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Quantum Distributed Algorithms for Approximate Steiner Trees and Directed Minimum Spanning Trees​

We present two algorithms in the Quantum CONGEST- CLIQUE model of distributed computation that succeed with high probability; one for producing an approximately optimal Steiner Tree, and one for producing an exact directed minimum spanning tree, each of which uses O ̃(n 1/4 ) rounds of communication and O ̃(n 9/4 ) messages, achieving a lower asymptotic round and message complexity than any known algorithms in the classical CONGEST-CLIQUE model. At a high level, we achieve these results by combining classical algorithms with fast quantum subroutines. Additionally, we characterize the constants and logarithmic factors involved in our algorithms, as well as related classical algorithms, revealing that advances are needed to render both practical.

quantum computing↗

Wildfire Segmentation From Remotely Sensed Data Using Quantum-Compatible Conditional Vector Quantized-Variational Autoencoders

Wildfires represent a critical environmental hazard with multifaceted implications for ecosystems, communities, and public health [1]. The escalating frequency and intensity of wildfires globally have intensified the urgency for robust segmentation methodologies to facilitate effective mitigation, response, and recovery strategies [2]. Accurate wildfire segmentation is pivotal for delineating fire boundaries, assessing progression patterns, and prioritizing resource allocation during emergency scenarios. Furthermore, precise segmentation enables stakeholders, including policymakers, environmental scientists, and emergency responders, to formulate evidence-based strategies, thereby minimizing socio-economic disruptions and ecological degradation. Consequently, advancing wildfire segmentation techniques through innovative technological interventions remains a paramount research imperative. Although foundational in wildfire segmentation, traditional deterministic models exhibit inherent limitations that compromise their efficacy in dynamic and uncertain environments. These models often operate on rigid algorithms prioritizing deterministic classifications, thereby overlooking the inherent complexities and uncertainties associated with wildfire behavior and satellite data variability. Such deterministic frameworks tend to produce oversimplified representations that fail to capture the intricate nuances of evolving fire dynamics, spatial heterogeneity, and environmental interactions [1]. Consequently, the deterministic approach’s propensity for uncertainty collapsing [1, 3] hampers the accuracy, reliability, and applicability of segmentation outcomes in real-world scenarios. Contrastingly, stochastic models offer a more nuanced and adaptable framework for wildfire segmentation. By integrating probabilistic elements into the modeling paradigm, stochastic approaches, particularly probabilistic approaches such as variational auto encoders (VAEs) [4], facilitate comprehensive uncertainty assessment, enabling researchers to quantify and incorporate uncertainties into segmentation outcomes effectively. This probabilistic nature empowers stochastic models to encapsulate variability, account for data inconsistencies, and adapt to evolving environmental conditions, enhancing segmentation accuracy, reliability, and robustness. Embracing stochastic methodologies thus catalyzes advancements in wildfire science by fostering a more holistic, adaptive, and resilient segmentation framework. Despite VAEs demonstrating significant promise in various applications, they come with inherent limitations that have garnered attention within the machine learning community. One of the primary drawbacks lies in their reliance on static priors, which essentially assume a fixed distribution for latent variables, thereby limiting the model’s flexibility to capture complex data structures effectively [5]. This static nature leads to suboptimal representations, especially when dealing with complex and high-dimensional data. Additionally, VAEs often struggle with generating sharp and realistic samples, a phenomenon commonly referred to as mode collapse [5, 7, 6]. Furthermore, the optimization process in VAEs, which involves balancing the reconstruction loss and the regularization term, can sometimes be challenging to fine-tune [7]. In recent efforts to address these shortcomings, alternative approaches like Vector Quantized Variational Auto encoders(VQ-VAEs) [7], address the challenges by incorporating discrete latent variables and leveraging techniques that enhance the quality and diversity of generated samples while maintaining efficient training dynamics. VQ-VAEs propose a dynamic prior distribution generation mechanism that diverges from the static priors commonly associated with traditional VAEs. This dynamic approach allows for more adaptive and context-aware latent variable representations, thereby potentially capturing complex data structures more effectively. Unlike autoregressive prior models such as PixelCNN, which, despite their ability to model dependencies across data dimensions, suffer from significant computational inefficiencies and lack flexibility in handling diverse datasets. In our work, we propose to use a generative quantum-compatible approach to help alleviate the shortcomings of autoregressive prior model in VQ-VAEs. Restricted Boltzmann Machines (RBMs) are a viable alternative prior model that can learn prior distributions in a faster and more flexible manner. In this research endeavor, we meticulously curate a state-of-the-art dataset leveraging satellite MODIS data in conjunction with VIIRS fire masks, derived from Fire Radiative Power (FRP), thereby encapsulating diverse wildfire scenarios and environmental contexts. We developed a conditional VQ-VAE architecture with the RBM prior model that is trained in a supervised manner for segmenting wildfire masks. This innovative approach synergistically harnesses deep learning capabilities, enabling the generation of segmentation maps characterized by heightened precision, granularity, and contextual relevance. Furthermore, replacing the autoregressive prior learning method proposed by the original VQ-VAE with a prior density approximation via quantum-compatible RBM facilitates expedited inference processes, augments flexibility in prior sampling, optimizes computational efficiency and establishes a groundbreaking benchmark in wildfire segmentation methodologies.

quantum machine learning↗

Optimization of two dimensional gratings for very long wavelength quantum well infrared photodetectors

We have performed a detailed study of two-dimensional grating coupling for quantum well infrared photodetectors in the very long wavelength spectral region lambda is approximately 16 - 17 microns. Using calculations based on the modal expansion method we quantitatively explain the double peaked responsivity spectrum. By optimizing the grating parameters we achieve a normal incidence responsivity and detectivity which are three times larger than the 45 deg angle of incidence geometry.

Sarusi, G.↗

Quantum-Accelerated Distributed Algorithms for Approximate Steiner Trees and Directed Minimum Spanning Trees

We present two algorithms in the Quantum CONGEST-CLIQUE model of distributed computation that succeed with high probability; one for producing an approximately optimal Steiner Tree, and one for producing an exact spanning arborescence of minimum weight, the analog of a Minimum Spanning Tree in a directed graph, each of which uses O~(n^(1/4)) rounds of communication and O~(n^(9/4)) messages, achieving a lower round and message complexity than any known algorithms in the classical CONGEST-CLIQUE model. The CONGEST distributed computational model allows limited-sized messages to be transmitted within a network described by a communication graph of size n in a series of rounds to address a computational problem. The size limitation for such messages isO(log(n)) bits at each edge of the communication graph per round. The communication graph in the CONGEST-CLIQUE model is fully connected. In the Quantum CONGEST-CLIQUE model, at most O(log(n)) classical and quantum bits (qubits) can be communicated across each edge of the communication graph per round. At a high level, we achieve these results by combining classical algorithms with fast quantum subroutines. These speedups further contribute to understanding what problems can be solved more efficiently when we allow quantum communication in this CONGEST-CLIQUE model of distributed computation.

quantum distributed algorithms↗

Quantum State Engineering Via Coherent-State Superpositions

The quantum interference between the two parts of the optical Schrodinger-cat state makes possible to construct a wide class of quantum states via discrete superpositions of coherent states. Even a small number of coherent states can approximate the given quantum states at a high accuracy when the distance between the coherent states is optimized, e. g. nearly perfect Fock state can be constructed by discrete superpositions of n + 1 coherent states lying in the vicinity of the vacuum state.

Janszky, Jozsef↗

Quantum Image Denoising: A Framework via Boltzmann Machines, QUBO, and Quantum Annealing

We investigate a framework for binary image denoising via restricted Boltzmann machines (RBMs) that introduces a denoising objective in quadratic unconstrained binary optimization (QUBO) form and is well-suited for quantum annealing. The denoising objective is attained by balancing the distribution learned by a trained RBM with a penalty term for derivations from the noisy image. We derive the statistically optimal choice of the penalty parameter assuming the target distribution has been well-approximated, and further suggest an empirically supported modification to make the method robust to that idealistic assumption. We also show under additional assumptions that the denoised images attained by our method are, in expectation, strictly closer to the noise-free images than the noisy images are. While we frame the model as an image denoising model, it can be applied to any binary data. As the QUBO formulation is well-suited for implementation on quantum annealers, we test the model on a D-Wave Advantage machine, and also test on data too large for current quantum annealers by approximating QUBO solutions through classical heuristics.

restricted Boltzmann machine↗

Surrogate Optimization for Quantum Circuits

Variational quantum Eigensolvers are touted as a near-term algorithm capable of impacting many applications. However, the potential has yet to be realized with few claims of quantum advantage and high resource estimates mainly due to the need for optimization in the presence of noise. Finding algorithms and methods to improve the convergence is essential to accelerate the capabilities of near-term hardware for VQE or more broad applications of hybrid methods in which optimization is required. To this goal we look to use modern approaches recently developed in circuit simulations and stochastic classical optimization that can be combined in a surrogate optimization approach to classical circuits. Using an approximate state vector simulator, we efficiently calculate an approximate Hessian, fed as an input for a detailed quantum circuit simulator. We demonstrate the capabilities of such an approach with and without sampling noise. We also show that this method outperforms Powell in the presence of quantum circuit shot noise by a factor of 2-4

quantum computing↗

Ab initio ground states of strongly-correlated materials on quantum computers

The accurate first-principles description of strongly-correlated materials is an important and challenging problem in condensed matter physics. Ab initio downfolding has emerged as a way of deriving accurate many-body Hamiltonians including strong correlations, representing a subspace of interest of a material, using density functional theory calculations as a starting point. However, the solution of these material-specific models can scale exponentially on classical computers, constituting a challenge. Here we propose that utilizing quantum computers for obtaining the properties of downfolded Hamiltonians yields an accurate description of the ground state properties of strongly-correlated systems, while circumventing the exponential scaling problem. We benchmark the solution of Hubbard-like models obtained through downfolding by utilizing a classical tensor network implementation of variational quantum eigensolvers (VQE), and we reveal a strategy for driving the optimization through a hybrid minimization of the energy and maximization of the overlap with an approximate solution obtained through low-cost computational methods. This results in a reduction of the energy error by orders of magnitude compared to conventional VQE approaches, and allows us to reproduce long-range correlations for the first time. We demonstrate our first-principles approach for diverse strongly-correlated materials, correctly predicting the antiferromagnetic state of one-dimensional cuprate Ca 2 CuO 3 , the excitonic ground state of monolayer WTe2, and the charge-ordered state of correlated metal SrVO 3 . Our efficient computational implementation allows us to simulate large systems with up to 54 qubits and encompassing up to four correlated bands, which is indicative of the complexity that our framework can address.

Antonios M Alvertis↗

High-Performance Computing Optimization for Aladyn – Adaptive Neural Network Molecular Dynamics Mini-Application

This report provides a description and performance evaluation of the optimization techniques for high performance computing (HPC) implementation of the open source Computational Materials mini-application Aladyn (https://github.com/nasa/aladyn). Aladyn is a basic molecular dynamics code written in FORTRAN 2003, which is designed to demonstrate the use of adaptive neural networks (ANNs) in atomistic simulations. The role of ANNs is to efficiently reproduce the very complex energy landscape resulting from the atomic interactions in materials with the accuracy of the more expensive quantum mechanics-based calculations. The ANN is trained on a large set of atomic structures calculated using the density functional theory (DFT) method. While achieving orders of magnitude faster computational performance than DFT, the ANN-based approach was still very computationally demanding compared to the conventional approach of using empirically fitted energy functions. After its initial development, Aladyn was evaluated and optimized by experts at the NASA Advanced Supercomputing (NAS) division to exploit modern supercomputer architectures. The code has been optimized for execution on multicore central processing units (CPUs), including Intel® Skylake microarchitecture, and on graphic accelerators, such as Nvidia® V100 graphic processing units (GPUs), using Open Multi-Processing (OpenMP) and Open Accelerators (OpenACC) programming interfaces. The optimization achieved a speedup of 4.7 times the baseline version on CPU performance and an additional 2.4 times on CPU+GPU performance. Atomistic computer simulations are a fundamental tool in materials research to model material properties form physics-based first principles. Atomic interaction, governed by Quantum Mechanics (QM) require sophisticated and highly computationally demanding mathematical models to calculate [1]. Classical methods use approximate functional forms, empirically fitted through a set of variable parameters to emulate atomic energies as direct functions of atomic coordinates [2]. While empirical potentials are computationally much simpler, allowing simulations of large-scale systems of up to a trillion (1012) atoms [3], they are substantially less accurate compared to quantum calculations and applicable only to very specific atomic configurations or predefined crystallographic phases. A recently suggested approach is to use heuristic machine learning methods [4], such as those based on Adaptive Neural Networks (ANNs) to predict atomic energies, after being trained on a sufficiently large database of QM-calculated structures [5,6]. This approach reduces significantly the computational complexity, allowing for simulations of orders of magnitude larger systems compared to QM-based methods without compromising accuracy. Still, compared to classical methods using empirical energy functions, ANN methods remain two- to three orders of magnitude more computationally demanding. Hence, the computational cost of simulations, together with the need for extensive training of ANNs, still makes the practical implementation of ANN-based methods quite challenging. The purpose of the Aladyn mini-application software [7], available as open source at https://github.com/nasa/aladyn, is to be a testbed for exploring possible optimization strategies to develop highly scalable parallel algorithms for ANN-based atomistic simulations. Aladyn is aimed at utilizing the architecture of the high-end modern highperformance computing (HPC) hardware based on multicore central processing units (CPUs) equipped with graphic processing unit (GPU) accelerators. Specifically, the goal is to optimize the performance on a single HPC compute node, before implementing scaling to multi-node parallelization using message passing interface (MPI). At the same time, the open source code of Aladyn can serve as a training model for students and professors in academia.

Yamakov, Vesselin I.↗

A Gaussian measure of quantum phase noise

We study the width of the semiclassical phase distribution of a quantum state in its dependence on the average number of photons (m) in this state. As a measure of phase noise, we choose the width, delta phi, of the best Gaussian approximation to the dominant peak of this probability curve. For a coherent state, this width decreases with the square root of (m), whereas for a truncated phase state it decreases linearly with increasing (m). For an optimal phase state, delta phi decreases exponentially but so does the area caught underneath the peak: all the probability is stored in the broad wings of the distribution.

Schleich, Wolfgang P.↗

Quantum Adiabatic Optimization and Combinatorial Landscapes

In this paper we analyze the performance of the Quantum Adiabatic Evolution (QAE) algorithm on a variant of Satisfiability problem for an ensemble of random graphs parametrized by the ratio of clauses to variables, gamma = M / N. We introduce a set of macroscopic parameters (landscapes) and put forward an ansatz of universality for random bit flips. We then formulate the problem of finding the smallest eigenvalue and the excitation gap as a statistical mechanics problem. We use the so-called annealing approximation with a refinement that a finite set of macroscopic variables (verses only energy) is used, and are able to show the existence of a dynamic threshold gamma = gammad, beyond which QAE should take an exponentially long time to find a solution. We compare the results for extended and simplified sets of landscapes and provide numerical evidence in support of our universality ansatz.

Smelyanskiy, V. N.↗

Toward astrometric tracking with the infrared spatial interferometer

Infrared interferometric demonstrations with the University of California, Berkeley's infrared spatial interferometer (ISI) on Mt. Wilson explore the potential of infrared and optical astrometry for deep space tracking, reference frame development, and DSN science. Astrometric data taken and analyzed over the last five years from the ISI have shown that instrumental and atmospheric effects limit current demonstrations. The benefits of sensitivity upgrades, which were performed in 1991 and 1992, have been demonstrated by comparing point-to-point phase fluctuations for the fall 1989 and fall 1992 observing epochs. This comparison showed that point-to-point phase fluctuations due to tropospheric and quantum noise, for optimal integration times of 0.2 sec, are approaching the 0.1-cycle level needed to reliably connect the interferometric phase. The increase in sensitivity, coupled with that arising from very recent hardware upgrades, will greatly enhance phase-connection capabilities necessary for astrometry in the presence of atmospheric refractivity fluctuations. The current data set suggests that atmospheric fluctuations on Mt. Wilson during the best seeing are dominated by a low-lying component, approximately 25 m high, which may be minimized with in situ calibration in the future. During poor seeing conditions that currently prohibit the interferometric phase connection necessary for astrometry, fluctuations seem to be generated by atmospheric inhomogeneities at much higher altitudes above Mt. Wilson. Data taken over the last year suggest that the ISI will soon be able to achieve 50- to 100-nrad astrometry in a single observing session, employing current ground-based laser distance interferometer calibrations to minimize atmospheric effects.

Treuhaft, R. N.↗

Ge:Be infrared photoconductors

Ge:Be photoconductors were optimized for the 30 to 50 micron wavelength range. Crystal growth of detector quality material requires good control of both the Be and residual impurity doping. Detective quantum efficiencies of n sub d = 46% at 5 A/W were achieved at a photon background of 10 to the 8th power p/s. The responsivity of Ge:Be detectors can be strongly temperature-dependent when the residual shallow levels in the material are closely compensated. Transient responses on the order of approximately 1 second were observed in some materials. The role of residual shallow impurities on the performance of photoconductors doped with semi-deep and deep impurities is discussed.

Haegel, N. M.↗

Low-background InSb array development

Photovoltaic indium antimonide (PV InSb) detector technology has matured over the past several years to enable a wide variety of applications to use this high-performance detector material to advantage. The operating conditions for most of the applications to date for back-side illuminated PV InSb arrays have encompassed focal plane temperatures ranging from 40 to approximately 95 K, with the majority in the narrower range between 60 and 80 K. Background flux conditions have ranged from 10 to the 10th power ph/sq cm/sec to 10 to the 16th power ph/sq cm/sec, most typically between 10 to the 12th power and 10 to the 14th power ph/sq cm/sec. Appropriately, the array parameters were optimized for maximum performance over these temperature and background ranges. The key parameters which were peaked in this process were the resistance-area product of the detectors and their quantum efficiency. The Space Infrared Telescope Facility (SIRTF) Infrared Array Camera requirements, however, present very low temperature and background operating conditions, plus the need for very high signal to noise ratios. Preliminary analysis indicates that back-side illuminated PV InSb arrays can be optimized for operation under these conditions, and some performance projections will be presented.

Thom, R. D.↗

Transition-Edge Sensor Pixel Parameter Design of the Microcalorimeter Array for the X-Ray Integral Field Unit on Athena

The focal plane of the X-ray integral field unit (X-IFU) for ESA's Athena X-ray observatory will consist of approximately 4000 transition edge sensor (TES) x-ray microcalorimeters optimized for the energy range of 0.2 to 12 kiloelectronvolts. The instrument will provide unprecedented spectral resolution of approximately 2.5 electronvolts at energies of up to 7 kiloelectronvolts and will accommodate photon fluxes of 1 milliCrab (90 counts per second) for point source observations. The baseline configuration is a uniform large pixel array (LPA) of 4.28 arcseconds pixels that is read out using frequency domain multiplexing (FDM). However, an alternative configuration under study incorporates an 18 by × 18 small pixel array (SPA) of 2 arcseconds pixels in the central approximately 36 arcseconds region. This hybrid array configuration could be designed to accommodate higher fluxes of up to 10 milliCrabs (900 counts per second) or alternately for improved spectral performance (less than 1.5 electronvolts) at low count-rates. In this paper we report on the TES pixel designs that are being optimized to meet these proposed LPA and SPA configurations. In particular we describe details of how important TES parameters are chosen to meet the specific mission criteria such as energy resolution, count-rate and quantum efficiency, and highlight performance trade-offs between designs. The basis of the pixel parameter selection is discussed in the context of existing TES arrays that are being developed for solar and x-ray astronomy applications. We describe the latest results on DC biased diagnostic arrays as well as large format kilo-pixel arrays and discuss the technical challenges associated with integrating different array types on to a single detector die.

Smith, S. J.↗

Receiver performance of laser ranging measurements between the Lunar Observer and a subsatellite for lunar gravity studies

The optimal receiver for a direct detection laser ranging system for slow Doppler frequency shift measurement is shown to consist of a phase tracking loop which can be implemented approximately as a phase lock loop with a 2nd or 3rd order loop filter. The laser transmitter consists of an AlGaAs laser diode at a wavelength of about 800 nm and is intensity modulated by a sinewave. The receiver performance is shown to be limited mainly by the preamplifier thermal noise when a silicon avalanche photodiode is used. A high speed microchannel plate photomultiplier tube is shown to outperform a silicon APD despite its relatively low quantum efficiency at wavelengths near 800 nm. The maximum range between the Lunar Observer and the subsatellite for lunar gravity studies is shown to be about 620 km when using a state-of-the-art silicon APD and about 1000 km when using a microchannel plate photomultiplier tube in order to achieve a relative velocity measurement accuracy of 1 millimeter per second. Other parameters such as the receiver time base jitter and drift also limit performance and have to be considered in the design of an actual system.

Davidson, Frederic M.↗

Accurate quantum chemical calculations

An important goal of quantum chemical calculations is to provide an understanding of chemical bonding and molecular electronic structure. A second goal, the prediction of energy differences to chemical accuracy, has been much harder to attain. First, the computational resources required to achieve such accuracy are very large, and second, it is not straightforward to demonstrate that an apparently accurate result, in terms of agreement with experiment, does not result from a cancellation of errors. Recent advances in electronic structure methodology, coupled with the power of vector supercomputers, have made it possible to solve a number of electronic structure problems exactly using the full configuration interaction (FCI) method within a subspace of the complete Hilbert space. These exact results can be used to benchmark approximate techniques that are applicable to a wider range of chemical and physical problems. The methodology of many-electron quantum chemistry is reviewed. Methods are considered in detail for performing FCI calculations. The application of FCI methods to several three-electron problems in molecular physics are discussed. A number of benchmark applications of FCI wave functions are described. Atomic basis sets and the development of improved methods for handling very large basis sets are discussed: these are then applied to a number of chemical and spectroscopic problems; to transition metals; and to problems involving potential energy surfaces. Although the experiences described give considerable grounds for optimism about the general ability to perform accurate calculations, there are several problems that have proved less tractable, at least with current computer resources, and these and possible solutions are discussed.

Bauschlicher, Charles W., Jr.↗