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Alex Hall

Publications and source records attributed to Alex Hall.

At least 19 recordsLinked to original sources

Temporal Coverage over Density: Parsimonious Training-Set Design for ML Climate Downscaling

High-resolution regional climate simulations provide critical information for climate impacts assessments but remain computationally expensive, motivating the development of machine-learning downscalers and emulators. A key challenge is determining how limited high-resolution simulations should be distributed across a changing climate trajectory to capture both forced climate response and internal variability. Using the CESM2 Large Ensemble over the western United States, we compare three training-year selection strategies under fixed data budgets: a contiguous block of historical years, years drawn from both the beginning and end of the simulation period, and years distributed throughout the full climate trajectory. Including both historical and future years consistently outperforms training on historical years alone, demonstrating the importance of exposing downscaling models to climate states outside the historical record and highlighting limitations of stationarity assumptions common in statistical downscaling. Training on years distributed throughout the full climate trajectory performs best overall, indicating that broad sampling of internal variability provides additional information beyond exposure to the forced climate response alone. Models trained on temporally distributed subsets more successfully reproduce variability in unseen ensemble members while retaining strong performance across a wide range of climate diagnostics. Even when trained on only one-tenth of the available high-resolution years, temporally distributed models remain highly competitive with full-data training. These results suggest that, under fixed computational budgets, broad sampling of climate states is more valuable than temporal continuity when allocating scarce high-resolution simulations. The findings provide practical guidance for regional climate downscaling and large-ensemble projection workflows.

cs.LG

cloelib: A Flexible Python Library for Computing Cosmological Observables in the Euclid Era

cloelib is a Python library developed to compute cosmological observables within the Cosmology Likelihood for Observables in Euclid (CLOE) ecosystem (cloe-org). As cosmology enters a precision era driven by galaxy survey missions such as Euclid, there is a growing need for flexible, efficient, and differentiable software capable of supporting next-generation inference pipelines. cloelib addresses these demands through a modular architecture that interfaces seamlessly with established Boltzmann solvers whilst incorporating JAX-based automatic differentiation to enable gradient-based methods. The library defines consistent protocols for background evolution, perturbations, and non-linear structure formation, and supports a wide range of observables, including photometric and spectroscopic large-scale structure probes, as well as cross-correlations with the Cosmic Microwave Background and galaxy clusters. In its finalised form, cloelib is intended to serve as the reference theory computation infrastructure for Euclid's first cosmological release, bridging traditional numerical cosmology with modern optimisation techniques and emerging machine learning approaches to inference.

astro-ph.CO

An Open-Source, Open Data Approach to Activity Classification from Triaxial Accelerometry in an Ambulatory Setting

The accelerometer has become an almost ubiquitous device, providing enormous opportunities in healthcare monitoring beyond step counting or other average energy estimates in 15-60 second epochs. Objective: To develop an open data set with associated open-source code for processing 50 Hz tri-axial accelerometry-based to classify patient activity levels and natural types of movement. Approach: Data were collected from 23 healthy subjects (16 males and seven females) aged between 23 and 62 years using an ambulatory device, which included a triaxial accelerometer and synchronous lead II equivalent ECG for an average of 26 minutes each. Participants followed a standardized activity routine involving five distinct activities: lying, sitting, standing, walking, and jogging. Two classifiers were constructed: a signal processing technique to distinguish between high and low activity levels and a convolutional neural network (CNN)-based approach to classify each of the five activities. Main results: The binary (high/low) activity classifier exhibited an F1 score of 0.79. The multi-class CNN-based classifier provided an F1 score of 0.83. The code for this analysis has been made available under an open-source license together with the data on which the classifiers were trained and tested. Significance: The classification of behavioral activity, as demonstrated in this study, offers valuable context for interpreting traditional health metrics and may provide contextual information to support the future development of clinical decision-making tools for patient monitoring, predictive analytics, and personalized health interventions.

q-bio.QM

Computing with many encoded logical qubits beyond break-even

High-rate quantum error correcting (QEC) codes encode many logical qubits in a given number of physical qubits, making them promising candidates for quantum computation. Implementing high-rate codes at a scale that both frustrates classical computing and improves performance by encoding requires both high fidelity gates and long-range qubit connectivity -- both of which are offered by trapped-ion quantum computers. Here, we demonstrate computations that outperform their unencoded counterparts in the high-rate $[[ k+2,\, k,\, 2 ]]$ iceberg quantum error detecting (QED) and $[[ (k_2 + 2)(k_1 + 2),\, k_2k_1,\, 4 ]]$ two-level concatenated iceberg QEC codes, using the 98-qubit Quantinuum Helios trapped-ion quantum processor. Utilizing new gadgets for encoded operations, we realize this "beyond break-even" performance with reasonable postselection rates across a range of fault-tolerant (FT) and partially-fault-tolerant (pFT) component and application benchmarks with between $48$ and $94$ logical qubits. These benchmarks include FT state preparation and measurement, QEC cycle benchmarking, logical gate benchmarking, GHZ state preparation, and a pFT quantum simulation of the three-dimensional $XY$ model of quantum magnetism. Additionally, we illustrate that postselection rates can be suppressed by increasing the code distance via concatenation. Our results represent state-of-the-art logical component and state fidelities and provide evidence that high-rate QED/QEC codes are viable on contemporary quantum computers for near-term beyond-classical-scale computation.

quant-ph

Illuminating the Physics of Cosmic Origin and Evolution: A UK Space Frontiers 2035 White Paper

Understanding the Universe's origins and evolution remains one of the most fundamental challenges in modern cosmology. This white paper explores three key science priorities in this field: unravelling the physics of cosmic inflation, investigating the accelerating expansion of the Universe, and precisely measuring the sum of the neutrino masses. Achieving these goals requires a dedicated survey to map the large-scale structure at high redshift in unprecedented detail. We describe how this can be achieved through a mission concept called SIRMOS, providing a high-throughput, highly multiplexed spectroscopic capability to obtain accurate redshifts for over 100 million galaxies over a wide sky area. Such a survey would leverage the deepest existing wide-area photometric catalogues for targeting, with spectra offering continuous 1.25-2.5~$\mu$m wavelength coverage at moderate resolution, allowing precise redshift measurements in the $1<z<4$ range with minimal bias. We outline the scientific opportunities this presents. Recent years have seen significant advances in instrumentation, including digital micromirror devices, complex telescope mirrors, large detector arrays, and data processing pipelines. While these technologies have been demonstrated in terrestrial applications, such a survey is a unique opportunity to apply these proven capabilities in space to address fundamental questions in cosmology. Participation in such a mission will simultaneously deliver a compelling science case, help align UK Space Agency and STFC strategies, demonstrate the UK's growing capability in end-to-end space missions, and strengthen the national space economy through high-value industrial participation.

astro-ph.IM

Comparing cosmic shear nulling methods for Stage-IV surveys

We present an analysis comparing nulling strategies for reducing the impact of baryon feedback on cosmic shear measurements. We consider three different approaches which aim to `null' the high-$k$ modes using transformations applied to the data vector: the Bernardeau-Nishimichi-Taruya (BNT) transform which operates on the lensing field, a new implementation of an LU factorisation of the discretized Limber integral (LUnul) which operates on the lensing two-point statistics, and finally a method which uses a correlated LSS tracers to suppress contributions from lower redshifts (cross-correlation). We compare these methods to un-nulled (or standard) cosmic shear at the data vector level and assess whether these methods are able to reduce the bias on cosmological constraints using a Fisher forecast. We find that the nulling techniques considered can have a large impact on reducing the bias on $S_8$ and Dark Energy parameters. The cross-correlation method is effective at reducing biases in $S_8$, but requires additional information from galaxy clustering. The LUnul method is the most aggressive of the methods and hence reduces biases most efficiently as $k_{\rm max}$ is increased, although this improvement in accuracy comes at the cost of precision. The BNT approach preserves more information than LUnul, and has a more rigorous theoretical grounding. We demonstrate that all three of these methods are effective at mitigating bias, and can be readily applied in forthcoming lensing analyses.

astro-ph.CO

Helios: A 98-qubit trapped-ion quantum computer

We report on Quantinuum Helios, a 98-qubit trapped-ion quantum processor based on the quantum charge-coupled device (QCCD) architecture. Helios features $^{137}$Ba$^{+}$ hyperfine qubits, all-to-all connectivity enabled by a rotatable ion storage ring connecting two quantum operation regions by a junction, speed improvements from parallelized operations, and a new software stack with real-time compilation of dynamic programs. Averaged over all operational zones in the system, we achieve average infidelities of $2.5(1)\times10^{-5}$ for single-qubit gates, $7.9(2)\times10^{-4}$ for two-qubit gates, and $4.8(6)\times10^{-4}$ for state preparation and measurement, none of which are fundamentally limited and likely able to be improved. These component infidelities are predictive of system-level performance in both random Clifford circuits and random circuit sampling, the latter demonstrating that Helios operates well beyond the reach of classical simulation and establishes a new frontier of fidelity and complexity for quantum computers.

quant-ph

Certified randomness amplification by dynamically probing remote random quantum states

Cryptography depends on truly unpredictable numbers, but physical sources emit biased or correlated bits. Quantum mechanics enables the amplification of imperfect randomness into nearly perfect randomness, but prior demonstrations have required physically co-located, loophole-free Bell tests, constraining the feasibility of remote operation. Here we realize certified randomness amplification across a network by dynamically probing large, entangled quantum states on Quantinuum's 98-qubit Helios trapped-ion quantum processor. Our protocol is secure even if the remote device acts maliciously or is compromised by an intercepting adversary, provided the samples are generated quickly enough to preclude classical simulation of the quantum circuits. We stream quantum gates in real time to the quantum processor, maintain quantum state coherence for $\approx 0.9$ seconds, and then reveal the measurement bases to the quantum processor only milliseconds before measurement. This limits the time for classical spoofing to 30 ms and constrains the location of hypothetical adversaries to a $4{,}500$ km radius. We achieve a fidelity of 0.586 on random circuits with 64 qubits and 276 two-qubit gates, enabling the amplification of realistic imperfect randomness with a low entropy rate into nearly perfect randomness.

quant-ph

Realization of a Quantum Streaming Algorithm on Long-lived Trapped-ion Qubits

Large classical datasets are often processed in the streaming model, with data arriving one item at a time. In this model, quantum algorithms have been shown to offer an unconditional exponential advantage in space. However, experimentally implementing such streaming algorithms requires qubits that remain coherent while interacting with an external data stream. In this work, we realize such a data-streaming model using Quantinuum Helios trapped-ion quantum computer with long-lived qubits that communicate with an external server. We implement a quantum pair sketch, which is the primitive underlying many quantum streaming algorithms, and use it to solve Hidden Matching, a problem known to exhibit a theoretical exponential quantum advantage in space. Furthermore, we compile the quantum streaming algorithm to fault-tolerant quantum architectures based on surface and bivariate bicycle codes and show that the quantum space advantage persists even with the overheads of fault-tolerance.

quant-ph

Superconducting pairing correlations on a trapped-ion quantum computer

The Fermi-Hubbard model is the starting point for the simulation of many strongly correlated materials, including high-temperature superconductors, whose modelling is a key motivation for the construction of quantum simulation and computing devices. However, the detection of superconducting pairing correlations has so far remained out of reach, both because of their off-diagonal character - which makes them inaccessible to local density measurements - and because of the difficulty of preparing superconducting states. Here, we report measurement of significant pairing correlations in three different regimes of Fermi-Hubbard models simulated on Quantinuum's Helios trapped-ion quantum computer. Specifically, we measure non-equilibrium pairing induced by an electromagnetic field in the half-filled square lattice model, d-wave pairing in an approximate ground state of the checkerboard Hubbard model at $1/6$-doping, and s-wave pairing in a bilayer model relevant to nickelate superconductors. These results show that a quantum computer can reliably create and probe physically relevant states with superconducting pairing correlations, opening a path to the exploration of superconductivity with quantum computers.

quant-ph

Shot noise in clustering power spectra

We show that the `shot noise' bias in angular clustering power spectra observed from discrete samples of points is not noise, but rather a known additive contribution that naturally arises due to degenerate pairs of points. In particular, we show that the true shot noise contribution cannot have a `non-Poissonian' value, even though all point processes with non-trivial two-point statistics are non-Poissonian. Apparent deviations from the `Poissonian' value can arise when significant correlations or anti-correlations are localised on small spatial scales. However, such deviations always correspond to a physical difference in two-point statistics, not a difference in noise. In the context of simulations, if clustering is treated as the tracer of a discretised underlying density field, any sub- or super-Poissonian sampling of the tracer induces such small-scale modifications and vice versa; we show this explicitly using recent innovations in angular power spectrum estimation from discrete catalogues. Finally, we show that the full covariance of clustering power spectra can also be computed explicitly: it depends only on the two-, three- and four-point statistics of the point process. The usual Gaussian covariance approximation appears as one term in the shot noise contribution, which is non-diagonal even for Gaussian random fields and Poisson sampling.

astro-ph.CO

Digital quantum magnetism on a trapped-ion quantum computer

Digital quantum matter -- realized when discrete quantum gates approximate continuous time evolution -- is susceptible to heating into chaotic, structureless states. If digitization errors are adequately suppressed, a long-lived transient regime of approximately energy-conserving dynamics can be observed on gate-based quantum computers. Conservation of energy, in turn, enables the exploration of a wide variety of complex behaviors observed in equilibrium systems, ranging from the nontrivial microscopic origins of thermalization itself to the stabilization of effective models hosting exotic emergent properties. Here, we use Quantinuum's system model H2 quantum computer to simulate digitized dynamics of the quantum Ising model, suppressing digitization errors well enough to observe thermalization on timescales that severely challenge classical simulation methods. Relaxation of an inhomogeneous state reveals an emergent hydrodynamics due to approximate energy conservation, and we compute the associated diffusion constant. By reprogramming our simulations to take place on a triangular lattice with periodic boundary conditions, we observe thermalization consistent with emergent gauge and topological constraints resulting from lattice frustration. Our results were enabled by continued advances in two-qubit gate quality (native partial entangler fidelities of $99.94(1)\%$), and establish digital quantum computers as powerful tools for studying (effectively) continuous-time dynamics.

quant-ph

Pixelization effects in cosmic shear angular power spectra

We conduct a comprehensive study into the impact of pixelization on cosmic shear, uncovering several sources of bias in standard pseudo-$C_\ell$ estimators based on discrete catalogues. We derive models that can bring residual biases to the percent level on small scales. We elucidate the impact of aliasing and the varying shape of HEALPix pixels on power spectra and show how the HEALPix pixel window function approximation is made in the discrete spin-2 setting. We propose several improvements to the standard estimator and its modelling, based on the principle that source positions and weights are to be considered fixed. We show how empty pixels can be accounted for either by modifying the mixing matrices or applying correction factors that we derive. We introduce an approximate interlacing scheme for the HEALPix grid and show that it can mitigate the effects of aliasing. We introduce bespoke pixel window functions adapted to the survey footprint and show that, for band-limited spectra, biases from using an isotropic window function can be effectively reduced to zero. This work partly intends to serve as a useful reference for pixel-related effects in angular power spectra, which are of relevance for ongoing and forthcoming lensing and clustering surveys.

astro-ph.CO

Mitigating baryon feedback bias in cosmic shear through a theoretical error covariance in the matter power spectrum

Forthcoming cosmic shear surveys will make precise measurements of the matter density field down to very small scales, scales which are dominated by baryon feedback. The modelling of baryon feedback is crucial to ensure unbiased cosmological parameter constraints; the most efficient approach is to use analytic models, but these are limited by how well they can capture the physics of baryon feedback. We investigate the fitting and residual errors of various baryon feedback models to a suite of hydrodynamic simulations, and propagate these to cosmological parameter constraints for cosmic shear. We present an alternative formalism to binary scale-cuts through the use of a theoretical error covariance, which is a well-motivated alternative using errors in the power spectrum modelling itself. We depart from previous works by modelling baryonic feedback errors directly in the matter power spectrum, which is the natural basis to do so and thus preserves information in the lensing kernels. When including angular multipoles up to $\ell_{\mathrm{max}} = 5000$, and assuming Euclid-like survey properties, we find that even multi-parameter models of baryon feedback can introduce significant levels of bias. In contrast, our theoretical error reduces the bias in $\Omega_{\mathrm{m}}$ and $S_{8}$ to acceptable levels, with only a modest increase in parameter variances. The theoretical error approach bypasses the need to directly determine the per-bin $\ell_{\mathrm{max}}$ values, as it naturally suppresses the biassing small-scale information. We also present a detailed study of how flexible HMCode-2020, a widely-used non-linear and baryonic feedback model, is at fitting a range of hydrodynamical simulations.

astro-ph.CO

The computational power of random quantum circuits in arbitrary geometries

Empirical evidence for a gap between the computational powers of classical and quantum computers has been provided by experiments that sample the output distributions of two-dimensional quantum circuits. Many attempts to close this gap have utilized classical simulations based on tensor network techniques, and their limitations shed light on the improvements to quantum hardware required to frustrate classical simulability. In particular, quantum computers having in excess of $\sim 50$ qubits are primarily vulnerable to classical simulation due to restrictions on their gate fidelity and their connectivity, the latter determining how many gates are required (and therefore how much infidelity is suffered) in generating highly-entangled states. Here, we describe recent hardware upgrades to Quantinuum's H2 quantum computer enabling it to operate on up to $56$ qubits with arbitrary connectivity and $99.843(5)\%$ two-qubit gate fidelity. Utilizing the flexible connectivity of H2, we present data from random circuit sampling in highly connected geometries, doing so at unprecedented fidelities and a scale that appears to be beyond the capabilities of state-of-the-art classical algorithms. The considerable difficulty of classically simulating H2 is likely limited only by qubit number, demonstrating the promise and scalability of the QCCD architecture as continued progress is made towards building larger machines.

quant-ph

Confronting primordial black holes with LIGO-Virgo-KAGRA and the Einstein Telescope

The detection of gravitational waves (GWs) from binary black hole (BBH) coalescences by the LIGO-Virgo-KAGRA (LVK) Collaboration has raised fundamental questions about the genesis of these events. In this chapter, we explore the possibility that PBHs, proposed candidates for dark matter, may serve as the progenitors of the BBHs observed by LVK. Employing a Bayesian analysis, we constrain the PBH model using the LVK third GW Transient Catalog (GWTC-3), revealing that stellar-mass PBHs cannot dominate cold dark matter. Considering a mixed population of astrophysical black holes (ABHs) and PBHs, we determine that approximately $1/4$ of the detectable events in the GWTC-3 can be attributed to PBH binaries. We also forecast detectable event rate distributions for PBH and ABH binaries by the third-generation ground-based GW detectors, such as the Einstein Telescope, offering a potential avenue to distinguish PBHs from ABHs based on their distinct redshift evolutions.

astro-ph.CO

Arrow's Impossibility Theorem: Computability in Social Choice Theory

Arrow's Impossibility Theorem establishes bounds on what we can require from voting systems. Given satisfaction of a small collection of "fairness" axioms, it shows votes can only exist as dictatorships in which one voter determines all outcomes. Votes are modelled as maps from a collection of partial orders, the preferences of voters, to a single verdict which is another aggregated partial ordering. This result is classic and has an extension called the Possibility Theorem that shows these dictatorships needn't exist with infinite voter sets. Mihara extends this work by examining the computability of each of these results. He found that the only voting systems that are in any sense computable are necessarily dictatorial, which takes away from the usefulness of the Possibility Theorem. In this paper we primarily survey the results of Mihara, focusing not on applied consequences, as much of the surrounding literature does, but going into greater details on the underlying Mathematics and Computability of the proofs. We give detailed exposition on the methods used and introduce all notation. We first see complete proofs of the classical results and a sufficient introduction to computability that an unfamiliar reader should be able to follow without prior knowledge of the field. We then expand into Mihara's results, and using our established knowledge of computability show the problems with trying to compute non-dictatorial social welfare functions. This involves introducing an extended definition of computability called pairwise computability.

math.LO

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