- (Pelissier, Le Moigne, et al., “Quantum Assisted Learning for Registration of MODIS Images”)
- (Pelissier, LeMoigne, et al., “Image Registration and Data Assimilation as a QUBO on the D-Wave Quantum Annealer”) at http://adsabs.harvard.edu/abs/2016AGUFMIN11D1640P
- (M. Halem, J. Dorband, et al., “Feasibility Studies of Quantum Enabled Annealing Algorithms for Estimating Terrestrial Carbon Fluxes”)
- (Nearing et al., “Data Assimilation on a Quantum Annealing Computer: Feasibility and Scalability”)
- (Shehab et al., “An overview of the quantum wavelet transform, focused on earth science applications”)
- (M. Halem, Radov, and Singh, “Comparisons of a Quantum Annealing and Classical Computer Neural Net Approach for Inferring Global Annual CO2 Fluxes over Land”)
- (Pelissier, Le Moigne, et al., “Quantum Assisted Learning for Registration of MODIS Images”)

- (Boyda et al., “Quantum Boosting and Fast Classical Metrics for Tree Cover Detection in Remote Sensing Data”)
- (Boyda et al., “Deploying a Quantum Annealing Processor to Detect Tree Cover in Aerial Imagery of California”)

- (J. E. Dorband, “Towards Finding the Global Minimum of the D-Wave Objective Function for Improved Neural Network Regressions”)
- (M. Halem, Radov, and Singh, “Comparisons of a Quantum Annealing and Classical Computer Neural Net Approach for Inferring Global Annual CO2 Fluxes over Land”)
- (O’Malley and Vesselinov, “Quo vadis: Hydrologic inverse analyses using high-performance computing and a D-Wave quantum annealer”)
- (Pelissier, Le Moigne, et al., “Quantum Assisted Learning for Registration of MODIS Images”)

- (Milton Halem, Computational Technologies: An Assessment of Hybrid Quantum Annealing Approaches for Inferring and Assimilating Satellite Surface Flux Data into Global Land Surface Models.)
- (Votava and Michaelis, Framework for Mining and Analysis of Petabyte-Size Time-Series on the NASA Earth Exchange (NEX))

E. Boyda et al. “Deploying a Quantum Annealing Processor to Detect Tree Cover in Aerial Imagery of California”. In: PLoS ONE 12(2) (Dec. 2017), e0172505.

Abstract: Quantum annealing is an experimental and potentially breakthrough computational technology for handling hard optimization problems, including problems of computer vision. We present a case study in training a production-scale classifier of tree cover in remote sensing imagery, using early-generation quantum annealing hardware built by D-wave Systems, Inc. Beginning within a known boosting framework, we train decision stumps on texture features and vegetation indices extracted from four-band, one-meterresolution aerial imagery from the state of California. We then impose a regulated quadratic training objective to select an optimal voting subset from among these stumps. The votes of the subset define the classifier. For optimization, the logical variables in the objective function map to quantum bits in the hardware device, while quadratic couplings encode as the strength of physical interactions between the quantum bits. Hardware design limits the number of couplings between these basic physical entities to five or six. To account for this limitation in mapping large problems to the hardware architecture, we propose a truncation and rescaling of the training objective through a trainable metaparameter. The boosting process on our basic 108- and 508-variable problems, thus constituted, returns classifiers that incorporate a diverse range of color- and texture-based metrics and discriminate tree cover with accuracies as high as 92% in validation and 90% on a test scene encompassing the open space preserves and dense suburban build of Mill Valley, CA.

E. Boyda et al. “Quantum Boosting and Fast Classical Metrics for Tree Cover Detection in Remote Sensing Data”. In: AGU Fall Meeting Abstracts, IN13D-08 (Dec. 2014), IN13D–08. Abstract: New volumes of high resolution remote sensing imagery hold greatpromise for Earth science, and with it, new challenges in machinelearning. Familiar heuristic training routines become impractical asdatasets scale to terabytes and beyond. Now, emerging quantumhardware from D-wave Systems allows us to explore alternatives basedon the principles of adiabatic quantum computation. As part of aprogram to develop tree cover estimates for the continental UnitedStates based on one-meter-resolution National Agriculture ImageryProgram (NAIP) data, we have implemented a binary classifier, known asQboost, to combine in a principled manner decision stumps definedon features extracted from 8x8 pixel squares. Qboost was originallydeveloped to be trained on D-wave hardware. Prototyped on NAIP datafor the state of California, the classifier discrimates tree-covered regions with a validationerror rate of 8%. Additionally, we identify quadratic combinationsof the Atmospherically Resistant Vegetation Index (ARVI) and standarddeviations of intensity or near-infrared reflectance that providefast, simple, classical metrics to identify tree cover. They cut by nearly half theerror rates of ARVI used alone or of our best single-featurediscriminant.

J. E. Dorband. “Towards Finding the Global Minimum of the D-Wave Objective Function for Improved Neural Network Regressions”. In: AGU Fall Meeting Abstracts (Dec. 2017). Abstract: The D-Wave 2X has successfully been used for regression analysis to derive carbon flux data from OCO-2 CO2 concentration using neural networks. The samples returned from the D-Wave should represent the minimum of an objective function presented to it. An accurate as possible minimum function value is needed for this analysis. Samples from the D-Wave are near minimum, but seldom are the global minimum of the function due to quantum noise. Two methods for improving the accuracy of minimized values represented by the samples returned from the D-Wave are presented. The first method finds a new sample with a minimum value near each returned D-Wave sample. The second method uses all the returned samples to find a more global minimum sample. We present three use-cases performed using the former method. In the first use case, it is demonstrated that an objective function with random qubits and coupler coefficients had an improved minimum. In the second use case, the samples corrected by the first method can improve the training of a Boltzmann machine neural network. The third use case demonstrated that using the first method can improve virtual qubit accuracy.The later method was also performed on the first use case.

**M. Halem et al.: Comparisons of a Quantum Annealing and Classical Computer Neural Net Approach for Inferring Global Annual CO2 Fluxes over Land 2017AGUFMIN13B0074H**
M. Halem, A. Radov, and D. Singh. “Comparisons of a Quantum Annealing and Classical Computer Neural Net Approach for Inferring Global Annual CO2 Fluxes over Land”. In: AGU Fall Meeting Abstracts (Dec. 2017).

Abstract: Investigations of mid to high latitude atmospheric CO2 show growing amplitudes in seasonal variations over the past several decades. Recent high-resolution satellite measurements of CO2 concentration are now available for three years from the Orbiting Carbon Observatory-2. The Atmospheric Radiation Measurement (ARM) program of DOE has been making long-term CO2-flux measurements (in addition to CO2 concentration and an array of other meteorological quantities) at several towers and mobile sites located around the globe at half-hour frequencies. Recent papers have shown CO2 fluxes inferred by assimilating CO2 observations into ecosystem models are largely inconsistent with station observations. An investigation of how the biosphere has reacted to changes in atmospheric CO2 is essential to our understanding of potential climate-vegetation feedbacks. Thus, new approaches for calculating CO2-flux for assimilation into land surface models are necessary for improving the prediction of annual carbon uptake. In this study, we calculate and compare the predicted CO2 fluxes results employing a Feed Forward Backward Propagation Neural Network model on two architectures, (i) an IBM Minsky Computer node and (ii) a hybrid version of the ARC D-Wave quantum annealing computer. We compare the neural net results of predictions of CO2 flux from ARM station data for three different DOE ecosystem sites; an arid plains near Oklahoma City, a northern arctic site at Barrows AL, and a tropical rainforest site in the Amazon. Training times and predictive results for the calculating annual CO2 flux for the two architectures for each of the three sites are presented. Comparative results of predictions as measured by RMSE and MAE are discussed. Plots and correlations of observed vs predicted CO2 flux are also presented for all three sites. We show the estimated training times for quantum and classical calculations when extended to calculating global annual Carbon Uptake over land. We also examine the efficiency, dependability and resilience of the quantum neural net approach relative to classical computer systems in predicting annual CO2 flux globally.

Milton Halem. Computational Technologies: An Assessment of Hybrid Quantum Annealing Approaches for Inferring and Assimilating Satellite Surface Flux Data into Global Land Surface Models.

Abstract: The objective of this proposal is to expand the research progress the investigators have made in developing Quantum Annealing algorithms that can contribute directly to supporting science related NASA Earth science mission products on the current Ames D- Wave 2X, but to also port and substantially extend these capabilities to the next generation D-Wave 2000Q, when and where available. In particular, having developed unique hybrid neural net algorithmic capabilities for the OCO-2 mission, we plan to expand our research to a broader class of Earth science mission data products and problems, namely calculating surface fluxes from other satellite data products and fusing these data for land surface model data assimilation This includes completing the development, testing and evaluation of Ensemble Quantum Kalman-filter algorithms applicable to current and planned Earth Science missions over the next two years and beyond. We will conduct extensive validation demonstrations of the potential of these D- Wave quantum annealing algorithms at ARC, which we believe will show significant scientific impacts and benefits, potentially more effective than what can be achieved with todays classical computers. It is our, and others, experience that NN optimization algorithms lend themselves especially well to quantum annealing architectures. If successful, this mission enhancing capability would lead to consideration of continued quantum computer technology infusion over the next four years for integration into an operational phase. As use cases, we initially focus on assessing the D-Wave quantum annealing capability to address (i) the Global Carbon Source and Sink budgets over land (ii) perform image registration for direct estimates of Vegetation Growth from Solar Induced Fluorescence employing a multi-satellite Triple Collocation NN quantum algorithm and (iii) conduct Data Information Fusion analysis of Satellite and In-Situ Sensor observations with Reanalysis Model Outputs. We will extend our 3-year OCO-2 data collection to 5-years to infer annual variations in quantum computed global gridded CO2 fluxes, and to the upcoming ISS based OCO- 3 if available in the next two years. We have successfully fitted a highly complex turbulent multivariate, non-linear ARM data set employing a feed forward and backward propagation neural net algorithm on a loosely coupled ARC D-Wave 2X system used as a co-processor accelerator with a remote cluster at UMBC for the general purpose computations. The algorithm performed thousands of samples and hundreds of epochs with two hidden layers. Utilizing these algorithms, we have shown that we can infer CO2 fluxes utilizing historical ARM data for training that is comparable with classic computers. We believe this is the first time one has successfully demonstrated that the D-Wave can perform feed forward regressions yielding comparable results to that obtained with classical computers by employing the D-Wave in such a hybrid algorithmic approach. In this follow-on proposal, we plan to completely couple the hidden layers, forming a Boltzmann Machine, as part of the feed forward algorithm and will test various methods for recalculating the training weights in the backward propagation, which should produce improved global optimizations. This could prove to be a unique quantum capability capable of improved global optimization not reasonably possible with conventional computers. We have added several additional Earth scientists to substantially broaden the quantum computational science scope of applications. Thus, if awarded, we expect to improve on the current TRL 3/4 quantum computing capabilities to achieve a TRL 5/6 by the end of the proposed solicitation, thereby moving quantum annealing computing well on its way towards operational infusion.

**
Nearing et al.: Data Assimilation on a Quantum Annealing Computer: Feasibility and Scalability 2014AGUFMIN11A3592N**

G. S. Nearing et al. “Data Assimilation on a Quantum Annealing Computer: Feasibility and Scalability”. In: AGU Fall Meeting Abstracts, IN11A-3592 (Dec. 2014), IN11A–3592.

Abstract: Data assimilation is one of the ubiquitous and computationally hard problems in the Earth Sciences. In particular, ensemble-based methods require a large number of model evaluations to estimate the prior probability density over system states, and variational methods require adjoint calculations and iteration to locate the maximum a posteriori solution in the presence of nonlinear models and observation operators. Quantum annealing computers (QAC) like the new D-Wave housed at the NASA Ames Research Center can be used for optimization and sampling, and therefore offers a new possibility for efficiently solving hard data assimilation problems. Coding on the QAC is not straightforward: a problem must be posed as a Quadratic Unconstrained Binary Optimization (QUBO) and mapped to a spherical Chimera graph. We have developed a method for compiling nonlinear 4D-Var problems on the D-Wave that consists of five steps: Emulating the nonlinear model and/or observation function using radial basis functions (RBF) or Chebyshev polynomials. Truncating a Taylor series around each RBF kernel. Reducing the Taylor polynomial to a quadratic using ancilla gadgets. Mapping the real-valued quadratic to a fixedprecision binary quadratic. Mapping the fully coupled binary quadratic to a partially coupled spherical Chimera graph using ancilla gadgets. At present the D-Wave contains 512 qbits (with 1024 and 2048 qbit machines due in the next two years); this machine size allows us to estimate only 3 state variables at each satellite overpass. However, QAC’s solve optimization problems using a physical (quantum) system, and therefore do not require iterations or calculation of model adjoints. This has the potential to revolutionize our ability to efficiently perform variational data assimilation, as the size of these computers grows in the coming years.

**O’Malley et al.: Quo vadis: Hydrologic inverse analyses using high-performance computing and a D-Wave quantum annealer 2017AGUFMIN13B0070O**

D. O’Malley and V. V. Vesselinov. “Quo vadis: Hydrologic inverse analyses using high-performance computing and a D-Wave quantum annealer”. In: AGU Fall Meeting Abstracts (Dec. 2017).

Abstract: Classical microprocessors have had a dramatic impact on hydrology for decades, due largely to the exponential growth in computing power predicted by Moore’s law. However, this growth is not expected to continue indefinitely and has already begun to slow. Quantum computing is an emerging alternative to classical microprocessors. Here, we demonstrated cutting edge inverse model analyses utilizing some of the best available resources in both worlds: high-performance classical computing and a D-Wave quantum annealer. The classical high-performance computing resources are utilized to build an advanced numerical model that assimilates data from O(105) observations, including water levels, drawdowns, and contaminant concentrations. The developed model accurately reproduces the hydrologic conditions at a Los Alamos National Laboratory contamination site, and can be leveraged to inform decision-making about site remediation. We demonstrate the use of a D-Wave 2X quantum annealer to solve hydrologic inverse problems. This work can be seen as an early step in quantum-computational hydrology. We compare and contrast our results with an early inverse approach in classical-computational hydrology that is comparable to the approach we use with quantum annealing. Our results show that quantum annealing can be useful for identifying regions of high and low permeability within an aquifer. While the problems we consider are small-scale compared to the problems that can be solved with modern classical computers, they are large compared to the problems that could be solved with early classical CPUs. Further, the binary nature of the high/low permeability problem makes it well-suited to quantum annealing, but challenging for classical computers.

**Pelissier et al.: Quantum Assisted Learning for Registration of MODIS Images
2017AGUFMIN12C04P**

C. Pelissier, J. Le Moigne, et al. “Quantum Assisted Learning for Registration of MODIS Images”. In: AGU Fall Meeting Abstracts (Dec. 2017).

Abstract: The advent of the first large scale quantum annealer by D-Wave has led to an increased interest in quantum computing. However, the quantum annealing computer of the D-Wave is limited to either solving Quadratic Unconstrained Binary Optimization problems (QUBOs) or using the ground state sampling of an Ising system that can be produced by the D-Wave. These restrictions make it challenging to find algorithms to accelerate the computation of typical Earth Science applications. A major difficulty is that most applications have continuous real-valued parameters rather than binary. Here we present an exploratory study using the ground state sampling to train artificial neural networks (ANNs) to carry out image registration of MODIS images. The key idea to using the D-Wave to train networks is that the quantum chip behaves thermally like Boltzmann machines (BMs), and BMs are known to be successful at recognizing patterns in images. The ground state sampling of the D-Wave also depends on the dynamics of the adiabatic evolution and is subject to other non-thermal fluctuations, but the statistics are thought to be similar and ANNs tend to be robust under fluctuations. In light of this, the D-Wave ground state sampling is used to define a Boltzmann like generative model and is investigated to register MODIS images. Image intensities of MODIS images are transformed using a Discrete Cosine Transform and used to train a several layers network to learn how to align images to a reference image. The network layers consist of an initial sigmoid layer acting as a binary filter of the input followed by a strict binarization using Bernoulli sampling, and then fed into a Boltzmann machine. The output is then classified using a soft-max layer. Results are presented and discussed.

**Pelissier et al.: Quantum Assisted Learning for Registration of MODIS Images
2017AGUFMIN12C..04P**

C. Pelissier, J. Le Moigne, et al. “Quantum Assisted Learning for Registration of MODIS Images”. In: AGU Fall Meeting Abstracts (Dec. 2017).

Abstract: The advent of the first large scale quantum annealer by D-Wave has led to an increased interest in quantum computing. However, the quantum annealing computer of the D-Wave is limited to either solving Quadratic Unconstrained Binary Optimization problems (QUBOs) or using the ground state sampling of an Ising system that can be produced by the D-Wave. These restrictions make it challenging to find algorithms to accelerate the computation of typical Earth Science applications. A major difficulty is that most applications have continuous real-valued parameters rather than binary. Here we present an exploratory study using the ground state sampling to train artificial neural networks (ANNs) to carry out image registration of MODIS images. The key idea to using the D-Wave to train networks is that the quantum chip behaves thermally like Boltzmann machines (BMs), and BMs are known to be successful at recognizing patterns in images. The ground state sampling of the D-Wave also depends on the dynamics of the adiabatic evolution and is subject to other non-thermal fluctuations, but the statistics are thought to be similar and ANNs tend to be robust under fluctuations. In light of this, the D-Wave ground state sampling is used to define a Boltzmann like generative model and is investigated to register MODIS images. Image intensities of MODIS images are transformed using a Discrete Cosine Transform and used to train a several layers network to learn how to align images to a reference image. The network layers consist of an initial sigmoid layer acting as a binary filter of the input followed by a strict binarization using Bernoulli sampling, and then fed into a Boltzmann machine. The output is then classified using a soft-max layer. Results are presented and discussed.

**Pelissier et al.: Image Registration and Data Assimilation as a QUBO on the D-Wave Quantum Annealer 2016AGUFM**

C. Pelissier, J. LeMoigne, et al. “Image Registration and Data Assimilation as a QUBO on the D-Wave Quantum Annealer”. In: AGU Fall Meeting Abstracts, IN11D-1640 (Dec. 2016), IN11D–1640.

Abstract: The advent of the commercially available D-Wave quantum annealer has for the first time allowed investigations of the potential of quantum effects to efficiently carry out certain numerical tasks. The DWave computer was initially promoted as a tool to solve Quadratic Unconstrained Binary Optimization problems (QUBOs), but currently, it is also being used to generate the Boltzmann statistics required to train Restricted Boltzmann machines (RBMs). We consider the potential of this new architecture in performing numerical computations required to estimate terrestrial carbon fluxes from OCO-2 observations using the LIS model. The use of RBMs is being investigated in this work, but here we focus on the D-Wave as a QUBO solver, and it’s potential to carry out image registration and data assimilation. QUBOs are formulated for both problems and results generated using the D-Wave 2Xtm at the NAS supercomputing facility are presented.

**
Shehab et al.: An overview of the quantum wavelet transform, focused on earth science applications 2015AGUFMIN31A1758S**

O. Shehab et al. “An overview of the quantum wavelet transform, focused on earth science applications”.
In: AGU Fall Meeting Abstracts, IN31A-1758 (Dec. 2015), IN31A–1758.

Abstract: Registering the images from the MODIS system and the OCO-2 satellite is currently being done by classical image registration techniques. One such technique is wavelet transformation. Besides image registration, wavelet transformation is also used in other areas of earth science, for example, processinga and compressing signal variation, etc. In this talk, we investigate the applicability of few quantum wavelet transformation algorithms to perform image registration on the MODIS and OCO-2 data. Most of the known quantum wavelet transformation algorithms are data agnostic. We investigate their applicability in transforming Flexible Representation for Quantum Images. Similarly, we also investigate the applicability of the algorithms in signal variation analysis. We also investigate the transformation of the models into pseudo-boolean functions to implement them on commercially available quantum annealing computers, such as the D-Wave computer located at NASA Ames.

**
Votava et al.: Framework for Mining and Analysis of Petabyte-Size Time-Series on the NASA Earth Exchange (NEX) PetrnAndy2016AISTGrant**

Petr Votava and Andrew Michaelis. Framework for Mining and Analysis of Petabyte-Size Time-Series on the NASA Earth Exchange (NEX).

Abstract: Time-series analysis is key to understanding and uncovering changes in the Earth system. However many currently available geospatial tools only provide easy access to the spatial rather than the temporal component. Therefore the burden is on the researchers to correctly extract the time-series from multiple files for further analysis. While inconvenient, this is often achievable on a small scale, but to search for trends across millions of time-series, quickly becomes a huge undertaking for individual researchers, because apart from scaling the analysis algorithm itself it requires much effort in large- scale data processing, metadata and data management. Additionally, for most researchers in Earth sciences, there are almost no tools that would enable easy time-series access, search and analysis. Finally, there are limited places where algorithms supporting novel time-series approaches can be tested and evaluated at scale. Given the importance of time-series analysis to Earth sciences, we view it as an opportunity to engage and bring together Earth science, machine learning and data mining communities - an important goal of the NASA Earth Exchange (NEX) project. The overall goal of the proposed effort is to develop a platform for fast and efficient analysis of time-series data from NASA’s satellite and derived datasets at large scale (billions of time-series from 100’s of terabytes to petabytes of data) that would be deployed on NEX and accessible in both supercomputing and cloud environments. While the initial focus will be on deploying the technology to support NEX and NASA users, the overall system will be developed as a flexible framework that can easily accommodate any user’s time-series data and codes and will be deployable outside NEX using Docker containers. The project will significantly enhance the scale of state-of-the-art in time-series analysis, currently several orders of magnitude below the needs of the Earth science community. To accomplish this goal, we will develop time-series indexing and search components based on the Symbolic Aggregate approXimation (SAX/iSAX) that will be able to extract and index billions of time-series from satellite, model and climate data, giving both science and application users an important analysis tool and lower a major barrier in Earth science research. Finally, as time-series analysis is very active field of research, the platform will be developed as a plug-in framework and will be able to accommodate new improvements in time-series analysis, such as different space reduction methods that are first step in the indexing process. Apart from production use on the NEX system, we will deploy the system as a test-bed for users that will drive advancements in time-series analysis research, while providing unified access to billions of time-series. Because of the symbolic nature of the SAX representation, it is possible to deploy a number of algorithms from text mining, deep learning and bioinformatics that will provide giant leap in our ability to analyze time-series data and are already showing good results in other fields. In terms of the current NRA, this project is proposing to develop a data- centric technology that will significantly reduce development time of Earth science research and increase accessibility and utility of NASA data. In terms of specific technology areas outlined in the NRA, the proposed project will provide new big data analytics capability, as well as tools for scalable data mining and machine learning. Through the use of flexible container-based architecture and building upon existing capabilities of NEX and OpenNEX, the system will be demonstrated in both high- performance computing (HPC) as well as cloud environment on AWS. Period of performance for the proposed project is 2 years. The entry TRL is 3 and exit TRL is 6.

Title

Div. Associate for Science

Intelligent Systems Division

DETAILED TO EARTH SCIENCE ACTING BRANCH CHIEF

Joseph C. Coughlan, Ph.D.

Intelligent Systems Division

Ames Research Center

Mail Stop 269-1

Bldg. 269, Rm. 282; P.O. Box 1

Moffett Field, CA 94035-0001

**Phone:** 650-604-5689

**Fax:** 650-604-3594

joseph.c.coughlan(at)

nasa(dot)

gov