arXiv subjects

Nathaniel Selub

Publications and source records attributed to Nathaniel Selub.

6 recordsLinked to original sources

arXiv2026

Local decoders for fault-tolerant quantum computation and translation-invariant stabilizer codes

We construct the first fully spatially local fault-tolerant quantum computer based on topological codes in fewer than four spatial dimensions. Our construction is a two-dimensional architecture that uses only geometrically local quantum and classical operations, bounded-speed classical communication and computation, and a constant density of quantum and classical resources. The core component is a new time-translation-invariant cellular-automaton decoder for the surface code. This decoder preserves logical information for a time stretched-exponential in the code distance and operates continuously during state injection, stabilizer-state preparation, lattice surgery, and transversal readout. We also prove that every translation-invariant topological Pauli stabilizer code is locally decodable under phenomenological noise.

quant-ph↗

arXiv2025

Exploring the Landscape of Non-Equilibrium Memories with Neural Cellular Automata

We investigate the landscape of many-body memories: families of local non-equilibrium dynamics that retain information about their initial conditions for thermodynamically long time scales, even in the presence of arbitrary perturbations. In two dimensions, the only well-studied memory is Toom's rule. Using a combination of rigorous proofs and machine learning methods, we show that the landscape of 2D memories is in fact quite vast. We discover memories that correct errors in ways qualitatively distinct from Toom's rule, have ordered phases stabilized by fluctuations, and preserve information only in the presence of noise. Taken together, our results show that physical systems can perform robust information storage in many distinct ways, and demonstrate that the physics of many-body memories is richer than previously realized. Interactive visualizations of the dynamics studied in this work are available at https://memorynca.github.io/2D.

cond-mat.stat-mech↗

arXiv2023

Dipole-independent measurements of nearly-zero CMB correlation: a possible symmetry of primordial causal quantum coherence

Anisotropy of space-time is measured on the scale of the cosmic horizon, using the angular correlation function $C(\Theta)$ of cosmic microwave background (CMB) temperature at large angular separation $\Theta$. Even-parity correlation $C_{\rm even}(\Theta)$ is introduced to obtain a direct, precise measure of horizon-scale curvature anisotropy independent of the unknown dipole, with uncertainty dominated by models of Galactic emission. In maps from WMAP and Planck, $C_{\rm even}(\Theta)$ at $\Theta\simeq 90^\circ\pm 15^\circ$ is found to be much closer to zero than in previously documented measurements. Variation from zero as small as that in the {\sl Planck} maps is estimated to occur by chance in a fraction $\simeq 10^{-4.3}$ to $\simeq 10^{-2.8}$ of standard realizations. Measurements are found to be consistent with zero correlation in a range of angles expected from quantum fluctuations during inflation whose spacelike coherence is bounded by inflationary horizons around every location at every epoch. This scale-invariant symmetry of cosmological initial conditions is incompatible with the standard quantum theory of initial conditions, but is broadly consistent with other cosmological measurements, and is subject to further tests.

astro-ph.CO↗

arXiv2023

Angular spectrum of quantum fluctuations in causal structure

Scaling arguments are used to constrain the angular spectrum of distortions on boundaries of macroscopic causal diamonds, produced by Planck-scale vacuum fluctuations of causally-coherent quantum gravity. The small-angle spectrum of displacement is derived from a form of scale invariance: the variance and fluctuation rate of distortions normal to the surface of a causal diamond of radius $R$ at transverse physical separation $c\tau\ll R$ should depend only on $\tau$, with a normalization set by the Planck time $t_P$, and should not depend on $R$. For measurements on scale $R$, the principle leads to universal scaling for variance on angular scale $\Theta$, $\langle\delta\tau^2\rangle_\Theta\simeq\tau\:\!t_p\sim\Theta R\:\!t_P/c$, and angular power spectrum $C_\ell\sim (R\:\!l_P)/\ell^3$ at $\ell\gg1$. This spectrum is consistent with a relational model of holographic noise based on causally coherent virtual null gravitational shocks, a general picture conjectured for all $\ell$. The high $\ell$ scaling is contrasted with that predicted in some other quantum models, which differ by one power of angular wavenumber $\ell$ and are shown to predict excessive blurring of images from distant sources.

gr-qc↗

arXiv2023

Angular correlations on causally-coherent inflationary horizons

We develop a model for correlations of cosmic microwave background anisotropy on the largest angular scales, based on standard causal geometrical relationships in slow-roll inflation. Unlike standard models based on quantized field modes, it describes perturbations with nonlocal directional coherence on spherical boundaries of causal diamonds. Causal constraints reduce the number of independent degrees of freedom, impose new angular symmetries, and eliminate cosmic variance for purely angular 2-point correlations. Distortions of causal structure from vacuum fluctuations are modeled as gravitational memory from randomly oriented outgoing and incoming gravitational null shocks, with nonlocally coherent directional displacements on curved surfaces of causal diamonds formed by standard inflationary horizons. The angular distribution is determined by axially symmetric shock displacements on circular intersections of the comoving sphere that represents the CMB photosphere with other inflationary horizons. Displacements on thin spheres at the end of inflation have a unique angular power spectrum $C_\ell$ that approximates the standard expectation on small angular scales, but differs substantially at large angular scales due to horizon curvature. For a thin sphere, the model predicts a universal angular correlation function $C(\Theta)$ with an exact ``causal shadow'' symmetry, $C(\pi/4<\Theta<3\pi/4)= 0$, and significant large-angle parity violation. We apply a rank statistic to compare models with WMAP and Planck satellite data, and find that a causally-coherent model with no shape parameters or cosmic variance agrees with the measured $C(\Theta)$ better than a large fraction ($> 0.9999$) of standard model realizations. Model-independent tests of holographic causal symmetries are proposed.

gr-qc↗

arXiv2021

Anomalies of Cosmic Anisotropy from Holographic Universality of Great-Circle Variance

We examine all-sky cosmic microwave background (CMB) temperature maps on large angular scales to compare their consistency with two scenarios: the standard inflationary quantum picture, and a distribution constrained to have a universal variance of primordial curvature perturbations on great circles. The latter symmetry is not a property of standard quantum inflation, but may be a symmetry of holographic models with causal quantum coherence on null surfaces. Since the variation of great-circle variance is dominated by the largest angular scale modes, in the latter case the amplitude and direction of the unobserved intrinsic dipole (that is, the $\ell=1$ harmonics) can be estimated from measured $\ell = 2, 3$ harmonics by minimizing the variance of great-circle variances including only $\ell =1, 2, 3$ modes. It is found that including the estimated intrinsic dipole leads to a nearly-null angular correlation function over a wide range of angles, in agreement with a null anti-hemispherical symmetry independently motivated by holographic causal arguments, but highly anomalous in standard cosmology. Simulations are used here to show that simultaneously imposing the constraints of universal great-circle variance and the vanishing of the angular correlation function over a wide range of angles tends to require patterns that are unusual in the standard picture, such as anomalously high sectorality of the $\ell = 3$ components, and a close alignment of principal axes of $\ell=2$ and $\ell = 3$ components, that have been previously noted on the actual sky. The precision of these results appears to be primarily limited by errors introduced by models of Galactic foregrounds.

astro-ph.CO↗