Related papers: The integer quantum Hall transition: an $S$-matrix…
Many classical randomized algorithms (e.g., approximation algorithms for #P-complete problems) utilize the following random walk algorithm for {\em almost uniform sampling} from a state space $S$ of cardinality $N$: run a symmetric ergodic…
Learning representations of nodes in a low dimensional space is a crucial task with many interesting applications in network analysis, including link prediction and node classification. Two popular approaches for this problem include matrix…
We consider the problem of selecting important nodes in a random network, where the nodes connect to each other randomly with certain transition probabilities. The node importance is characterized by the stationary probabilities of the…
We study the tunneling between two quantum Hall systems, along a quasi one-dimensional interface. A detailed analysis relates microscopic parameters, characterizing the potential barrier, with the effective field theory model for the…
We consider the localization of independent electron orbitals in double-layer two-dimensional electron systems in the strong magnetic field limit. Our study is based on numerical Thouless number calculations for realistic microscopic models…
The Iterative Quasi-Monte Carlo (iQMC) method is a recently developed hybrid method for neutron transport simulations. iQMC replaces standard quadrature techniques used in deterministic linear solvers with Quasi-Monte Carlo simulation for…
We propose a natural quantization of a standard neural network, where the neurons correspond to qubits and the activation functions are implemented via quantum gates and measurements. The simplest quantized neural network corresponds to…
We propose a modification to Nielsen's circuit complexity for Hamiltonian simulation using the Suzuki-Trotter (ST) method, which provides a network like structure for the quantum circuit. This leads to an optimized gate counting linear in…
Advances in recent years have made it possible to explore quantum dots as a viable technology for scalable quantum information processing. Charge qubits for example can be realized in the lowest bound states of coupled quantum dots and the…
We consider network models for localisation problems belonging to symmetry class C. This symmetry class arises in a description of the dynamics of quasiparticles for disordered spin-singlet superconductors which have a Bogoliubov - de…
This article is an introductory review of random matrix theory (RMT) and its applications, with special focus on quantum chaos. Random matrices were first used by Wigner to understand the spectra of complex nuclei from a statistical…
The standard approach to realize a quantum repeater relies upon probabilistic but heralded entangled state manipulations and the storage of quantum states while waiting for successful events. In the literature on this class of repeaters,…
The certification of randomness is essential for both fundamental science and information technologies. Unlike traditional random number generators, randomness obtained from nonlocal correlations is fundamentally guaranteed to be…
The Hall conductance $\sigma_{xy}$ of two-dimensional {\it lattice} electrons with random potential is investigated. The change of $\sigma_{xy}$ due to randomness is focused on. It is a quantum phase transition where the {\it sum rule} of…
A new universality class distinct from the standard Wigner-Dyson ones is identified. This class is realized by putting a metallic quantum dot in contact with a superconductor, while applying a magnetic field so as to make the pairing field…
Network centrality has important implications well beyond its role in physical and information transport analysis; as such, various quantum walk-based algorithms have been proposed for measuring network vertex centrality. In this work, we…
In this work, we propose novel families of positional encodings tailored to graph neural networks obtained with quantum computers. These encodings leverage the long-range correlations inherent in quantum systems that arise from mapping the…
A two dimensional disordered system of non-interacting fermions in a homogeneous magnetic field is investigated numerically. By introducing a new magnetic gauge, we explore the renormalization group (RG) flow of the longitudinal and Hall…
The duration of bidirectional transfer protocols in 1D topological models usually scales exponentially with distance. In this work, we propose transfer protocols in multidomain SSH chains and Creutz ladders that lose the exponential…
With the rapid progress in quantum hardware and software, the need for verification of quantum systems becomes increasingly crucial. While model checking is a dominant and very successful technique for verifying classical systems, its…