of fascinating structures of which a subgroup share a particular, yet critically under…
We present the first examples of topological phases of matter with uniform power for measurement-based quantum computation. This is possible thanks to a new framework for analyzing the computational properties of phases of matter that is…
We present numerical methods to solve the Generalized Hartree-Fock theory for fermionic systems in lattices, both in thermal equilibrium and out of equilibrium. Specifically, we show how to determine the covariance matrix corresponding to…
Quantum computing promises to revolutionize many-body simulations for quantum chemistry, but its potential is constrained by limited qubits and noise in current devices. In this work, we introduce the Lossy Quantum Selected Configuration…
Many quantum condensed-matter systems, and probably the quantum vacuum of our Universe, are strongly correlated and strongly interacting fermionic systems, which cannot be treated perturbatively. However, physics which emerges in the…
In this work, we study the representation space of contextualized embeddings and gain insight into the hidden topology of large language models. We show there exists a network of latent states that summarize linguistic properties of…
Tensor networks have found a wide use in a variety of applications in physics and computer science, recently leading to both theoretical insights as well as practical algorithms in machine learning. In this work we explore the connection…
Recent work by Wu {\em et al.} [arXiv:1910.11011] proposed a numerical method, so-called matrix product operator-matrix product state (MPO-MPS) method, by which several types of quantum many-body wave functions, in particular, the projected…
Spin networks, essentially labeled graphs, are ``good quantum numbers'' for the quantum theory of geometry. These structures encompass a diverse range of techniques which may be used in the quantum mechanics of finite dimensional systems,…
A scheme is proposed to construct integer and fractional topological quantum states of fermions in two spatial dimensions. We devise models for such states by coupling wires of non-chiral Luttinger liquids of electrons, that are arranged in…