ACMD Postdoctoral Opportunities

This document describes National Research Council Postdoctoral Research Associateships tenable within the Applied and Computational Mathematics Division (ACMD) of the NIST Information Technology Laboratory. Research areas of interest include computational materials science, computational electromagnetics, computational biology, computational

chemistry, orthogonal polynomials and special functions, applied optimization and simulation, complex systems and networks, data mining, scientific visualization, parallel and distributed algorithms, and quantum information science. See below for more details on these opportunities and the research advisors associated with them. **Candidates are urged to contact potential advisors in advance of formal application.** Candidates and their research proposals are evaluated in a competitive process managed by the National Research Council (NRC) Associateship Programs. For further details on the application process, see the link below. For further information on the program within ACMD, contact Ronald Boisvert (boisvert [at] nist.gov (boisvert[at]nist[dot]gov)).

- NIST Postdoctoral Research Associateships Program details
- Application Deadline: February 1 or August 1
- U.S. Citizenship Required

- Validated Computation of Special Functions: DLMF Standard Reference Tables on Demand
- Mathematical Modeling of Magnetic Systems
- Applied Optimization and Simulation
- Mathematical Modeling and Simulation
- Finite Element Analysis of Material Microstructure
- Complex Systems and Networks: Performance, Control, and Security
- Quantum Information and Cryptography
- Quantum and Classical Error Correction
- Quantum Communication
- Quantum Network Testbeds
- Quantum Frequency Conversion for Hybrid Quantum Networks
- Quantum Optical Metrology
- Autonomous Control of Quantum Systems
- Scientific Datamining
- Real-time Quantitative Visualization
- Immersive Visualization
- Immersive Scientific Visualization
- Analysis and Theory of Microfluidic Systems
- Applied Mathematics of Soft, Fluid, and Active Matter

- Quantum Information Science
- Quantum Networking
- Statistics for Quantum Systems
- Uncertainty Quantification and Computational Materials Science
- Computational Electromagnetics
- Physics-Based Computation

Contact: Bonita Saunders

We are developing an online system for generating validated tables of special function values with an error certification computed to user-specified precision. A typical user might be a researcher or software developer testing his own code or confirming the accuracy of results obtained from a commercial or publicly available package. The goal is to create a standalone system, but also link to and from the NIST Digital Library of Mathematical Functions (DLMF).

The project, DLMF Standard Reference Tables on Demand (DLMF Tables), is a collaborative effort with the University of Antwerp Computational Mathematics Research Group (CMA) led by Annie Cuyt. A beta site based on CMA’s MpIeee, a multiprecision IEEE 754/854 compliant C++ floating point arithmetic library, is already available at http://dlmftables.uantwerpen.be/. The successful candidate will have the opportunity to advance our current efforts in the field of validated computing through the continued research and development of multiple precision function software providing guaranteed error bounds at arbitrary precision. The associate will also help expand DLMF Tables into a full-fledged site, as well as investigate the enhancement of existing multiprecision libraries for possible inclusion in DLMF Tables.

References:

*NIST Digital Library of Mathematical Functions*. http://dlmf.nist.gov/, Release 1.0.22 of 2019-03-15. F. W. J. Olver, A. B. Olde Daalhuis, D. W. Lozier, B. I. Schneider, R. F. Boisvert, C. W. Clark, B. R. Miller, and B. V. Saunders, eds.

B. I. Schneider, B. R. Miller, and B. V. Saunders. NIST’s Digital Library of Mathematical Functions. *Physics Today* 71:2 (2018), 48. DOI: 10.1063/PT.3.3846.>

F. Backeljauw, S. Becuwe, A. Cuyt, J. Van Deun, and D. Lozier. Validated Evaluation of Special Mathematical Functions. *Science of Computer Programming* 90 (2014), 2-20. https://doi.org/10.1016/j.scico.2013.05.006.

Opportunity Number: 50.77.11.C0297

Contact: Mike Donahue

We work with scientists in other NIST laboratories to develop tools for computer simulation and analysis of magnetic systems at the nanometer scale. Model verification is achieved by comparison against experiment and by development of reference problems. Important issues include controlling round-off and truncation error to obtain high accuracy solutions in complex, large scale simulations, and the development towards this end of efficient, highly parallel software running on commodity hardware. Novel methods to compute the stray field from magnetized material with attention to interface and boundary effects are of particular interest. Applications include MRAM, field sensors, and magnetic logic devices.

Opportunity Number: 50.77.11.B4449

Contact: Anthony Kearsley

Applied Optimization and simulation form an area of engineering that sits between mathematics and computer science. They include computational tools used to solve important problems in engineering, economics, and all branches of science. Current concerns include the development and analysis of algorithms for the solution of problems of estimation, simulation and control of complex systems, and their implementations on computers. We are particularly interested in nonlinear optimization problems, which involve computationally intensive function evaluations. Such problems are ubiquitous; they arise in simulations with finite elements, in making statistical estimates, or simply in dealing with functions that are very difficult to handle. The comparability among the various techniques for numerical approximation through optimization algorithms is very important. What makes one formulation for the solution of a problem more desirable than another? This work requires the study and understanding of the delicate balance between the choices of mathematical approximation, computer architecture, data structures, and other factors - a balance crucial to the solution of many application-driven problems.

Opportunity Number: 50.77.11.B4450

Contact: Ryan Evans

Mathematical modeling forms the basis for understanding, simulating, optimizing and controlling numerous scientific phenomenon and associated measurements. Mathematical models frequently take the form of an ordinary or partial differential equations, and are often nonlinear. There are a few instances where analytic solutions are available and in other cases solutions can be sought through the design of efficient and accurate numerical solutions. Analytic solutions to similar problems or numerical approximations can be used to validate mathematical models through comparison with physical experiments, measured quantities of interest, and optimized experimental design. Methods that yield analytic solutions are often employed to reduce the complexity of mathematical models and can, in turn help describe and improve instrument behavior in physically relevant limits. Abundant examples are found in physics, chemistry, and biology. We are interested developing new mathematical models to simulate scientific experiments that produce measurements. This research often leads to numerical implementations and associated testing, to numerical analysis of accuracy, to optimization, optimal control or optimal design of instrument performance.

Opportunity Number: 50.77.11.C0761

Contact: Stephen Langer

We are developing object-oriented computational tools for the analysis of material microstructure. The goal is to predict the macroscopic behavior of a material from knowledge of its microscopic geometry. Starting from a digitized micrograph, the program identifies features in the image, assigns material properties to them, generates a finite element mesh, and performs virtual measurements to determine the effect of the microstructure on the macroscopic properties of the system. More information is available at http://www.ctcms.nist.gov/oof/. Opportunities exist in image analysis, materials science, physics, and computer science.

Opportunity Number: 50.77.11.B4451

Contact: Vladimir Marbukh

We are developing novel methodologies and approaches to modeling complex systems consisting of a large number of interacting elements. The models should not only have predictive power, but should also provide guidance for controlling complex systems. Since performance of complex systems is characterized by multiple competing criteria, which include economic efficiency, resilience, and security, the purpose of control is optimization of the corresponding trade-offs. In a situation of complex systems comprised of selfish elements, control should take advantage of market mechanisms, which elicit desirable behavior through incentives. Resilience, robustness, and security should be modeled against malicious agents attempting to cause deterioration in the system performance.

Opportunity Number: 50.77.11.B7430

Contact: Yi-Kai Liu

Quantum mechanical devices can perform certain information processing tasks that are impossible using only classical physics. However, the construction of such devices requires new ideas from computer science, mathematics, and physics. We are interested in a broad range of topics in this area, including quantum devices that implement novel cryptographic functionalities, methods for testing and characterizing experimental quantum information processors, and classical cryptosystems that are secure against quantum adversaries. We are also interested in related areas such as quantum algorithms, complexity theory, and machine learning.

Opportunity Number: 50.77.11.B7913

Contact: Victor Albert

Error correction is what ensures that the audio in your phone calls remains sharp, your hard drives do not deteriorate too quickly, and signals can be reliably transmitted to remote satellites. Over multiple decades, and with the explosion of the information age, an enormous variety of error-correction schemes were developed. Recently, a radically new type of error correction was introduced, one that can protect the quantum information that is stored in a quantum computer or that is communicated over a quantum network. We perform state-of-the-art research in the theory quantum error correction and related topics, as well as maintain the error-correction zoo --- a repository of several hundred classical and quantum codes.

Opportunity Number: 50.77.11.C0764

Contact: Lijun Ma and Oliver Slattery

Transmitting quantum states of single photons from one location to another is one of the most important routines of any quantum communication system. Our current research areas in quantum communication include single photon creation, transmission, storage, transduction and detection - these are the fundamental building blocks for the quantum communication systems of the future. In such systems, one will encode information into strategically created single photons (flying Qubits), transmit them and interface them with an atomic quantum memory (stationary Qubits) for storage and processing. A typical example of such systems are quantum repeaters that can extend operation distance for quantum key distribution (QKD) systems, and/or connect quantum computers to form the large-scale quantum networks of the future. Our current research is focused on the following areas: (1) Entangled photon pair sources: Based on parametric frequency down conversion or four-wave mixing, single photon pairs are generated in a resonant cavity to ensure the linewidth is sufficiently narrow to match the atomic systems for high efficiency; (2) Quantum memories: Our current approach is based on electromagnetically induced transparency (EIT) using warm atomic vapor or cold atomic ensambles in a magneto-optical trap (MOT); (3) Quantum interface: By using nonlinear optical materials, wavelengths of the generated single photons can be converted between atomic transition lines for storage and processing and telecommunication bands for long distance transmission; (4) Bell state measurement: The measurement results provide information for quantum teleportation and; (5) Electronics and software for final integration of a quantum repeater.

Opportunity Number: 50.77.11.B6541

Contact: Oliver Slattery

Quantum Networks require optimized performance in terms of losses, synchronization, entanglement distribution management, noise, etc., and these performance metrics have to be improved by orders of magnitude compared to classical networks. The project focusses on establishing a quantum network testbed at the NIST Gaithersburg campus to: (1) study quantum (qubit) systems (such as entangled photon sources, detectors, memories, interfaces) and their performance in a real life heterogenized quantum network setting, including to understand the impacts from other connected systems and links on the performance of certain critical quantum systems; (2) develop methods to integrate quantum components into a real life heterogenized quantum network setting; (3) develop and implement methods to study the performance of quantum network links (such as tomography measurements, fiber characterization, etc.); (4) design, implement and test methods for optimization of photonic quantum networks (such as for timing synchronization, phase control, polarization control, etc.); (5) develop and test management protocols for quantum communications over a quantum network (such as a quantum network manager); and (6) develop and execute of quantum experiments (such as entanglement distribution) and quantum communications (such as teleportation) on a quantum network.

Opportunity Number: 50.77.11.C0672

Contact: Paulina Kuo

Future quantum networks will consist of a mixture of different technologies that operate at different wavelengths. Our research focuses on photonic devices that can bridge these different wavelengths while maintaining the quantum properties. We study quantum frequency conversion (QFC) using high efficiency, nonlinear optical frequency conversion (sum- and difference-frequency generation). We are interested in properties of QFC devices, such as efficiency, noise, and bandwidth, and potential integration of QFC devices with qubit technologies.

Opportunity Number: 50.77.11.B8345

Contact: Thomas Gerrits

Optical quantum metrology encompasses the generation, detection, characterization, and verification of quantum states of light, including the use of quantum entanglement to enhance sensitivity compared to classical methods. The project develops cutting-edge single-photon sources and uses state-of-the-art (photon-number-resolving) single-photon detectors to investigate fundamental aspects of optical quantum metrology. Further, the project focusses on the implementation of newly developed measurement protocols and characterization tools for single-photon sources, detectors, and components. These tools and protocols are used for applications such as entanglement distribution in quantum networks, synchronization of distant quantum network nodes, quantum component characterization and quantum-enhanced measurements using exotic and non-Gaussian quantum states of light.

Opportunity Number: 50.77.12.C0669

Contact: Justyna Zwolak

Machine Learning and AI are having great impacts across a number of fields of physics, from probing the evolution of galaxies to calculating quantum wave functions to discovering new states of matter. This research opportunity revolves around building machine learning-driven autonomous systems for calibration and control of quantum information science systems.

Working closely with scientists in other NIST laboratories, as well as several external collaborators, we are developing machine learning-driven autonomous systems for calibration and control of quantum information science systems. In particular, we are combining machine learning algorithms for in situ classification of quantum experimental systems (i.e., in real-time, during the experiment) with custom optimization algorithms to design an automated control protocol. The proposed protocols are implemented and validated experimentally.

The current applications of interest include, but are not limited to, tunable quantum dots and cold atom systems.

[1] S. S. Kalantre, J. P. Zwolak et al. Machine learning techniques for state recognition and auto-tuning in quantum dots. npj Quantum Inf. 5 (6): 1–10 (2019).

[2] J.P. Zwolak, T. McJunkin et al. Auto-tuning of double dot devices in situ with machine learning. arXiv:1909.08030 (2019).

Opportunity Number: 50.77.11.C0388

Contact: Judith Terrill

NIST scientists are currently automating experiments resulting in increasing amounts of generated data in multidimensional spaces. The data come primarily from combinatorial experiments in materials science. This type of data consists of image data with additional measurements at each pixel. Other experiments result in spectra-like measurements taken over spatial domains. These datasets require techniques that can sift through large amounts of data for items of potential interest, as well as for discovery. We are collaborating with these scientists on ways to mine this data for scientific insight. Opportunities exist for the application of datamining techniques such as classification, rule finding, and automated model building to these datasets, as well as for the development of new techniques.

Opportunity Number: 50.77.11.B4825

Contact: Judith Terrill

We are working to create visualization systems that serve as precision measurement instruments, supporting interactive probing of "samples" to derive quantitative data to enable scientific discovery. We use virtual samples, built from data obtained from either physical measurement or computational simulation. Our ability to extend measurement science to the virtual world is enabled by advances in the speed and capability of graphics processing units (GPUs). In particular, visualization techniques that employ shaders have the potential to play a central role in measurement and analysis tools within a visualization system because these programs can perform substantial numeric processing within the visualization pipeline, where they have direct access to the geometric data describing the objects of study. Additionally, this allows access to the information needed to determine uncertainties, a prerequisite for precision measurement. This research opportunity focuses on all aspects of quantitative visualization, i.e., measurement and analysis applied to visualization objects directly in real time.

Opportunity Number: 50.77.11.B7763

Contact: Judith Terrill

With the continuing increase in speed and capability of commodity graphics processors, immersive visualization offers increasing opportunities to express scientifically meaningful results. Data at NIST spans a wide range from nano to cement to models that exhibit complex dynamics. This research will build on our open source software that runs on a linux desktop as well as immersively. Opportunities exist for (1) investigating the use of immersive visualization as a scientific instrument for exploration and representation of data; (2) developing interactive measurement techniques on visualizations; (3) developing ways to merge analysis with visualization and provide quantitative feedback into the visualization; (4) exploring and expressing uncertainties due to the data as well as the visualization methods; (5) harnessing the growing capability of graphics processors to provide insight; (6) advancing the use of abstraction to express meaning in data; and (7) developing user interaction methods, including direct manipulation techniques.

Opportunity Number: 50.77.11.B6663

Contact: Simon Su

With the continuing increase in speed and capability of commodity graphics hardware, immersive visualization offers increasing opportunities to express scientifically meaningful results. Data at NIST spans a wide range from nano to cement to models that exhibit complex dynamics. This research will build on open source software that runs on a desktop environment as well as in an immersive environment. Opportunities exist for (1) investigating the use of immersive visualization as a scientific instrument for exploration and representation of data; (2) developing interactive measurement techniques on visualizations; (3) developing ways to merge analysis with visualization and provide quantitative feedback into the visualization; (4) exploring and expressing uncertainties due to the data as well as the visualization methods; (5) harnessing the growing capability of graphics processors to provide insight; (6) advancing the use of abstraction to express meaning in data; and (7) developing user interaction methods, including direct manipulation techniques.

Opportunity Number: 50.77.11.C0664

Contact: Paul Patrone

Microfluidics offers unprecedented avenues for controlling and characterizing the behavior of physical, chemical, and biological systems. However, in order to leverage the full potential of microfluidic devices as *measurement tools*, the community requires a deeper theoretical understanding of how they operate. Our current research addresses this problem by developing and analyzing mathematical models of such systems. We use a variety of approaches -- applied analysis, asymptotics, numerical methods, and optimization -- to understand how such models can be used as the basis for measuring properties of particles and other systems in flow. We also work closely with experimentalists in the Physical Measurement Laboratory to develop new microfluidic devices and measurement tools, and to validate our mathematical approaches.

Opportunity Number: 50.77.11.C0256

Contact: Leroy Jia

Despite their starring role in enabling the miracle of life, micro- and nanoscale biological systems have historically defied the suite of mathematical techniques that has proven "unreasonably effective" at modeling their macroscopic counterparts. The computational challenges that characterize such systems include: 1) a large number of interacting degrees of freedom, rendering many traditional models intractable; 2) sensitive, deformable components that exhibit compositional disorder and nonlinear responses; and 3) active agents capable of self-propulsion, creating systems that are inherently out of equilibrium. Our mission is to illuminate the physical principles governing complex biological and bioinspired systems possessing one or more of these characteristics by synthesizing applied analysis, continuum mechanics, differential geometry, and numerical simulation.

Opportunity Number: 50.77.11.C0860

Contact: E. (Manny) Knill

Quantum information science covers the theoretical and experimental areas involving the use of quantum mechanics in communication and computation. We are particularly interested in benchmarking proposed physical system's performance on quantum information processing tasks, scalably realizing logical qubits, and developing algorithms that take advantage of quantum resources. The research is inspired by and will contribute to the technologies being developed at NIST.

Opportunity Number: 50.77.12.B5623

Contact: E. (Manny) Knill

Distributed quantum computing requires quantum networks that can carry flying qubits. Such networks can be used to scale up small quantum computers and enable quantum communication protocols such as blind quantum computing for certified execution of quantum algorithms. This project involves a joint theoretical-experimental effort to develop and test quantum networking infrastructure, protocols and devices to convert computational qubits such as superconducting and electrically defined quantum dot qubits to flying qubits. This opportunity is for the theoretical component of the project.

Opportunity Number: 50.77.12.C0180

Contact: S. Glancy or E. (Manny) Knill

Sophisticated, rigorous statistical tools are required to analyze data from experiments that manipulate and measure quantum systems with the goals of quantum computation, communication, and measurement. This project works to develop new methods for data analysis from quantum experiments. Particular applications of interest include quantum state and process tomography, certifying violation of local realism (e.g., in Bell tests), certification/quantification of randomness, and use of quantum resources to improve measurement precision. We work in close collaboration with experimental groups at NIST (trapped ions, superconducting qubits, photons) to assist experiment design and analysis and to inspire new theoretical research.

Opportunity Number: 50.77.12.B7973

Contact: A. Dienstfrey

We research and develop mathematical and statistical analysis and tools for uncertainty quantification in scientific computing, with particular emphasis on problems in computational material science. Application areas include, but are not limited to structural composites and electronic materials. This work, which is performed in collaboration with the NIST Material Measurement Laboratory, is in response to the multi-agency Materials Genome Initiative (http://www.whitehouse.gov/mgi/), which strives to reduce the time and costs for materials discovery, optimization, and deployment through the promotion of a new research and development paradigm in which computational modeling, simulation, and analysis will decrease the reliance on physical experimentation.

Opportunity Number: 50.77.12.B7897

Contact: Zydrunas Gimbutas

We are developing high order integral equation methods and numerical tools for computational electromagnetics. This research focuses on the frequency domain electromagnetic field solvers that involve automatic geometry preprocessing/compressing in the presence of geometric singularities and coupling the obtained discretizations to the wideband fast multipole method based accelerators and direct solvers. Applications will include benchmarking, verification, and error analysis of magnetic resonance imaging simulators and electromagnetic scattering codes.

Opportunity Number: 50.77.12.B7912

Contact: Andrew Dienstfrey

Physics-based computation is a branch of unconventional computing which uses physical systems evolving by their native dynamics to process information in a controlled way. Our research covers a broad range of areas from theory, to algorithmic, to computational prototypes in novel hardware. At the foundational level we are interested in explorations of the fundamental computational capacity of dynamical systems, for example, spiking-neural networks. Additionally, we are interested in the fundamental limits of computation arising from statistical mechanics and thermodynamic considerations. Research and development of hardware-aware, fault-tolerant training strategies that can be used for in-situ training of neuromorphic hardware are examples of our algorithmic work [1], [2]. At the hardware level, we have ongoing collaborations with NIST and external research groups developing novel devices for next-generation neuromorphic computing including, for example, resistive crossbar structures [3], superconducting optoelectronics [4], and Josephson Junctions [5]. We look forward to having you join us in this exciting area.

[1] A. N. McCaughan, B. G. Oripov, N. Ganesh, S. W. Nam, A. Dienstfrey, S. M. Buckley, "Multiplexed gradient descent: Fast online training of modern datasets on hardware neural networks without backpropagation," APL Machine Learning, v1#2 (2023).

[2] J. Zhao, S. Huang, O. Yousuf, Y. Gao, B. D. Hoskins, G. C. Adam, "Gradient decomposition methods for training neural networks with non-ideal synaptic devices," Frontiers in Neuroscience, v15 (2021)

[3] O. Yousuf, I. Hossen, M. W. Daniels, M. Leuker-Boden, A. Dienstfrey, G. C. Adam, "Device Modeling Bias in ReRAM-Based Neural Network Simulations", IEEE Journal on Emerging and Selected Topics in Circuits and Systems, v13#1 (2023)

[4] S. Khan, B. A. Primavera, J. Chiles, A. N. McCaughan, S. M. Buckley, A. N. Tait, et. al., "Superconducting optoelectronic single-photon synapses," Nature Electronics, v5#10 (2022)

[5] M. L. Schneider, E. M. Jué, M. R. Pufall, K. Segall, C. W. Anderson, "Self-training superconducting neuromorphic circuits using reinforcement learning rules," arXiv:2404.18774 (2024)

Opportunity Number: 50.77.12.C0949

Created May 10, 2010, Updated August 13, 2024