Related papers: Local box-counting dimensions of discrete quantum …

We evaluate the spectral dimension in causal set quantum gravity by simulating random walks on causal sets. In contrast to other approaches to quantum gravity, we find an increasing spectral dimension at small scales. This observation can…

It is a challenge to manage infinite- or high-dimensional data in situations where storage, transmission, or computation resources are constrained. In the simplest scenario when the data consists of a noisy infinite-dimensional signal, we…

Here, using two real non-zero parameters $\lambda$ and $\mu$, we construct Gaussian pseudo-orthogonal ensembles of a large number $N$ of $n \times n$ ($n$ even and large) real pseudo-symmetric matrices under the metric $\eta$ using $…

In this note we explore the chaotic behavior of non-integrable QFTs and compare them to integrable ones. We choose as prototypes the double sine-Gordon and the sine-Gordon models. We analyze their discrete spectrum determined by a…

We review the ideas of how random matrix theory has to be properly applied to quantum physics; particularly we focus on how the spectrum has to be properly prepared and the random matrix correctly identified before the random matrix and the…

In a recent note, Hance and Hossenfelder (arXiv:2211.01331) recall that "locally causal completions of quantum mechanics are possible, if they violate the assumption [called statistical independence or measurement independence] that the…

The distribution of the ratios of consecutive eigenvalue spacings of random matrices has emerged as an important tool to study spectral properties of many-body systems. This article numerically investigates the eigenvalue ratios…

We discuss a number of techniques for determining the Minkowski dimension of bounded subsets of some Euclidean space of any dimension, including: the box-counting dimension and equivalent definitions based on various box-counting functions;…

Given a quantum state in the finite-dimensional Hilbert space $ \C^n $, the range of possible values of a quantum observable is usually identified with the discrete spectrum of eigenvalues of a corresponding Hermitian matrix. Here any such…

This paper describes a simple, causally deterministic model of quantum measurement based on an amplitude threshold detection scheme. Surprisingly, it is found to reproduce many phenomena normally thought to be uniquely quantum in nature. To…

The conjectured three generic local bulk statistics amongst all non-Hermitian random matrix symmetry classes have recently been extended to three generic local edge statistics. We study analytically and numerically complex spacing ratios…

Estimating the quantiles of a large dataset is a fundamental problem in both the streaming algorithms literature and the differential privacy literature. However, all existing private mechanisms for distribution-independent quantile…

We consider statistical tasks in high dimensions whose loss depends on the data only through its projection into a fixed-dimensional subspace spanned by the parameter vectors and certain ground truth vectors. This includes classifying…

The number resolution of solid-state artificial atoms is of fundamental interest for the study of quantum few-body systems, yet remains experimentally challenging. Quantum optical experiments offer a non-invasive approach which links up…

We present a real-space adaptive-coordinate method, which combines the advantages of the finite-difference approach with the accuracy and flexibility of the adaptive coordinate method. The discretized Kohn-Sham equations are written in…

This paper presents a realistic, stochastic, and local model that reproduces nonrelativistic quantum mechanics (QM) results without using its mathematical formulation. The proposed model only uses integer-valued quantities and operations on…

We consider the local statistics of $H = V^* X V + U^* Y U$ where $V$ and $U$ are independent Haar-distributed unitary matrices, and $X$ and $Y$ are deterministic real diagonal matrices. In the bulk, we prove that the gap statistics and…

We investigate the nodal count of eigenvectors of random matrices interpreted as operators on signed complete graphs. Our focus is on orthogonally invariant ensembles, with particular attention to the Gaussian Orthogonal Ensemble (GOE). We…

The authors previously found a model of universal quantum computation by making use of the coset structure of subgroups of a free group $G$ with relations. A valid subgroup $H$ of index $d$ in $G$ leads to a 'magic' state…

We show that the presented real-number quantum theories, compatible with the independent source assumption, require the inclusion of a nonlocal map. This means that if the independent source assumption holds, in these models, complex-number…