arXiv subjects

Alex Hall

Publications and source records attributed to Alex Hall.

At least 37 records · Page 2Linked to original sources

arXiv2022

Characterizing a non-equilibrium phase transition on a quantum computer

At transitions between phases of matter, physical systems can exhibit universal behavior independent of their microscopic details. Probing such behavior in quantum many-body systems is a challenging and practically important problem that can be solved by quantum computers, potentially exponentially faster than by classical computers. In this work, we use the Quantinuum H1-1 quantum computer to realize a quantum extension of a simple classical disease spreading process that is known to exhibit a non-equilibrium phase transition between an active and absorbing state. Using techniques such as qubit-reuse and error avoidance based on real-time conditional logic (utilized extensively in quantum error correction), we are able to implement large instances of the model with $73$ sites and up to $72$ circuit layers, and quantitatively determine the model's critical properties. This work demonstrates how quantum computers capable of mid-circuit resets, measurements, and conditional logic enable the study of difficult problems in quantum many-body physics: the simulation of open quantum system dynamics and non-equilibrium phase transitions.

quant-ph↗

arXiv2022

Testing Quadratic Maximum Likelihood estimators for forthcoming Stage-IV weak lensing surveys

Headline constraints on cosmological parameters from current weak lensing surveys are derived from two-point statistics that are known to be statistically sub-optimal, even in the case of Gaussian fields. We study the performance of a new fast implementation of the Quadratic Maximum Likelihood (QML) estimator, optimal for Gaussian fields, to test the performance of Pseudo-Cl estimators for upcoming weak lensing surveys and quantify the gain from a more optimal method. Through the use of realistic survey geometries, noise levels, and power spectra, we find that there is a decrease in the errors in the statistics of the recovered E-mode spectra to the level of ~20% when using the optimal QML estimator over the Pseudo-Cl estimator on the largest angular scales, while we find significant decreases in the errors associated with the B-modes for the QML estimator. This raises the prospects of being able to constrain new physics through the enhanced sensitivity of B-modes for forthcoming surveys that our implementation of the QML estimator provides. We test the QML method with a new implementation that uses conjugate-gradient and finite-differences differentiation methods resulting in the most efficient implementation of the full-sky QML estimator yet, allowing us to process maps at resolutions that are prohibitively expensive using existing codes. In addition, we investigate the effects of apodisation, B-mode purification, and the use of non-Gaussian maps on the statistical properties of the estimators. Our QML implementation is publicly available and can be accessed from GitHub.

astro-ph.CO↗

arXiv2022

Non-Gaussian likelihood of weak lensing power spectra

The power spectrum of weak lensing fluctuations has a non-Gaussian distribution due to its quadratic nature. On small scales the Central Limit Theorem acts to Gaussianize this distribution but non-Gaussianity in the signal due to gravitational collapse is increasing and the functional form of the likelihood is unclear. Analyses have traditionally assumed a Gaussian likelihood with non-linearity incorporated into the covariance matrix; here we provide the theory underpinning this assumption. We calculate, for the first time, the leading-order correction to the distribution of angular power spectra from non-Gaussianity in the underlying signal and study the transition to Gaussianity. Our expressions are valid for an arbitrary number of correlated maps and correct the Wishart distribution in the presence of weak (but otherwise arbitrary) non-Gaussianity in the signal. Surprisingly, the resulting distribution is not equivalent to an Edgeworth expansion. The leading-order effect is to broaden the covariance matrix by the usual trispectrum term, with residual skewness sourced by the trispectrum and the square of the bispectrum. Using lognormal lensing maps we demonstrate that our likelihood is uniquely able to model both large and mildly non-linear scales. We provide easy-to-compute statistics to quantify the size of the non-Gaussian corrections. We show that the full non-Gaussian likelihood can be accurately modelled as a Gaussian on small, non-linear scales. On large angular scales non-linearity in the lensing signal imparts a negligible correction to the likelihood, which takes the Wishart form in the full-sky case. Our formalism is equally applicable to any kind of projected field.

astro-ph.CO↗

arXiv2022

An accurate model for the primordial black hole mass distribution from a peak in the power spectrum

We examine the shape of the primordial black hole mass distribution arising from a peak in the primordial power spectrum. In light of improvements to the modelling, we revisit the claim that the effects of critical collapse produce a distribution that is not described by the commonly assumed lognormal, showing that this conclusion remains valid, particularly for narrow peaks where the shape of the mass distribution is insensitive to the peak properties and critical collapse determines a minimum width. We propose some alternative models that may better describe the shape, both for the narrow peak case and for much broader peaks where the effect of the peak shape is significant. We highlight the skew-lognormal and a generalised model motivated by the physics of critical collapse as the best of these possible alternatives. These models can be used as an accurate and fast approximation to the numerically calculated mass distribution, allowing for efficient implementation in an MCMC analysis. We advocate the use of one of these two models instead of the lognormal with sufficiently accurate data, such as future LIGO-Virgo observations, or when considering strongly mass dependent constraints on the PBH abundance.

astro-ph.CO↗

arXiv2021

Cosmology from weak lensing alone and implications for the Hubble tension

We investigate the origin of $Λ$CDM parameter constraints in weak lensing, with a focus on the Hubble constant. We explain why current cosmic shear data are sensitive to the parameter combination $S_8 \propto σ_8 Ω_m^{0.5}$, improving upon previous studies through use of the halo model. Motivated by the ongoing discrepancy in measurements of the Hubble constant from high and low redshift, we explain why cosmic shear provides almost no constraint on $H_0$ by showing how the lensing angular power spectrum depends on physical length scales in the dark matter distribution. We derive parameter constraints from galaxy lensing in KiDS and cosmic microwave background weak lensing from Planck and SPTpol, separately and jointly, showing how degeneracies between $σ_8$ and $Ω_m$ can be broken. Using lensing and Big Bang Nucleosynthesis to calibrate the sound horizon measured in projection by baryon acoustic oscillations gives $H_0 = 67.4 \pm 0.9 \; \mathrm{km} \, \mathrm{s}^{-1} \, \mathrm{Mpc}^{-1}$, consistent with previous results from Planck and the Dark Energy Survey. We find that a toy Euclid-like lensing survey provides only weak constraints on the Hubble constant due to degeneracies with other parameters that affect the shape of the lensing correlation functions. If external priors on $n_s$, the baryon density, and the amplitude of baryon feedback are available then sub-percent $H_0$ constraints are achievable with forthcoming lensing surveys.

astro-ph.CO↗

arXiv2021

Entanglement from tensor networks on a trapped-ion QCCD quantum computer

The ability to selectively measure, initialize, and reuse qubits during a quantum circuit enables a mapping of the spatial structure of certain tensor-network states onto the dynamics of quantum circuits, thereby achieving dramatic resource savings when using a quantum computer to simulate many-body systems with limited entanglement. We experimentally demonstrate a significant benefit of this approach to quantum simulation: In addition to all correlation functions, the entanglement structure of an infinite system -- specifically the half-chain entanglement spectrum -- is conveniently encoded within a small register of "bond qubits" and can be extracted with relative ease. Using a trapped-ion QCCD quantum computer equipped with selective mid-circuit measurement and reset, we quantitatively determine the near-critical entanglement entropy of a correlated spin chain directly in the thermodynamic limit and show that its phase transition becomes quickly resolved upon expanding the bond-qubit register.

quant-ph↗

arXiv2020

Emergent constraints on climate sensitivities

Despite major advances in climate science over the last 30 years, persistent uncertainties in projections of future climate change remain. Climate projections are produced with increasingly complex models which attempt to represent key processes in the Earth system, including atmospheric and oceanic circulations, convection, clouds, snow, sea-ice, vegetation and interactions with the carbon cycle. Uncertainties in the representation of these processes feed through into a range of projections from the many state-of-the-art climate models now being developed and used worldwide. For example, despite major improvements in climate models, the range of equilibrium global warming due to doubling carbon dioxide still spans a range of more than three. Here we review a promising way to make use of the ensemble of climate models to reduce the uncertainties in the sensitivities of the real climate system. The emergent constraint approach uses the model ensemble to identify a relationship between an uncertain aspect of the future climate and an observable variation or trend in the contemporary climate. This review summarises previous published work on emergent constraints, and discusses the huge promise and potential dangers of the approach. Most importantly, it argues that emergent constraints should be based on well-founded physical principles such as the fluctuation-dissipation theorem. It is hoped that this review will stimulate physicists to contribute to the rapidly developing field of emergent constraints on climate projections, bringing to it much needed rigour and physical insights.

physics.ao-ph↗

arXiv2020

Bayesian analysis of LIGO-Virgo mergers: Primordial vs. astrophysical black hole populations

We conduct a thorough Bayesian analysis of the possibility that the black hole merger events seen in gravitational waves are primordial black hole (PBH) mergers. Using the latest merger rate models for PBH binaries drawn from a lognormal mass function we compute posterior parameter constraints and Bayesian evidences using data from the first two observing runs of LIGO-Virgo. We account for theoretical uncertainty due to possible disruption of the binary by surrounding PBHs, which can suppress the merger rate significantly. We also consider simple astrophysically motivated models and find that these are favoured decisively over the PBH scenario, quantified by the Bayesian evidence ratio. Paying careful attention to the influence of the parameter priors and the quality of the model fits, we show that the evidence ratios can be understood by comparing the predicted chirp mass distribution to that of the data. We identify the posterior predictive distribution of chirp mass as a vital tool for discriminating between models. A model in which all mergers are PBH binaries is strongly disfavoured compared with astrophysical models, in part due to the over-prediction of heavy systems having $\mathcal{M}_{\rm chirp} \gtrsim 40 \, M_\odot$ and positive skewness over the range of observed masses which does not match the observations. We find that the fit is not significantly improved by adding a maximum mass cut-off, a bimodal mass function, or imposing that PBH binaries form at late times. We argue that a successful PBH model must either modify the lognormal shape of the initial mass function significantly or abandon the hypothesis that all observed merging binaries are primordial. We develop and apply techniques for analysing PBH models with gravitational wave data which will be necessary for robust statistical inference as the gravitational wave source sample size increases.

astro-ph.CO↗

arXiv2020

Towards determining the neutrino mass hierarchy: weak lensing and galaxy clustering forecasts with baryons and intrinsic alignments

The capacity of Stage IV lensing surveys to measure the neutrino mass sum and differentiate between the normal and inverted mass hierarchies depends on the impact of nuisance parameters describing small-scale baryonic astrophysics and intrinsic alignments. For a Euclid-like survey, we perform the first combined weak lensing and galaxy clustering Fisher analysis with baryons, intrinsic alignments, and massive neutrinos for both hierarchies. We use a matter power spectrum generated from a halo model that captures the impact of baryonic feedback and adiabatic contraction. For weak lensing, we find that baryons cause severe degradation to forecasts of the neutrino mass sum, $Σ$, approximately doubling $σ_Σ$. We show that including galaxy clustering constraints from Euclid and BOSS, and cosmic microwave background (CMB) Planck priors, can reduce this degradation to $σ_Σ$ to 9% and 16% for the normal and inverted hierarchies respectively. The combined forecasts, $σ_{Σ_{\rm{NH}}}=0.034\, \rm{eV}$ and $σ_{Σ_{\rm{IH}}}=0.034\, \rm{eV}$, preclude a meaningful distinction of the hierarchies but could be improved upon with future CMB priors on $n_s$ and information from neutrinoless double beta decay to achieve a 2$σ$ distinction. The effect of intrinsic alignments on forecasts is shown to be minimal, with $σ_Σ$ even experiencing mild improvements due to information from the intrinsic alignment signal. We find that while adiabatic contraction and intrinsic alignments will require careful calibration to prevent significant biasing of $Σ$, there is less risk presented by feedback from energetic events like AGN and supernovae.

astro-ph.CO↗

arXiv2020

Impact of our local environment on cosmological statistics

We conduct a thorough investigation into the possibility that residing in an overdense region of the Universe may induce bias in measurements of the large-scale structure. We compute the conditional correlation function and angular power spectrum of density and lensing fluctuations while holding the local spherically averaged density fixed and show that for Gaussian fields this has no effect on the angular power at $l>0$. We identify a range of scales where a perturbative approach allows analytic progress to be made, and we compute leading-order conditional power spectra using an Edgeworth expansion and second-order perturbation theory. We find no evidence for any significant bias to cosmological power spectra from our local density contrast. We show that when smoothed over a large region around the observer, conditioning on the local density typically affects density power spectra by less than a percent at cosmological distances, below cosmic variance. We find that while typical corrections to the lensing angular power spectrum can be at the 10% level on the largest angular scales and for source redshifts $z_s \lesssim 0.1$, for the typical redshifts targeted by upcoming wide imaging surveys the corrections are sub-percent and negligible, in contrast to previous claims in the literature. Using an estimate of the local spherically averaged density from a composite galaxy redshift catalogue we find that the corrections from conditioning on our own local density are below cosmic variance and subdominant to other non-linear effects. We discuss the potential implications of our results for cosmology and point out that a measurement of the local density contrast may be used as a consistency test of cosmological models.

astro-ph.CO↗

arXiv2020

Primordial black hole merger rates: distributions for multiple LIGO observables

We have calculated the detectable merger rate of primordial black holes, as a function of the redshift, as well as the binary's mass ratio, total mass and chirp mass (observables that have not previously been explored in great detail for PBHs). We consider both the current and design sensitivity of LIGO and five different primordial black hole mass functions, as well as showing a comparison to a predicted astrophysical black hole merger rate. We show that the empirical preference for nearly equal-mass binaries in current LIGO/Virgo data can be consistent with a PBH hypothesis once observational selection effects are taken into account. However, current data do exclude some PBH mass distributions, and future data may be able to rule out the possibility that all observed BH mergers had a primordial origin.

astro-ph.CO↗

arXiv2019

Cosmology with extragalactic proper motions: harmonic formalism, estimators, and forecasts

We conduct a thorough study into the feasibility of measuring large-scale correlated proper motions of galaxies with astrometric surveys. We introduce a harmonic formalism for analysing proper motions and their correlation functions on the sphere based on spin-weighted spherical harmonics, and study the statistics of the transverse velocity field induced by large-scale structure. We use a likelihood formalism to derive optimal estimators for the secular parallax due to the Solar System's motion relative to distant objects, and compute the variance and bias due to peculiar velocities and relativistic aberration. We use a simulated catalogue of galaxy proper motions with radial distributions and noise properties similar to those expected from Gaia to forecast the detectability of the proper motion dipole, whose amplitude may be considered a proxy for the Hubble constant. We find cosmic variance to be the limiting source of noise for this measurement, forecasting a detectability of $1$-$2σ$ on a single component of the local velocity, increasing to $2$-$4σ$ (equivalent to a 25%-50% measurement of the Hubble constant) if the CMB dipole is included as prior information. We conduct a thorough study into the radial dependence of the signal-to-noise, finding that most of the information comes from galaxies closer than a few hundred Mpc. We forecast that the amplitude of peculiar transverse velocities can potentially be measured with 10$σ$ significance; such a measurement would offer a unique probe of cosmic flows and a valuable test of the cosmological model.

astro-ph.CO↗

arXiv2018

A Bayesian method for combining theoretical and simulated covariance matrices for large-scale structure surveys

Accurate and precise covariance matrices will be important in enabling planned cosmological surveys to detect new physics. Standard methods imply either the need for many N-body simulations in order to obtain an accurate estimate, or a precise theoretical model. We combine these approaches by constructing a likelihood function conditioned on simulated and theoretical covariances, consistently propagating noise from the finite number of simulations and uncertainty in the theoretical model itself using an informative Inverse-Wishart prior. Unlike standard methods, our approach allows the required number of simulations to be less than the number of summary statistics. We recover the linear 'shrinkage' covariance estimator in the context of a Bayesian data model, and test our marginal likelihood on simulated mock power spectrum estimates. We conduct a thorough investigation into the impact of prior confidence in different choices of covariance models on the quality of model fits and parameter variances. In a simplified setting we find that the number of simulations required can be reduced if one is willing to accept a mild degradation in the quality of model fits, finding that even weakly informative priors can help to reduce the simulation requirements. We identify the correlation matrix of the summary statistics as a key quantity requiring careful modelling. Our approach can be easily generalized to any covariance model or set of summary statistics, and elucidates the role of hybrid estimators in cosmological inference.

astro-ph.CO↗

arXiv2018

A hierarchical statistical framework for emergent constraints: application to snow-albedo feedback

Emergent constraints use relationships between future and current climate states to constrain projections of climate response. Here, we introduce a statistical, hierarchical emergent constraint (HEC) framework in order to link future and current climate with observations. Under Gaussian assumptions, the mean and variance of the future state is shown analytically to be a function of the signal-to-noise (SNR) ratio between data-model error and current-climate uncertainty, and the correlation between future and current climate states. We apply the HEC to the climate-change, snow-albedo feedback, which is related to the seasonal cycle in the Northern Hemisphere. We obtain a snow-albedo-feedback prediction interval of $(-1.25, -0.58)$ \%$K^{-1}$. The critical dependence on SNR and correlation shows that neglecting these terms can lead to bias and under-estimated uncertainty in constrained projections. The flexibility of using HEC under general assumptions throughout the Earth System is discussed.

physics.ao-ph↗

arXiv2018

The impact of baryons on the sensitivity of dark energy measurements

Baryonic effects on large-scale structure, if not accounted for, can significantly bias dark energy constraints. As the detailed physics of the baryons is not yet well-understood, correcting for baryon effects introduces additional parameters which must be marginalized over, increasing the uncertainties on the inferred cosmological parameters. Forthcoming weak lensing surveys are aiming for percent-level precision on the dark energy equation of state, so the problem must be thoroughly examined. We use a halo model with analytic modifications which capture the impact of adiabatic contraction of baryons and feedback on the matter power spectrum, and generalize the Navarro-Frenk-White profile to account for a possible inner core. A Fisher analysis predicts degradations of 40% in the $w_0$-$w_a$ Figure of Merit for a Euclid-like survey, and up to 80% for other cosmological parameters. We forecast potential inner core constraints of a few $\mathrm{kpc}$, while for a fixed inner core, adiabatic concentration and feedback parameters are constrained to a few percent. We explore the scales where baryons and dark energy contribute most to the Fisher information, finding that probing to increasingly non-linear scales does little to reduce degradation. Including external baryon information improves our forecasts, but limiting degradation to 1% requires strong priors. Adding Planck cosmic microwave background priors improves the Figure of Merit by a factor of 2.7 and almost completely recovers the individual marginalized errors on $w_0$ and $w_a$. We also quantify the calibration of baryon modelling required to reduce biases of dark energy forecasts to acceptable levels for forthcoming lensing surveys.

astro-ph.CO↗

arXiv2017

Measuring cosmic velocities with 21cm intensity mapping and galaxy redshift survey cross-correlation dipoles

We investigate the feasibility of measuring the effects of peculiar velocities in large-scale structure using the dipole of the redshift-space cross-correlation function. We combine number counts of galaxies with brightness-temperature fluctuations from 21cm intensity mapping, demonstrating that the dipole may be measured at modest significance ($\lesssim 2σ$) by combining the upcoming radio survey CHIME with the future redshift surveys of DESI and Euclid. More significant measurements ($\lesssim~10σ$) will be possible by combining intensity maps from the SKA with these of DESI or Euclid, and an even higher significance measurement ($\lesssim 100σ$) may be made by combining observables completely internally to the SKA. We account for effects such as contamination by wide-angle terms, interferometer noise and beams in the intensity maps, non-linear enhancements to the power spectrum, stacking multiple populations, sensitivity to the magnification slope, and the possibility that number counts and intensity maps probe the same tracers. We also derive a new expression for the covariance matrix of multi-tracer redshift-space correlation function estimators with arbitrary orientation weights, which may be useful for upcoming surveys aiming at measuring redshift-space clustering with multiple tracers.

astro-ph.CO↗

arXiv2017

Perturbative Gaussianizing transforms for cosmological fields

Constraints on cosmological parameters from large-scale structure have traditionally been obtained from two-point statistics. However, non-linear structure formation renders these statistics insufficient in capturing the full information content available, necessitating the measurement of higher-order moments to recover information which would otherwise be lost. We construct quantities based on non-linear and non-local transformations of weakly non-Gaussian fields that Gaussianize the full multivariate distribution at a given order in perturbation theory. Our approach does not require a model of the fields themselves and takes as input only the first few polyspectra, which could be modelled or measured from simulations or data, making our method particularly suited to observables lacking a robust perturbative description such as the weak-lensing shear. We apply our method to simulated density fields, finding a significantly reduced bispectrum and an enhanced correlation with the initial field. We demonstrate that our method reconstructs a large proportion of the linear baryon acoustic oscillations, improving the information content over the raw field by 35%. We apply the transform to toy 21cm intensity maps, showing that our method still performs well in the presence of complications such as redshift-space distortions, beam smoothing, pixel noise, and foreground subtraction. We discuss how this method might provide a route to constructing a perturbative model of the fully non-Gaussian multivariate likelihood function.

astro-ph.CO↗

arXiv2017

Emission-angle and polarization-rotation effects in the lensed CMB

Lensing of the CMB is an important effect, and is usually modelled by remapping the unlensed CMB fields by a lensing deflection. However the lensing deflections also change the photon path so that the emission angle is no longer orthogonal to the background last-scattering surface. We give the first calculation of the emission-angle corrections to the standard lensing approximation from dipole (Doppler) sources for temperature and quadrupole sources for temperature and polarization. We show that while the corrections are negligible for the temperature and E-mode polarization, additional large-scale B-modes are produced with a white spectrum that dominates those from post-Born field rotation (curl lensing). On large scales about one percent of the total lensing-induced B-mode amplitude is expected to be due to this effect. However, the photon emission angle does remain orthogonal to the perturbed last-scattering surface due to time delay, and half of the large-scale emission-angle B modes cancel with B modes from time delay to give a total contribution of about half a percent. While not important for planned observations, the signal could ultimately limit the ability of delensing to reveal low amplitudes of primordial gravitational waves.We also derive the rotation of polarization due to multiple deflections between emission and observation. The rotation angle is of quadratic order in the deflection angle, and hence negligibly small: polarization typically rotates by less than an arcsecond, orders of magnitude less than a small-scale image rotates due to post-Born field rotation (which is quadratic in the shear). The field-rotation B modes dominate the other effects on small scales.

astro-ph.CO↗