arXiv subjects

Aaron Smith

Publications and source records attributed to Aaron Smith.

At least 127 records · Page 7Linked to original sources

arXiv2022

Universal logic with encoded spin qubits in silicon

Qubits encoded in a decoherence-free subsystem and realized in exchange-coupled silicon quantum dots are promising candidates for fault-tolerant quantum computing. Benefits of this approach include excellent coherence, low control crosstalk, and configurable insensitivity to certain error sources. Key difficulties are that encoded entangling gates require a large number of control pulses and high-yielding quantum dot arrays. Here we show a device made using the single-layer etch-defined gate electrode architecture that achieves both the required functional yield needed for full control and the coherence necessary for thousands of calibrated exchange pulses to be applied. We measure an average two-qubit Clifford fidelity of $97.1 \pm 0.2\%$ with randomized benchmarking. We also use interleaved randomized benchmarking to demonstrate the controlled-NOT gate with $96.3 \pm 0.7\%$ fidelity, SWAP with $99.3 \pm 0.5\%$ fidelity, and a specialized entangling gate that limits spreading of leakage with $93.8 \pm 0.7\%$ fidelity.

quant-ph↗

arXiv2022

Rapid Convergence of Informed Importance Tempering

Informed Markov chain Monte Carlo (MCMC) methods have been proposed as scalable solutions to Bayesian posterior computation on high-dimensional discrete state spaces, but theoretical results about their convergence behavior in general settings are lacking. In this article, we propose a class of MCMC schemes called informed importance tempering (IIT), which combine importance sampling and informed local proposals, and derive generally applicable spectral gap bounds for IIT estimators. Our theory shows that IIT samplers have remarkable scalability when the target posterior distribution concentrates on a small set. Further, both our theory and numerical experiments demonstrate that the informed proposal should be chosen with caution: the performance of some proposals may be very sensitive to the shape of the target distribution. We find that the "square-root proposal weighting" scheme tends to perform well in most settings.

stat.CO↗

arXiv2022

The THESAN project: properties of the intergalactic medium and its connection to Reionization-era galaxies

The high-redshift intergalactic medium (IGM) and the primeval galaxy population are rapidly becoming the new frontier of extra-galactic astronomy. We investigate the IGM properties and their connection to galaxies at $z\geq5.5$ under different assumptions for the ionizing photon escape and the nature of dark matter, employing our novel THESAN radiation-hydrodynamical simulation suite, designed to provide a comprehensive picture of the emergence of galaxies in a full reionization context. Our simulations have realistic `late' reionization histories, match available constraints on global IGM properties and reproduce the recently-observed rapid evolution of the mean free path of ionizing photons. We additionally examine high-z Lyman-$α$ transmission. The optical depth evolution is consistent with data, and its distribution suggests an even-later reionization than simulated, although with a strong sensitivity to the source model. We show that the effects of these two unknowns can be disentangled by characterising the spectral shape and separation of Lyman-$α$ transmission regions, opening up the possibility to observationally constrain both. For the first time in simulations, THESAN reproduces the modulation of the Lyman-$α$ flux as a function of galaxy distance, demonstrating the power of coupling a realistic galaxy formation model with proper radiation-hydrodynamics. We find this feature to be extremely sensitive on the timing of reionization, while being relatively insensitive to the source model. Overall, THESAN produces a realistic IGM and galaxy population, providing a robust framework for future analysis of the high-z Universe.

astro-ph.CO↗

arXiv2022

Reconstruction of Line-Embeddings of Graphons

Consider a random graph process with $n$ vertices corresponding to points $v_{i} \sim {Unif}[0,1]$ embedded randomly in the interval, and where edges are inserted between $v_{i}, v_{j}$ independently with probability given by the graphon $w(v_{i},v_{j}) \in [0,1]$. Following Chuangpishit et al. (2015), we call a graphon $w$ diagonally increasing if, for each $x$, $w(x,y)$ decreases as $y$ moves away from $x$. We call a permutation $σ\in S_{n}$ an ordering of these vertices if $v_{σ(i)} < v_{σ(j)}$ for all $i < j$, and ask: how can we accurately estimate $σ$ from an observed graph? We present a randomized algorithm with output $\hatσ$ that, for a large class of graphons, achieves error $\max_{1 \leq i \leq n} | σ(i) - \hatσ(i)| = O^{*}(\sqrt{n})$ with high probability; we also show that this is the best-possible convergence rate for a large class of algorithms and proof strategies. Under an additional assumption that is satisfied by some popular graphon models, we break this "barrier" at $\sqrt{n}$ and obtain the vastly better rate $O^{*}(n^ε)$ for any $ε> 0$. These improved seriation bounds can be combined with previous work to give more efficient and accurate algorithms for related tasks, including: estimating diagonally increasing graphons, and testing whether a graphon is diagonally increasing.

math.PR↗

arXiv2021

Consistency of Spectral Seriation

Consider a random graph $G$ of size $N$ constructed according to a \textit{graphon} $w \, : \, [0,1]^{2} \mapsto [0,1]$ as follows. First embed $N$ vertices $V = \{v_1, v_2, \ldots, v_N\}$ into the interval $[0,1]$, then for each $i < j$ add an edge between $v_{i}, v_{j}$ with probability $w(v_{i}, v_{j})$. Given only the adjacency matrix of the graph, we might expect to be able to approximately reconstruct the permutation $σ$ for which $v_{σ(1)} < \ldots < v_{σ(N)}$ if $w$ satisfies the following \textit{linear embedding} property introduced in [Janssen 2019]: for each $x$, $w(x,y)$ decreases as $y$ moves away from $x$. For a large and non-parametric family of graphons, we show that (i) the popular spectral seriation algorithm [Atkins 1998] provides a consistent estimator $\hatσ$ of $σ$, and (ii) a small amount of post-processing results in an estimate $\tildeσ$ that converges to $σ$ at a nearly-optimal rate, both as $N \rightarrow \infty$.

math.ST↗

arXiv2021

Real and counterfeit cores: how feedback expands halos and disrupts tracers of inner gravitational potential in dwarf galaxies

The tension between the diverging density profiles in Lambda Cold Dark Matter ($Λ$CDM) simulations and the constant-density inner regions of observed galaxies is a long-standing challenge known as the `core-cusp' problem. We demonstrate that the \texttt{SMUGGLE} galaxy formation model implemented in the \textsc{Arepo} moving mesh code forms constant-density cores in idealized dwarf galaxies of $M_\star \approx 8 \times 10^7$ M$_{\odot}$ with initially cuspy dark matter halos of $M_{200} \approx 10^{10}$ M$_{\odot}$. Identical initial conditions run with the Springel and Hernquist (2003; SH03) feedback model preserve cuspiness. Literature on the subject has pointed to the low density threshold for star formation, $ρ_\text{th}$, in SH03-like models as an obstacle to baryon-induced core formation. Using a \texttt{SMUGGLE} run with equal $ρ_\text{th}$ to SH03, we demonstrate that core formation can proceed at low density thresholds, indicating that $ρ_\text{th}$ is insufficient on its own to determine whether a galaxy develops a core. We suggest that the ability to resolve a multiphase interstellar medium at sufficiently high densities is a more reliable indicator of core formation than any individual model parameter. In \texttt{SMUGGLE}, core formation is accompanied by large degrees of non-circular motion, with gas rotational velocity profiles that consistently fall below the circular velocity $v_\text{circ} = \sqrt{GM/R}$ out to $\sim 2$ kpc. This may artificially mimic larger core sizes when derived from observable quantities compared to the size measured from the dark matter distribution ($\sim 0.5$ kpc), highlighting the need for careful modeling in the inner regions of dwarfs to infer the true distribution of dark matter.

astro-ph.GA↗

arXiv2021

Generation of optical potentials for ultracold atoms using a superluminescent diode

We report on the realization and characterisation of optical potentials for ultracold atoms using a superluminescent diode. The light emitted by this class of diodes is characterised by high spatial coherence but low temporal coherence. On the one hand, this implies that it follows Gaussian propagation similar to lasers, allowing for high intensities and well-collimated beams. On the other, it significantly reduces those interference effects that lead to severe distortions in imaging. By using a high-resolution optical setup, we produce patterned optical potentials with a digital micromirror device and demonstrate that the quality of the patterns produced by our superluminescent diode is consistently and substantially higher than those produced by our laser. We show that the resulting optical potentials can be used to arrange the atoms in arbitrary structures and manipulate them dynamically. Our results can open new opportunities in the fields of quantum simulations and atomtronics.

cond-mat.quant-gas↗

arXiv2020

Arepo-MCRT: Monte Carlo Radiation Hydrodynamics on a Moving Mesh

We present Arepo-MCRT, a novel Monte Carlo radiative transfer (MCRT) radiation-hydrodynamics (RHD) solver for the unstructured moving-mesh code Arepo. Our method is designed for general multiple scattering problems in both optically thin and thick conditions. We incorporate numerous efficiency improvements and noise reduction schemes to help overcome efficiency barriers that typically inhibit convergence. These include continuous absorption and energy deposition, photon weighting and luminosity boosting, local packet merging and splitting, path-based statistical estimators, conservative (face-centered) momentum coupling, adaptive convergence between time steps, implicit Monte Carlo algorithms for thermal emission, and discrete-diffusion Monte Carlo techniques for unresolved scattering, including a novel advection scheme. We primarily focus on the unique aspects of our implementation and discussions of the advantages and drawbacks of our methods in various astrophysical contexts. Finally, we consider several test applications including the levitation of an optically thick layer of gas by trapped infrared radiation. We find that the initial acceleration phase and revitalized second wind are connected via self-regulation of the RHD coupling, such that the RHD method accuracy and simulation resolution each leave important imprints on the long-term behavior of the gas.

astro-ph.GA↗

arXiv2020

Nonstandard Representation of the Dirichlet Form

The Dirichlet form is a generalization of the Laplacian, heavily used in the study of many diffusion-like processes. In this paper we present a nonstandard representation theorem for the Dirichlet form, showing that the usual Dirichlet form can be well-approximated by a hyperfinite sum. One of the main motivations for such a result is to provide a tool for directly translating results about Dirichlet forms on finite or countable state spaces to results on more general state spaces, without having to translate the details of the proofs. As an application, we prove a generalization of a well-known comparison theorem for Markov chains on finite state spaces, and also relate our results to previous generalization attempts.

math.PR↗

arXiv2020

Resonant-line radiative transfer within power-law density profiles

Star-forming regions in galaxies are surrounded by vast reservoirs of gas capable of both emitting and absorbing Lyman-alpha (Lya) radiation. Observations of Lya emitters and spatially extended Lya haloes indeed provide insights into the formation and evolution of galaxies. However, due to the complexity of resonant scattering, only a few analytic solutions are known in the literature. We discuss several idealized but physically motivated scenarios to extend the existing formalism to new analytic solutions, enabling quantitative predictions about the transport and diffusion of Lya photons. This includes a closed form solution for the radiation field and derived quantities including the emergent flux, peak locations, energy density, average internal spectrum, number of scatters, outward force multiplier, trapping time, and characteristic radius. To verify our predictions, we employ a robust gridless Monte Carlo radiative transfer (GMCRT) method, which is straightforward to incorporate into existing ray-tracing codes but requires modifications to opacity-based calculations, including dynamical core-skipping acceleration schemes. We primarily focus on power-law density and emissivity profiles, however both the analytic and numerical methods can be generalized to other cases. Such studies provide additional intuition and understanding regarding the connection between the physical environments and observational signatures of galaxies throughout the Universe.

astro-ph.GA↗

arXiv2020

Fast and memory-optimal dimension reduction using Kac's walk

In this work, we analyze dimension reduction algorithms based on the Kac walk and discrete variants. (1) For $n$ points in $\mathbb{R}^{d}$, we design an optimal Johnson-Lindenstrauss (JL) transform based on the Kac walk which can be applied to any vector in time $O(d\log{d})$ for essentially the same restriction on $n$ as in the best-known transforms due to Ailon and Liberty [SODA, 2008], and Bamberger and Krahmer [arXiv, 2017]. Our algorithm is memory-optimal, and outperforms existing algorithms in regimes when $n$ is sufficiently large and the distortion parameter is sufficiently small. In particular, this confirms a conjecture of Ailon and Chazelle [STOC, 2006] in a stronger form. (2) The same construction gives a simple transform with optimal Restricted Isometry Property (RIP) which can be applied in time $O(d\log{d})$ for essentially the same range of sparsity as in the best-known such transform due to Ailon and Rauhut [Discrete Comput. Geom., 2014]. (3) We show that by fixing the angle in the Kac walk to be $π/4$ throughout, one obtains optimal JL and RIP transforms with almost the same running time, thereby confirming -- up to a $\log\log{d}$ factor -- a conjecture of Avron, Maymounkov, and Toledo [SIAM J. Sci. Comput., 2010]. Our moment-based analysis of this modification of the Kac walk may also be of independent interest.

cs.DS↗

arXiv2020

Drift, Minorization, and Hitting Times

The "drift-and-minorization" method, introduced and popularized in (Rosenthal, 1995; Meyn and Tweedie, 1994; Meyn and Tweedie, 2012), remains the most popular approach for bounding the convergence rates of Markov chains used in statistical computation. This approach requires estimates of two quantities: the rate at which a single copy of the Markov chain "drifts" towards a fixed "small set", and a "minorization condition" which gives the worst-case time for two Markov chains started within the small set to couple with moderately large probability. In this paper, we build on (Oliveira, 2012; Peres and Sousi, 2015) and our work (Anderson, Duanmu, Smith, 2019a; Anderson, Duanmu, Smith, 2019b) to replace the "minorization condition" with an alternative "hitting condition" that is stated in terms of only one Markov chain, and illustrate how this can be used to obtain similar bounds that can be easier to use.

math.PR↗

arXiv2020

The Origin and Evolution of Lyman-alpha Blobs in Cosmological Galaxy Formation Simulations

High-redshift Lyman-alpha blobs (LABs) are an enigmatic class of objects that have been the subject of numerous observational and theoretical investigations. It is of particular interest to determine the dominant power sources for the copious luminosity, as direct emission from HII regions, cooling gas, and fluorescence due to the presence of active galactic nuclei (AGN) can all contribute significantly. In this paper, we present the first theoretical model to consider all of these physical processes in an attempt to develop an evolutionary model for the origin of high-z LABs. This is achieved by combining a series of high-resolution cosmological zoom-in simulations with ionization and Lyman-alpha (Lya) radiative transfer models. We find that massive galaxies display a range of Lya luminosities and spatial extents (which strongly depend on the limiting surface brightness used) over the course of their lives, though regularly exhibit luminosities and sizes consistent with observed LABs. The model LABs are typically powered from a combination of recombination in star-forming galaxies, as well as cooling emission from gas associated with accretion. When AGN are included in the model, the fluorescence caused by AGN-driven ionization can be a significant contributor to the total Lya luminosity as well. We propose that the presence of an AGN may be predicted from the Gini coefficient of the blob's surface brightness. Within our modeled mass range, there are no obvious threshold physical properties that predict appearance of LABs, and only weak correlations of the luminosity with the physical properties of the host galaxy. This is because the emergent Lya luminosity from a system is a complex function of the gas temperature, ionization state, and Lya escape fraction.

astro-ph.GA↗

arXiv2019

Cutoff for the Square Plaquette Model on a Critical Length Scale

Plaquette models are short range ferromagnetic spin models that play a key role in the dynamic facilitation approach to the liquid glass transition. In this paper we study the dynamics of the square plaquette model at the smallest of the three critical length scales discovered in arXiv:1707.03036. Our main result is that the plaquette model with periodic boundary conditions, on this length scale, exhibits a sharp transition in the convergence to equilibrium, known as cutoff. This substantially refines our coarse understanding of mixing from previous work arXiv:1807.00634.

math.PR↗

arXiv2019

Mixing of the Square Plaquette Model on a Critical Length Scale

Plaquette models are short range ferromagnetic spin models that play a key role in the dynamic facilitation approach to the liquid glass transition. In this paper we study the dynamics of the square plaquette model at the smallest of the three critical length scales discovered in arXiv:1707.03036. Our main result is the computation of the spectral gap, and mixing times, for two natural boundary conditions. We observe that these time scales depend heavily on the boundary condition in this scaling regime.

math.PR↗

arXiv2019

Supermassive Black Holes in the Early Universe

The emergence of the first black holes during the first billion years of cosmic history marks a key event in cosmology. Their formation is part of the overall process of ending the cosmic dark ages, when the first stars appeared in low-mass dark matter haloes about a few 100 million years after the Big Bang. The first stars, galaxies, and black holes transformed the Universe from its simple initial state into one of ever increasing complexity. We review recent progress on our emerging theoretical picture of how the first black holes appeared on the cosmic scene, and how they impacted the subsequent history of the Universe. Our focus is on supermassive black holes, in particular assessing possible pathways to the formation of the billion-solar-mass black holes inferred to power the luminous quasars at high redshifts. We conclude with a discussion of upcoming empirical probes, such as the James Webb Space Telescope (JWST), and the Laser Interferometer Space Antenna (LISA), further ahead in time.

astro-ph.GA↗

arXiv2019

Mixing Times and Hitting Times for General Markov Processes

The hitting and mixing times are two fundamental quantities associated with Markov chains. In Peres and Sousi[PS2015] and Oliveira[Oli2012], the authors show that the mixing times and "worst-case" hitting times of reversible Markov chains on finite state spaces are equal up to some universal multiplicative constant. We use tools from nonstandard analysis to extend this result to reversible Markov chains on general state spaces that satisfy the strong Feller property. Finally, we show that this asymptotic equivalence can be used to find bounds on the mixing times of a large class of Markov chains used in MCMC, such as typical Gibbs samplers and Metroplis-Hastings chains, even though they usually do not satisfy the strong Feller property.

math.PR↗

arXiv2018

The physics of Lyman-alpha escape from high-redshift galaxies

Lyman-alpha (Lyα) photons from ionizing sources and cooling radiation undergo a complex resonant scattering process that generates unique spectral signatures in high-redshift galaxies. We present a detailed Lyα radiative transfer study of a cosmological zoom-in simulation from the Feedback In Realistic Environments (FIRE) project. We focus on the time, spatial, and angular properties of the Lyα emission over a redshift range of z = 5-7, after escaping the galaxy and being transmitted through the intergalactic medium (IGM). Over this epoch, our target galaxy has an average stellar mass of $M_{\rm star} \approx 5 \times 10^8 {\rm M}_\odot$. We find that many of the interesting features of the Lyα line can be understood in terms of the galaxy's star formation history. The time variability, spatial morphology, and anisotropy of Lyα properties are consistent with current observations. For example, the rest frame equivalent width has a ${\rm EW}_{{\rm Ly}α,0} > 20 {\rm Å}$ duty cycle of 62% with a non-negligible number of sightlines with $> 100 {\rm Å}$, associated with outflowing regions of a starburst with greater coincident UV continuum absorption, as these conditions generate redder, narrower (or single peaked) line profiles. The lowest equivalent widths correspond to cosmological filaments, which have little impact on UV continuum photons but efficiently trap Lyα and produce bluer, broader lines with less transmission through the IGM. We also show that in dense self-shielding, low-metallicity filaments and satellites Lyα radiation pressure can be dynamically important. Finally, despite a significant reduction in surface brightness with increasing redshift, Lyα detections and spectroscopy of high-$z$ galaxies with the upcoming James Webb Space Telescope is feasible.

astro-ph.GA↗