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DOE OSTI2021

The Markov gap for geometric reflected entropy

The reflected entropy S R (A : B) of a density matrix ρ AB is a bipartite correlation measure lower-bounded by the quantum mutual information I(A : B). In holographic states satisfying the quantum extremal surface formula, where the reflected entropy is related to the area of the entanglement wedge cross-section, there is often an order-N 2 gap between S R and I. We provide an information-theoretic interpretation of this gap by observing that S R - I is related to the fidelity of a particular Markov recovery problem that is impossible in any state whose entanglement wedge cross-section has a nonempty boundary; for this reason, we call the quantity S R - I the Markov gap. We then prove that for time-symmetric states in pure AdS 3 gravity, the Markov gap is universally lower bounded by log(2)ℓ AdS /2G N times the number of endpoints of the cross-section. We provide evidence that this lower bound continues to hold in the presence of bulk matter, and comment on how it might generalize above three bulk dimensions. Finally, we explore the Markov recovery problem controlling S R - I using fixed area states. This analysis involves deriving a formula for the quantum fidelity — in fact, for all the sandwiched Rényi relative entropies — between fixed area states with one versus two fixed areas, which may be of independent interest. We discuss, throughout the paper, connections to the general theory of multipartite entanglement in holography.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Quantum Extremal Surfaces and the Holographic Entropy Cone

Quantum states with geometric duals are known to satisfy a stricter set of entropy inequalities than those obeyed by general quantum systems. The set of allowed entropies derived using the Ryu-Takayanagi (RT) formula defines the Holographic Entropy Cone (HEC). These inequalities are no longer satisfied once general quantum corrections are included by employing the Quantum Extremal Surface (QES) prescription. Nevertheless, the structure of the QES formula allows for a controlled study of how quantum contributions from bulk entropies interplay with HEC inequalities. In this paper, we initiate an exploration of this problem by relating bulk entropy constraints to boundary entropy inequalities. In particular, we show that requiring the bulk entropies to satisfy the HEC implies that the boundary entropies also satisfy the HEC. Further, we also show that requiring the bulk entropies to obey monogamy of mutual information (MMI) implies the boundary entropies also obey MMI.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Transient anisotropic kernel for probabilistic learning on manifolds

PLoM (Probabilistic Learning on Manifolds) is a method introduced in 2016 for handling small training datasets by projecting an Itô equation from a stochastic dissipative Hamiltonian dynamical system, acting as the MCMC generator, for which the KDE-estimated probability measure with the training dataset is the invariant measure. PLoM performs a projection on a reduced-order vector basis related to the training dataset, using the diffusion maps (DMAPS) basis constructed with a time-independent isotropic kernel. In this paper, we propose a new ISDE projection vector basis built from a transient anisotropic kernel, providing an alternative to the DMAPS basis to improve statistical surrogates for stochastic manifolds with heterogeneous data. The construction ensures that for times near the initial time, the DMAPS basis coincides with the transient basis. For larger times, the differences between the two bases are characterized by the angle of their spanned vector subspaces. The optimal instant yielding the optimal transient basis is determined using an estimation of mutual information from Information Theory, which is normalized by the entropy estimation to account for the effects of the number of realizations used in the estimations. Consequently, this new vector basis better represents statistical dependencies in the learned probability measure for any dimension. Three applications with varying levels of statistical complexity and data heterogeneity validate the proposed theory, showing that the transient anisotropic kernel improves the learned probability measure.

Diffusion maps↗
DOE OSTI2025

DOME: Directional medical embedding vectors from Electronic Health Records

Motivation: The increasing availability of Electronic Health Record (EHR) systems has created enormous potential for translational research. Recent developments in representation learning techniques have led to effective large-scale representations of EHR concepts along with knowledge graphs that empower downstream EHR studies. However, most existing methods require training with patient-level data, limiting their abilities to expand the training with multi-institutional EHR data. On the other hand, scalable approaches that only require summary-level data do not incorporate temporal dependencies between concepts. Methods: We introduce a DirectiOnal Medical Embedding (DOME) algorithm to encode temporally directional relationships between medical concepts, using summary-level EHR data. Specifically, DOME first aggregates patient-level EHR data into an asymmetric co-occurrence matrix. Then it computes two Positive Pointwise Mutual Information (PPMI) matrices to correspondingly encode the pairwise prior and posterior dependencies between medical concepts. Following that, a joint matrix factorization is performed on the two PPMI matrices, which results in three vectors for each concept: a semantic embedding and two directional context embeddings. They collectively provide a comprehensive depiction of the temporal relationship between EHR concepts. Results: We highlight the advantages and translational potential of DOME through three sets of validation studies. First, DOME consistently improves existing direction-agnostic embedding vectors for disease risk prediction in several diseases, for example achieving a relative gain of 5.5% in the area under the receiver operating characteristic (AUROC) for lung cancer. Second, DOME excels in directional drug-disease relationship inference by successfully differentiating between drug side effects and indications, correspondingly achieving relative AUROC gain over the state-of-the-art methods by 10.8% and 6.6%. Finally, DOME effectively constructs directional knowledge graphs, which distinguish disease risk factors from comorbidities, thereby revealing disease progression trajectories. The source codes are provided at https://github.com/celehs/Directional-EHRembedding.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

Ensemble variational Fokker-Planck methods for data assimilation

Particle flow filters solve Bayesian inference problems by smoothly transforming a set of particles into samples from the posterior distribution. Particles move in state space under the flow of an McKean-Vlasov-Itˆo process. This work introduces the Variational Fokker-Planck (VFP) framework for data assimilation, a general approach that includes previously known particle flow filters as special cases. The McKean-Vlasov-Itˆo process that transforms particles is defined via an optimal drift that depends on the selected diffusion term. It is established that the underlying probability density - sampled by the ensemble of particles - converges to the Bayesian posterior probability density. For a finite number of particles the optimal drift contains a regularization term that nudges particles toward becoming independent random variables. Based on this analysis, we derive computationally-feasible approximate regularization approaches that penalize the mutual information between pairs of particles, and avoid particle collapse. Moreover, the diffusion plays a role akin to a particle rejuvenation approach that aims to alleviate particle collapse. The VFP framework is very flexible. Different assumptions on prior and intermediate probability distributions can be used to implement the optimal drift, and localization and covariance shrinkage can be applied to alleviate the curse of dimensionality. A robust implicit-explicit method is discussed for the efficient integration of stiff McKean- Vlasov-Itˆo processes. Here, the effectiveness of the VFP framework is demonstrated on three progressively more challenging test problems, namely the Lorenz ’63, Lorenz ’96 and the quasi-geostrophic equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Energy consumption and cooperation for optimal sensing

Abstract The reliable detection of environmental molecules in the presence of noise is an important cellular function, yet the underlying computational mechanisms are not well understood. We introduce a model of two interacting sensors which allows for the principled exploration of signal statistics, cooperation strategies and the role of energy consumption in optimal sensing, quantified through the mutual information between the signal and the sensors. Here we report that in general the optimal sensing strategy depends both on the noise level and the statistics of the signals. For joint, correlated signals, energy consuming (nonequilibrium), asymmetric couplings result in maximum information gain in the low-noise, high-signal-correlation limit. Surprisingly we also find that energy consumption is not always required for optimal sensing. We generalise our model to incorporate time integration of the sensor state by a population of readout molecules, and demonstrate that sensor interaction and energy consumption remain important for optimal sensing.

Ngampruetikorn, Vudtiwat↗
DOE OSTI2022

Small-world complex network generation on a digital quantum processor

Abstract Quantum cellular automata (QCA) evolve qubits in a quantum circuit depending only on the states of their neighborhoods and model how rich physical complexity can emerge from a simple set of underlying dynamical rules. The inability of classical computers to simulate large quantum systems hinders the elucidation of quantum cellular automata, but quantum computers offer an ideal simulation platform. Here, we experimentally realize QCA on a digital quantum processor, simulating a one-dimensional Goldilocks rule on chains of up to 23 superconducting qubits. We calculate calibrated and error-mitigated population dynamics and complex network measures, which indicate the formation of small-world mutual information networks. These networks decohere at fixed circuit depth independent of system size, the largest of which corresponding to 1,056 two-qubit gates. Such computations may enable the employment of QCA in applications like the simulation of strongly-correlated matter or beyond-classical computational demonstrations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Variational quantum eigensolver with reduced circuit complexity

Abstract The variational quantum eigensolver (VQE) is one of the most promising algorithms to find eigenstates of a given Hamiltonian on noisy intermediate-scale quantum devices (NISQ). The practical realization is limited by the complexity of quantum circuits. Here we present an approach to reduce quantum circuit complexity in VQE for electronic structure calculations. Our ClusterVQE algorithm splits the initial qubit space into clusters which are further distributed on individual (shallower) quantum circuits. The clusters are obtained based on mutual information reflecting maximal entanglement between qubits, whereas inter-cluster correlation is taken into account via a new “dressed” Hamiltonian. ClusterVQE therefore allows exact simulation of the problem by using fewer qubits and shallower circuit depth at the cost of additional classical resources, making it a potential leader for quantum chemistry simulations on NISQ devices. Proof-of-principle demonstrations are presented for several molecular systems based on quantum simulators as well as IBM quantum devices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Fluctuating hydrodynamics of chiral active fluids

Active materials are characterized by continuous injection of energy at the microscopic level and typically cannot be adequately described by equilibrium thermodynamics. Here we study a class of active fluids in which equilibrium-like properties emerge when fluctuating and activated degrees of freedom are statistically decoupled, such that their mutual information is negligible. We analyse three paradigmatic systems: chiral active fluids composed of spinning frictional particles that are free to translate, oscillating granular gases and active Brownian rollers. In all of these systems, a single effective temperature generated by activity parameterizes both the equation of state and the emergent Boltzmann statistics. The same effective temperature, renormalized by velocity correlations, relates viscosities to steady-state stress fluctuations via a Green–Kubo relation. To rationalize these observations, we develop a theory for the fluctuating hydrodynamics of these non-equilibrium fluids and validate it through large-scale molecular dynamics simulations. Our work sheds light on the microscopic origin of odd viscosities and stress fluctuations characteristic of parity-violating fluids, in which mirror symmetry and detailed balance are broken.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2022

Conformational spread drives the evolution of the calcium–calmodulin protein kinase II

The calcium calmodulin (Ca 2+ /CaM) dependent protein kinase II (CaMKII) decodes Ca 2+ frequency oscillations. The CaMKIIα isoform is predominantly expressed in the brain and has a central role in learning. I matched residue and organismal evolution with collective motions deduced from the atomic structure of the human CaMKIIα holoenzyme to learn how its ring architecture abets function. Protein dynamic simulations showed its peripheral kinase domains (KDs) are conformationally coupled via lateral spread along the central hub. The underlying β-sheet motions in the hub or association domain (AD) were deconvolved into dynamic couplings based on mutual information. They mapped onto a coevolved residue network to partition the AD into two distinct sectors. A second, energetically stressed sector was added to ancient bacterial enzyme dimers for assembly of the ringed hub. The continued evolution of the holoenzyme after AD–KD fusion targeted the sector’s ring contacts coupled to the KD. Among isoforms, the α isoform emerged last and, it alone, mutated rapidly after the poikilotherm–homeotherm jump to match the evolution of memory. The correlation between dynamics and evolution of the CaMKII AD argues single residue substitutions fine-tune hub conformational spread. The fine-tuning could increase CaMKIIα Ca 2+ frequency response range for complex learning functions.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Uncertainty-Aware and Explainable Human Error Detection in the Operation of Nuclear Power Plants

The timely and accurate identification of incidents, such as human factor error, is important to restore nuclear power plants (NPPs) to a stable state. However, the identification of abnormal operating conditions is difficult because of the existence of multiple scenarios. In addition, to implement mitigation actions rapidly after an incident occurs, operators must accurately identify an incident by monitoring the trends of many variables. The mental burden posed by this can increase human error and cause failure in identifying incidents. Failure to identify incidents directly results in erroneous mitigation measures, which are detrimental to NPPs. In this study, we leverage uncertainty-aware models to identify such errors and thereby increase the chances of mitigating them. We use the data collected from a physical test bed. The goal is to identify both certain and accurate models. For this, the two main aspects of focus in this study are explainable artificial intelligence (XAI) and uncertainty quantification (UQ). While XAI elucidates the decision pathway, UQ evaluates decision reliability. Their integration paints a comprehensive picture, signifying that understanding decisions and their confidence should be interlinked. Thus, in this study we leverage UQ measures (e.g. entropy and mutual information) along with Shapley additive explanations to gain insights into the features contributing to both accuracy and uncertainty in error identification. Furthermore, our results show that uncertainty-aware models combined with XAI tools can explain the artificial intelligence–prescribed decisions, with the potential of better explaining errors for the operators.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2023

Diel, seasonal, and inter-annual variation in carbon dioxide effluxes from lakes and reservoirs

Abstract Accounting for temporal changes in carbon dioxide (CO 2 ) effluxes from freshwaters remains a challenge for global and regional carbon budgets. Here, we synthesize 171 site-months of flux measurements of CO 2 based on the eddy covariance method from 13 lakes and reservoirs in the Northern Hemisphere, and quantify dynamics at multiple temporal scales. We found pronounced sub-annual variability in CO 2 flux at all sites. By accounting for diel variation, only 11% of site-months were net daily sinks of CO 2 . Annual CO 2 emissions had an average of 25% (range 3%–58%) interannual variation. Similar to studies on streams, nighttime emissions regularly exceeded daytime emissions. Biophysical regulations of CO 2 flux variability were delineated through mutual information analysis. Sample analysis of CO 2 fluxes indicate the importance of continuous measurements. Better characterization of short- and long-term variability is necessary to understand and improve detection of temporal changes of CO 2 fluxes in response to natural and anthropogenic drivers. Our results indicate that existing global lake carbon budgets relying primarily on daytime measurements yield underestimates of net emissions.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Predicting the von Neumann entanglement entropy using a graph neural network

Calculating the von Neumann entanglement entropy from experimental data is challenging due to its dependence on the complete wavefunction, forcing reliance on approximations such as classical mutual information (MI). We propose a machine learning approach using a graph neural network to predict the von Neumann entropy directly from experimentally accessible bitstrings. We test this approach on a Rydberg ladder system and achieve a mean absolute error of $3.6\,\times 10^{-3}$ when evaluating within the training range on a dataset with entropy values ranging from 0 to 1.9. The model achieves a mean absolute percentage error of 1.44% and outperforms MI-based bounds. When tested beyond the training range, the model maintains reasonable accuracy. Furthermore, we demonstrate that fine-tuning the model with small datasets significantly improves performance on data outside the original training range.

graph neural networks↗
DOE OSTI2020

Connecting SDSS central galaxies to their host haloes using total satellite luminosity

ABSTRACT The total luminosity of satellite galaxies around a central galaxy, Lsat, is a powerful metric for probing dark matter haloes. We utilize data from the Sloan Digital Sky Survey and DESI Legacy Imaging Surveys to explore the relationship between Lsat and galaxy properties for a sample of 117 966 central galaxies with z ≤ 0.15. At fixed stellar mass, we find that every galaxy property we explore correlates with Lsat, suggesting that dark matter haloes can influence them. We quantify these correlations by computing the mutual information between Lsat and secondary properties and explore how this varies as a function of stellar mass and star-formation activity. We find that absolute r-band magnitude correlates more strongly with Lsat than stellar mass across all galaxy populations; and that effective radius, velocity dispersion, and Sérsic index do so as well for star-forming and quiescent galaxies. Lsat is influenced by the mass of the host halo as well as the halo formation history, with younger haloes having higher Lsat. Lsat cannot distinguish between these two effects, but measurements of galaxy large-scale environment can break this degeneracy. For star-forming centrals, Reff, σv, and Sérsic index all correlate with large-scale density, implying that the halo age affects these properties. For quiescent galaxies, all secondary properties are independent of environment, implying that correlations with Lsat are driven only by halo mass. These results are a significant step forward in quantifying the extent of the galaxy–halo connection, and present a new test of galaxy formation models.

Alpaslan, Mehmet↗
DOE OSTI2020

Systematically localizable operators for quantum simulations of quantum field theories

Correlations and measures of entanglement in ground-state wave functions of relativistic quantum field theories are spatially localized over length scales set by the mass of the field. We utilize this localization to design digital quantum circuits for preparing the ground states of lattice scalar quantum field theories. Controlled rotations that are exponentially localized in their position-space extent are found to provide exponentially convergent wave function fidelity. These angles scale with the correlation between sites and the classical two-point correlation function, as opposed to the more localized mutual information or the hyperlocalized (1×1)-site negativity. We anticipate that further investigations will uncover quantum circuit designs with controlled rotations dictated by the measures of entanglement. This work is expected to impact quantum simulations of systems of importance to nuclear physics, high-energy physics, and basic energy sciences research.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Number of bits returned by a quantum estimation

We give two upper bounds to the mutual information in arbitrary quantum estimation strategies. The first is based on some simple Fourier properties of the estimation apparatus. The second is derived using the first, but, interestingly, depends only on the Fisher information of the parameter, so it is valid even beyond quantum estimation. We illustrate the usefulness of these bounds by characterizing the quantum phase estimation algorithm in the presence of noise. In addition, for the noiseless case, we extend the analysis beyond applying the bound and we discuss the optimal entangled and adaptive strategies, clarifying inaccuracies appearing on this topic in the literature.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Measurement-induced criticality in random quantum circuits

We investigate the critical behavior of the entanglement transition induced by projective measurements in (Haar) random unitary quantum circuits. Using a replica approach, we map the calculation of the entanglement entropies in such circuits onto a two-dimensional statistical-mechanics model. In this language, the area- to volume-law entanglement transition can be interpreted as an ordering transition in the statistical-mechanics model. We derive the general scaling properties of the entanglement entropies and mutual information near the transition using conformal invariance. We analyze in detail the limit of infinite on-site Hilbert space dimension in which the statistical-mechanics model maps onto percolation. In particular, we compute the exact value of the universal coefficient of the logarithm of subsystem size in the n th Rényi entropies for n ≥ 1 in this limit using relatively recent results for the conformal field theory describing the critical theory of two-dimensional (2D) percolation, and we discuss how to access the generic transition at finite on-site Hilbert space dimension from this limit, which is in a universality class different from 2D percolation. Here, we also comment on the relation to the entanglement transition in random tensor networks, studied previously in Vasseur et al. [Phys. Rev. B 100, 134203 (2019)].

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Universal tripartite entanglement signature of ungappable edge states

Gapped two-dimensional topological phases can feature ungappable edge states which are robust even in the absence of protecting symmetries. In this Letter we argue that a multipartite entanglement measure recently proposed in the context of holography, the Markov gap, provides a universal diagnostic of ungappable edge states. Defined as a difference of the reflected entropy and mutual information h(A:B)=S R (A:B)-I(A:B) between two parties, we argue that for A,B being adjacent subregions in the bulk h=$\frac{c+}{3}$ ln 2, where c + is the minimal total central charge of the boundary theory. As evidence, we prove that h=0 for string-net models and numerically verify that h=$\frac{|C|}{3}$ ln 2 for a Chern-C insulator. Our Letter establishes a unique bulk entanglement criteria for the presence of a conformal field theory on the boundary.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗