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The most advanced techniques using fault-tolerant quantum computers to estimate the ground-state energy of a chemical Hamiltonian involve compression of the Coulomb operator through tensor factorizations, enabling efficient block-encodings of the Hamiltonian. A natural challenge of these methods is the degree to which block-encoding costs can be reduced. We address this challenge through the technique of spectrum amplification, which magnifies the spectrum of the low-energy states of Hamiltonians that can be expressed as sums of squares. Spectrum amplification enables estimating ground-state energies with significantly improved cost scaling in the block encoding normalization factor $\Lambda$ to just $\sqrt{2\Lambda E_{\text{gap}}}$, where $E_{\text{gap}} \ll \Lambda$ is the lowest energy of the sum-of-squares Hamiltonian. To achieve this, we show that sum-of-squares representations of the electronic structure Hamiltonian are efficiently computable by a family of classical simulation techniques that approximate the ground-state energy from below. In order to further optimize, we also develop a novel factorization that provides a trade-off between the two leading Coulomb integral factorization schemes -- namely, double factorization and tensor hypercontraction -- that when combined with spectrum amplification yields a factor of 4 to 195 speedup over the state of the art in ground-state energy estimation for models of Iron-Sulfur complexes and a CO$_{2}$-fixation catalyst.

Current- and next-generation Cosmic Microwave Background (CMB) experiments will measure polarization anisotropies with unprecedented sensitivities. The need for high precision in these measurements underscores the importance of gaining a comprehensive understanding of instrument properties, with a particular emphasis on the study of the beam properties and, in particular, their polarization characteristics, and the measurement of the polarization angle. In this context, a major challenge lies in the scarcity of millimeter polarized astrophysical sources with sufficient brightness and calibration knowledge to meet the stringent accuracy requirements of future CMB missions. This led to the development of a drone-borne calibration source designed for frequency band centered on approximately 90 GHz band, matching a commonly used channel in ground based CMB measurements. The PROTOtype CALibrator for Cosmology, PROTOCALC, has undergone thorough in-lab testing, and its properties have been subsequently modeled through simulation software integrated into the standard Simons Observatory (SO) analysis pipeline. Moreover, the PROTOCALC system has been tested in the field, having been deployed twice on calibration campaigns with CMB telescopes in the Atacama desert. The data collected constrain the roll angle of the source with a statistical accuracy of $0.045^\circ$.

Graph Neural Networks (GNNs) are routinely used in molecular physics, social sciences, and economics to model many-body interactions in graph-like systems. However, GNNs are inherently local and can suffer from information flow bottlenecks. This is particularly problematic when modeling large molecular systems, where dispersion forces and local electric field variations drive collective structural changes. Existing solutions face challenges related to computational cost and scalability. We introduce RANGE, a model-agnostic framework that employs an attention-based aggregation-broadcast mechanism that significantly reduces oversquashing effects, and achieves remarkable accuracy in capturing long-range interactions at a negligible computational cost. Notably, RANGE is the first virtual-node message-passing implementation to integrate attention with positional encodings and regularization to dynamically expand virtual representations. This work lays the foundation for next-generation of machine-learned force fields, offering accurate and efficient modeling of long-range interactions for simulating large molecular systems.

Responsible disclosure limitation is an iterative exercise in risk assessment and mitigation. From time to time, as disclosure risks grow and evolve and as data users' needs change, agencies must consider redesigning the disclosure avoidance system(s) they use. Discussions about candidate systems often conflate inherent features of those systems with implementation decisions independent of those systems. For example, a system's ability to calibrate the strength of protection to suit the underlying disclosure risk of the data (e.g., by varying suppression thresholds), is a worthwhile feature regardless of the independent decision about how much protection is actually necessary. Having a principled discussion of candidate disclosure avoidance systems requires a framework for distinguishing these inherent features of the systems from the implementation decisions that need to be made independent of the system selected. For statistical agencies, this framework must also reflect the applied nature of these systems, acknowledging that candidate systems need to be adaptable to requirements stemming from the legal, scientific, resource, and stakeholder environments within which they would be operating. This paper proposes such a framework. No approach will be perfectly adaptable to every potential system requirement. Because the selection of some methodologies over others may constrain the resulting systems' efficiency and flexibility to adapt to particular statistical product specifications, data user needs, or disclosure risks, agencies may approach these choices in an iterative fashion, adapting system requirements, product specifications, and implementation parameters as necessary to ensure the resulting quality of the statistical product.

Radiotherapy is a crucial cancer treatment that demands precise planning to balance tumor eradication and preservation of healthy tissue. Traditional treatment planning (TP) is iterative, time-consuming, and reliant on human expertise, which can potentially introduce variability and inefficiency. We propose a novel framework to transform a large multimodal foundation model (MLM) into an action model for TP using a few-shot reinforcement learning (RL) approach. Our method leverages the MLM's extensive pre-existing knowledge of physics, radiation, and anatomy, enhancing it through a few-shot learning process. This allows the model to iteratively improve treatment plans using a Monte Carlo simulator. Our results demonstrate that this method outperforms conventional RL-based approaches in both quality and efficiency, achieving higher reward scores and more optimal dose distributions in simulations on prostate cancer data. This proof-of-concept suggests a promising direction for integrating advanced AI models into clinical workflows, potentially enhancing the speed, quality, and standardization of radiotherapy treatment planning.

We present a transfer function-based method to estimate angular power spectra from filtered maps for cosmic microwave background (CMB) surveys. This is especially relevant for experiments targeting the faint primordial gravitational wave signatures in CMB polarisation at large scales, such as the Simons Observatory (SO) small aperture telescopes. While timestreams can be filtered to mitigate the contamination from low-frequency noise, usual methods that calculate the mode coupling at individual multipoles can be challenging for experiments covering large sky areas or reaching few-arcminute resolution. The method we present here, although approximate, is more practical and faster for larger data volumes. We validate it through the use of simulated observations approximating the first year of SO data, going from half-wave plate-modulated timestreams to maps, and using simulations to estimate the mixing of polarisation modes induced by an example of time-domain filtering. We show its performance through an example null test and with an end-to-end pipeline that performs inference on cosmological parameters, including the tensor-to-scalar ratio $r$. The performance demonstration uses simulated observations at multiple frequency bands. We find that the method can recover unbiased parameters for our simulated noise levels., Comment: 15 figures, 2 tables. Comments are welcome

We present measurements of large-scale cosmic microwave background (CMB) E-mode polarization from the Cosmology Large Angular Scale Surveyor (CLASS) 90 GHz data. Using 115 det-yr of observations collected through 2024 with a variable-delay polarization modulator, we achieved a polarization sensitivity of $78\,\mathrm{\mu K\,arcmin}$, comparable to Planck at similar frequencies (100 and 143 GHz). The analysis demonstrates effective mitigation of systematic errors and addresses challenges to large-angular-scale power recovery posed by time-domain filtering in maximum-likelihood map-making. A novel implementation of the pixel-space transfer matrix is introduced, which enables efficient filtering simulations and bias correction in the power spectrum using the quadratic cross-spectrum estimator. Overall, we achieved an unbiased time-domain filtering correction to recover the largest angular scale polarization, with the only power deficit, arising from map-making non-linearity, being characterized as less than $3\%$. Through cross-correlation with Planck, we detected the cosmic reionization at $99.4\%$ significance and measured the reionization optical depth $\tau=0.053^{+0.018}_{-0.019}$, marking the first ground-based attempt at such a measurement. At intermediate angular scales ($\ell>30$), our results, both independently and in cross-correlation with Planck, remain fully consistent with Planck's measurements., Comment: 24 pages, 19 figures, 3 tables; submitted to ApJ

This document proposes an algorithm for a mobile application designed to monitor multidimensional child growth through digital phenotyping. Digital phenotyping offers a unique opportunity to collect and analyze high-frequency data in real time, capturing behavioral, psychological, and physiological states of children in naturalistic settings. Traditional models of child growth primarily focus on physical metrics, often overlooking multidimensional aspects such as emotional, social, and cognitive development. In this paper, we introduce a Bayesian artificial intelligence (AI) algorithm that leverages digital phenotyping to create a Multidimensional Index of Child Growth (MICG). This index integrates data from various dimensions of child development, including physical, emotional, cognitive, and environmental factors. By incorporating probabilistic modeling, the proposed algorithm dynamically updates its learning based on data collected by the mobile app used by mothers and children. The app also infers uncertainty from response times, adjusting the importance of each dimension of child growth accordingly. Our contribution applies state-of-the-art technology to track multidimensional child development, enabling families and healthcare providers to make more informed decisions in real time., Comment: 15 pages, 0 figures

This study explores a Bayesian algorithmic approach to personalized fragrance recommendation by integrating hierarchical Relevance Vector Machines (RVM) and Jungian personality archetypes. The paper proposes a structured model that links individual scent preferences for top, middle, and base notes to personality traits derived from Jungian archetypes, such as the Hero, Caregiver, and Explorer, among others. The algorithm utilizes Bayesian updating to dynamically refine predictions as users interact with each fragrance note. This iterative process allows for the personalization of fragrance experiences based on prior data and personality assessments, leading to adaptive and interpretable recommendations. By combining psychological theory with Bayesian machine learning, this approach addresses the complexity of modeling individual preferences while capturing user-specific and population-level trends. The study highlights the potential of hierarchical Bayesian frameworks in creating customized olfactory experiences, informed by psychological and demographic factors, contributing to advancements in personalized product design and machine learning applications in sensory-based industries., Comment: 15 pages, 0 figures

The Workflows Community Summit gathered 111 participants from 18 countries to discuss emerging trends and challenges in scientific workflows, focusing on six key areas: time-sensitive workflows, AI-HPC convergence, multi-facility workflows, heterogeneous HPC environments, user experience, and FAIR computational workflows. The integration of AI and exascale computing has revolutionized scientific workflows, enabling higher-fidelity models and complex, time-sensitive processes, while introducing challenges in managing heterogeneous environments and multi-facility data dependencies. The rise of large language models is driving computational demands to zettaflop scales, necessitating modular, adaptable systems and cloud-service models to optimize resource utilization and ensure reproducibility. Multi-facility workflows present challenges in data movement, curation, and overcoming institutional silos, while diverse hardware architectures require integrating workflow considerations into early system design and developing standardized resource management tools. The summit emphasized improving user experience in workflow systems and ensuring FAIR workflows to enhance collaboration and accelerate scientific discovery. Key recommendations include developing standardized metrics for time-sensitive workflows, creating frameworks for cloud-HPC integration, implementing distributed-by-design workflow modeling, establishing multi-facility authentication protocols, and accelerating AI integration in HPC workflow management. The summit also called for comprehensive workflow benchmarks, workflow-specific UX principles, and a FAIR workflow maturity model, highlighting the need for continued collaboration in addressing the complex challenges posed by the convergence of AI, HPC, and multi-facility research environments.

At frequencies below 1\,Hz, fluctuations in atmospheric emission in the Chajnantor region in northern Chile are the primary source of interference for bolometric millimeter-wave observations. This paper focuses on the statistics of these fluctuations using measurements from the Atacama Cosmology Telescope (ACT) and the Atacama Pathfinder Experiment (APEX) water vapor radiometer. After introducing a method for separating atmospheric effects from other systematic effects, we present a direct measurement of the temporal outer scale of turbulence of $\tau_0\approx50$s corresponding to a spatial scale of $L_0\approx500$m. At smaller scales, the fluctuations are well described by the Kolmogorov 2/3 power law until, at yet smaller scales, the effects of beam smearing become important. As a part of this study, we present measurements of the atmosphere by the APEX radiometer over 20 years, focused on fluctuations in precipitable water vapor (PWV). We find that the 30-minute mean of the total PWV is not in general a robust estimator of the level of fluctuations. We show that the microwave frequency spectrum of these fluctuations is in good agreement with predictions by the \texttt{am} code for bands above 90~GHz. We then show that the variance of fluctuations in ACT's mm-wave bands correlates with the variance of fluctuations in PWV measured by APEX, even though the observatories are 6\,km apart and observe different lines of sight. We find that ACT's atmosphere-determined optical efficiencies are consistent with previous planet-based results., Comment: 13 pages plus appendix, 17 figures. Submitted to PRD

Quantum error correction provides a path to reach practical quantum computing by combining multiple physical qubits into a logical qubit, where the logical error rate is suppressed exponentially as more qubits are added. However, this exponential suppression only occurs if the physical error rate is below a critical threshold. In this work, we present two surface code memories operating below this threshold: a distance-7 code and a distance-5 code integrated with a real-time decoder. The logical error rate of our larger quantum memory is suppressed by a factor of $\Lambda$ = 2.14 $\pm$ 0.02 when increasing the code distance by two, culminating in a 101-qubit distance-7 code with 0.143% $\pm$ 0.003% error per cycle of error correction. This logical memory is also beyond break-even, exceeding its best physical qubit's lifetime by a factor of 2.4 $\pm$ 0.3. We maintain below-threshold performance when decoding in real time, achieving an average decoder latency of 63 $\mu$s at distance-5 up to a million cycles, with a cycle time of 1.1 $\mu$s. To probe the limits of our error-correction performance, we run repetition codes up to distance-29 and find that logical performance is limited by rare correlated error events occurring approximately once every hour, or 3 $\times$ 10$^9$ cycles. Our results present device performance that, if scaled, could realize the operational requirements of large scale fault-tolerant quantum algorithms., Comment: 10 pages, 4 figures, Supplementary Information

We define the Cartesian, Categorical, and Lexicographic, and Strong products of quantum graphs. We provide bounds on the quantum chromatic number of these products in terms of the quantum chromatic number of the factors. To adequately describe bounds on the lexicographic product of quantum graphs, we provide a notion of a quantum $b$-fold chromatic number for quantum graphs.

In this paper we present techniques to incrementally harvest and query arbitrary metadata from machine learning pipelines, without disrupting agile practices. We center our approach on the developer-favored technique for generating metadata -- log statements -- leveraging the fact that logging creates context. We show how hindsight logging allows such statements to be added and executed post-hoc, without requiring developer foresight. Relational views of incomplete metadata can be queried to dynamically materialize new metadata in bulk and on demand across multiple versions of workflows. This is done in a "metadata later" style, off the critical path of agile development. We realize these ideas in a system called FlorDB and demonstrate how the data context framework covers a range of both ad-hoc metadata as well as special cases treated today by bespoke feature stores and model repositories. Through a usage scenario -- including both ML and human feedback -- we illustrate how the component techniques come together to resolve classic software engineering trade-offs between agility and discipline.

Simulating quantum dynamics is one of the most important applications of quantum computers. Traditional approaches for quantum simulation involve preparing the full evolved state of the system and then measuring some physical quantity. Here, we present a different and novel approach to quantum simulation that uses a compressed quantum state that we call the ``shadow state''. The amplitudes of this shadow state are proportional to the time-dependent expectations of a specific set of operators of interest, and it evolves according to its own Schr\"odinger equation. This evolution can be simulated on a quantum computer efficiently under broad conditions. Applications of this approach to quantum simulation problems include simulating the dynamics of exponentially large systems of free fermions or free bosons, the latter example recovering a recent algorithm for simulating exponentially many classical harmonic oscillators. These simulations are hard for classical methods and also for traditional quantum approaches, as preparing the full states would require exponential resources. Shadow Hamiltonian simulation can also be extended to simulate expectations of more complex operators such as two-time correlators or Green's functions, and to study the evolution of operators themselves in the Heisenberg picture.

In the minimal Scotogenic model with fermionic dark matter, the neutrino Yukawa matrix is fine-tuned to satisfy current bounds on $\mu \rightarrow e \gamma$ while producing dark matter through thermal freeze-out. One way to avoid this bound is to open a new annihilation channel for dark matter (DM) with a scalar field that breaks the lepton number spontaneously. This introduces a physical Goldstone boson $a$, which can constitute a light relic and opens up the lepton flavor violating channel $\mu\rightarrow e a$. In this work, we introduce a model that contains the new annihilation channel for fermionic dark matter but avoids the introduction of the Goldstone boson by using a discrete $\mathbb{Z}_4$ instead of a continuous symmetry. In this way, cosmological constraints on the light relic and experimental limits on lepton flavor violating decays to the Goldstone boson are avoided. We analyze the experimental viability of the model, identifying the region of parameter space where lepton flavor violating constraints are not saturated, DM has the correct relic density, and DM direct detection experiments are sensitive to the DM candidate., Comment: 16 pages, 9 figures. A study of the scotogenic case was added. This version matches the publication in Physical Review D

Cosmic Microwave Background experiments need to measure polarization properties of the incoming radiation very accurately to achieve their scientific goals. As a result of that, it is necessary to properly characterize these instruments. However, there are not natural sources that can be used for this purpose. For this reason, we developed the PROTOtype CALibrator for Cosmology, PROTOCALC, which is a calibrator source designed for the 90 GHz band of these telescopes. This source is purely polarized and the direction of the polarization vector is known with an accuracy better than 0.1 deg. This source flew for the first time in May 2022 showing promising result., Comment: Presented at SPIE Astronomical Telescopes 2024. arXiv admin note: text overlap with arXiv:2207.07595

(abridged) The Atacama Large Aperture Submillimeter Telescope (AtLAST) is undergoing a design study for a large (50 meter) single-dish submm-wavelength Ritchey-Chr\'etien telescope to be located 5050 meters above sea level in the Atacama Desert in northern Chile. It will allow for observations covering 30 to 950 GHz. Observing at such high frequencies with a 50~m primary mirror will be challenging, and has never been attempted thus far. This observational capability demands exquisite control of systematics to ensure a reliable beam shape, and to mitigate the expected sidelobe levels. Among them, critical issues that large telescopes like AtLAST need to deal with are introduced by the panel gap pattern, the secondary mirror supporting struts, mirror deformations produced by thermal and gravitational effects, and Ruze scattering due to surface roughness. Proprietary software such as TICRA-Tools allows for full-wave, complex-field physical optics simulations taking into account these features. Such calculations can be computationally expensive since the mirror surfaces are gridded (meshed) into a fine array in which each element is treated as a current source. If the telescope size is large and the wavelengths are short this may lead to very long running times. Here we present a set of physical optics results that allow us to estimate the performance of the telescope in terms of beam shape, directivity, sidelobes level and stray light. We also discuss how we addressed the computational challenges, and provide caveats on how to shorten the run times. Above all, we conclude that the scattering effects from the gaps and tertiary support structure are minimal, and subdominant to the Ruze scattering., Comment: Submitted to SPIE Proceedings

In this work, firstly, we propose how to experimentally demonstrate the single photon steering phenomenon in a simple way. The quantum steering phenomenon was discovered by Erwin Schrodinger, who reason that the laws of quantum mechanics obliges us to admit that by suitable measurements taken on one of two entangled system, then the state of the other system can be determined and steered. On the other hand, the first proposal about the nonlocal property of a single photon focus on showing the Bell nonlocality by using the single-photon path entanglement. Here, we propose a new experimental scheme that, by incorporating and manipulating the internal degree of freedom (IDF) of the photon, easily demonstrate the nonlocal steering phenomenon of single-photon's states. The experimental set-up that we propose differs from those published in the quantum optics' literature to shown the single photon nonlocality, which generally use the path entanglement of photons and homodyne measurements. Secondly, by incorporating its IDF, we show that the single photon steering and the quantum mechanical interaction-free measurement (QM-IFM) are identical phenomena; we will argue that QM-IFM is just a particular instance of the single-photon steering. In short, both the single photon steering and QM-IFM (being identical phenomena) have a common cause: the nonlocality of the wave function. In conclusion, we have demonstrated that it is possible to produce a nonlocal phenomena by manipulating the single photon internal degree of freedom. On the other hand, this unification between steering and QM-IFM could establish a strong support to counterfactual quantum communication and computation., Comment: 26 pages, 7 figures. submitted. arXiv admin note: text overlap with arXiv:2109.01058

Interactive notebooks, such as Jupyter, have revolutionized the field of data science by providing an integrated environment for data, code, and documentation. However, their adoption by robotics researchers and model developers has been limited. This study investigates the logging and record-keeping practices of robotics researchers, drawing parallels to the pre-interactive notebook era of data science. Through interviews with robotics researchers, we identified the reliance on diverse and often incompatible tools for managing experimental data, leading to challenges in reproducibility and data traceability. Our findings reveal that robotics researchers can benefit from a specialized version of interactive notebooks that supports comprehensive data entry, continuous context capture, and agile data staging. We propose extending interactive notebooks to better serve the needs of robotics researchers by integrating features akin to traditional lab notebooks. This adaptation aims to enhance the organization, analysis, and reproducibility of experimental data in robotics, fostering a more streamlined and efficient research workflow.

We present the simulation of nuclear magnetic resonance (NMR) spectroscopy of small organic molecules with two promising quantum computing platforms, namely IBM's quantum processors based on superconducting qubits and IonQ's Aria trapped ion quantum computer addressed via Amazon Braket. We analyze the impact of noise on the obtained NMR spectra, and we formulate an effective decoherence rate that quantifies the threshold noise that our proposed algorithm can tolerate. Furthermore we showcase how our noise analysis allows us to improve the spectra. Our investigations pave the way to better employ such application-driven quantum tasks on current noisy quantum devices., Comment: 10 pages, 13 figures

Algorithmic cooling can be used to find correlated states of many-body quantum systems. It is based on quantum circuits that perform nonunitary operations, whose implementation can be challenging on near-term quantum computers. In this work we develop a method that uses inherent qubit noise to implement nonunitary operations and algorithmic cooling. In our approach, qubit decay during quantum computation is used to simulate dissipation of auxiliary-spin bath, which cools down a simulated system towards its ground state. We test the algorithm on IBM-Q devices and demonstrate the relaxation of system spins to ferromagnetic and antiferromagnetic ordering, controlled by the definition of the system Hamiltonian. The ordering is stable as long as the algorithm is run. We are able to perform cooling and state stabilization for global systems of up to three system spins and four auxiliary spins. Our work paves the way for useful quantum simulations of many-body quantum systems on near-term quantum computers., Comment: 19 pages, 12 figures in total: 11 pages main text with 6 figures

In multi-agent reinforcement learning (MARL), coordination plays a crucial role in enhancing agents' performance beyond what they could achieve through cooperation alone. The interdependence of agents' actions, coupled with the need for communication, leads to a domain where effective coordination is crucial. In this paper, we introduce and define $\textit{Multi-Agent Synchronization Tasks}$ (MSTs), a novel subset of multi-agent tasks. We describe one MST, that we call $\textit{Synchronized Predator-Prey}$, offering a detailed description that will serve as the basis for evaluating a selection of recent state-of-the-art (SOTA) MARL algorithms explicitly designed to address coordination challenges through the use of communication strategies. Furthermore, we present empirical evidence that reveals the limitations of the algorithms assessed to solve MSTs, demonstrating their inability to scale effectively beyond 2-agent coordination tasks in scenarios where communication is a requisite component. Finally, the results raise questions about the applicability of recent SOTA approaches for complex coordination tasks (i.e. MSTs) and prompt further exploration into the underlying causes of their limitations in this context., Comment: Adaptive Learning Agents Workshop at AAMAS 2024

We undertake a comprehensive study of structural properties of graph products of von Neumann algebras equipped with faithful, normal states, as well as properties of the graph products relative to subalgebras coming from induced subgraphs. Among the technical contributions in this paper include a complete bimodule calculation for subalgebras arising from subgraphs. As an application, we obtain a complete classification of when two subalgebras coming from induced subgraphs can be amenable relative to each other. We also give complete characterizations of when the graph product can be full, diffuse, or a factor. Our results are obtained in a broad generality, and we emphasize that they are new even in the tracial setting. They also allow us to deduce new results about when graph products of groups can be amenable relative to each other.

Graph independence (also known as $\epsilon$-independence or $\lambda$-independence) is a mixture of classical independence and free independence corresponding to graph products or groups and operator algebras. Using conjugation by certain random permutation matrices, we construct random matrix models for graph independence with amalgamation over the diagonal matrices. This yields a new probabilist,ic proof that graph products of sofic groups are sofic., Comment: 29 pages, multiple figures. Minor replacements, correcting typos etc. arXiv admin note: substantial text overlap with arXiv:2305.19463

We consider the task of simulating time evolution under a Hamiltonian $H$ within its low-energy subspace. Assuming access to a block-encoding of $H'=(H-E)/\lambda$ for some $E \in \mathbb R$, the goal is to implement an $\epsilon$-approximation to $e^{-itH}$ when the initial state is confined to the subspace corresponding to eigenvalues $[-1, -1+\Delta/\lambda]$ of $H'$. We present a quantum algorithm that uses $O(t\sqrt{\lambda\Gamma} + \sqrt{\lambda/\Gamma}\log(1/\epsilon))$ queries to the block-encoding for any $\Gamma$ such that $\Delta \leq \Gamma \leq \lambda$. When $\log(1/\epsilon) = o(t\lambda)$ and $\Delta/\lambda = o(1)$, this result improves over generic methods with query complexity $\Omega(t\lambda)$. Our quantum algorithm leverages spectral gap amplification and the quantum singular value transform. Using standard access models for $H$, we show that the ability to efficiently block-encode $H'$ is equivalent to $H$ being what we refer to as a "gap-amplifiable" Hamiltonian. This includes physically relevant examples such as frustration-free systems, and it encompasses all previously considered settings of low-energy simulation algorithms. We also provide lower bounds for low-energy simulation. In the worst case, we show that the low-energy condition cannot be used to improve the runtime of Hamiltonian simulation. For gap-amplifiable Hamiltonians, we prove that our algorithm is tight in the query model with respect to $t$, $\Delta$, and $\lambda$. In the practically relevant regime where $\log (1/\epsilon) = o(t\Delta)$ and $\Delta/\lambda = o(1)$, we also prove a matching lower bound in gate complexity (up to log factors). To establish the query lower bounds, we consider $\mathrm{PARITY}\circ\mathrm{OR}$ and degree bounds on trigonometric polynomials. To establish the lower bound on gate complexity, we use a circuit-to-Hamiltonian reduction acting on a low-energy state., Comment: 58 pages. Abstract shortened to fit within the arXiv limit