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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Writable spin wave nanochannels in an artificial-spin-ice-mediated ferromagnetic thin film

We report magnonics, which employs spin-waves to transmit and process information, is a promising venue for low-power data processing. One of the major challenges is the local control of the spin-wave propagation path. Here, we introduce the concept of writable magnonics by taking advantage of the highly flexible reconfigurability and rewritability of artificial spin ice systems. Using micromagnetic simulations, we show that globally switchable spin-wave propagation and locally writable spin-wave nanochannels can be realized in a ferromagnetic thin film underlying an artificial pinwheel spin ice. The rewritable magnonics enabled by reconfigurable spin wave nanochannels provides a unique setting to design programmable magnonic circuits and logic devices for ultra-low power applications.

42 ENGINEERING↗
DOE OSTI2025

ON THE EFFECTIVENESS OF LLMS IN UNIT TEST GENERATION FOR STRUCTURED TEXT PROGRAMS

The reliability of industrial automation systems heavily depends on the correctness of Programmable Logic Controller (PLC) programs, which are often written in Structured Text (ST). While Large Language Models (LLMs) have shown promise in automating test generation for mainstream programming languages, their effectiveness for the syntactically strict ST language remains underexplored. This thesis presents a systematic empirical evaluation of three state-of-the-art LLMs—GPT-4o, Gemini 2.5 Pro, and Claude Sonnet 4.5—for generating ST unit tests. We examine three prompting strategies: Natural Language (NL), Code Language (CL), and Chain-of-Thought (CoT), across a curated set of 11 ST function blocks. The quality of the generated tests is assessed using Compilation Success Rate (CSR), Statement Coverage (SC), and Branch Coverage (BC). In the zero-shot setting, Claude Sonnet 4.5 achieves the highest CSR, while Gemini 2.5 Pro consistently delivers the best statement and branch coverage, particularly under CL prompts. By incorporating a one-shot CL prompt, all models exhibit substantial improvements—most notably GPT-4o, whose CSR increases from 45.45% to 90.91%, with substantial gains in both SC and BC. To further contextualize these findings, we compare GPT-4o’s one-shot results with PLCAutoTester, a state-ofthe- art ST unit test generation tool, on an additional benchmark dataset. While LLMgenerated tests approach competitive coverage levels, PLCAutoTester maintains significantly higher and more stable coverage across programs. This study provides the first comprehensive benchmark of modern LLMs for ST unit testing, highlighting their strengths, limitations, and improvements through one-shot prompting, and positioning their performance relative to specialized automated testing tools in industrial automation.

42 ENGINEERING↗
DOE OSTI2021

Improving Discovery, Sharing, and Use of Water Data: Initial Findings and Suggested Future Work

Collaborative management of water resources requires a broad suite of “water data” that extends beyond basic information about water quantity and quality to other related topics such as water infrastructure, aquatic ecosystem health, socioeconomic factors, and power generation. Water data are disparate in nature because they are collected and provided by many entities, and in some cases, remain challenging to access and use. The U.S. Department of Energy’s Water Power Technologies Office initiated a project to characterize relevant categories of water data; describe the current state of accessing, using, and visualizing water data; and outline investigatory pathways for future efforts aimed at improving the discovery, sharing, and use of water data. Input on these topics was solicited from a small but diverse cross section of members of the water resources community. Fourteen broad categories of water data were identified: dams; ecology; flood control; hydroclimatology; hydrography; hydrology; hydropower; management landscape; migratory barriers; recreation and aesthetic importance; socioeconomic; water quality; water availability and use; and weather. Stakeholder perspectives on the accessibility and usability of water data indicate these aspects are affected by a complex set of technical and social factors. However, stakeholders generally agreed that better access to water data can provide a range of benefits to water management, and they stressed the need to generate broad support from water data users and producers. Two investigatory pathways were outlined that, taken together, provide a logical progression toward the goals of the project. The first pathway emphasizes further investigation to better define target audiences and data needs, identify opportunities for collaboration between related efforts, and conduct value demonstration activities to generate further support for improving discovery and access of water data. The second pathway focuses on creating a comprehensive vision for potential solutions that improve the discovery of water data. Several activities that align with the first pathway are suggested for the next phase of the project.

13 HYDRO ENERGY↗
DOE OSTI2025

Fast Machine Learning for Quantum Control of Microwave Qudits on Edge Hardware

Quantum optimal control is a promising approach to improve the accuracy of quantum gates, but it relies on complex algorithms to determine the best control settings. CPU or GPU-based approaches often have delays that are too long to be applied in practice. It is paramount to have systems with extremely low delays to quickly and with high fidelity adjust quantum hardware settings, where fidelity is defined as overlap with a target quantum state. Here, we utilize machine learning (ML) models to determine control-pulse parameters for preparing Selective Number-dependent Arbitrary Phase (SNAP) gates in microwave cavity qudits, which are multi-level quantum systems that serve as elementary computation units for quantum computing. The methodology involves data generation using classical optimization techniques, ML model development, design space exploration, and quantization for hardware implementation. Our results demonstrate the efficacy of the proposed approach, with optimized models achieving low gate trace infidelity near $10^{-3}$ and efficient utilization of programmable logic resources.

Sanders, Flor [Columbia U.]↗
DOE OSTI2023

A Pulse Generation Framework with Augmented Program-aware Basis Gates and Criticality Analysis

Near-term intermediate scale quantum (NISQ) de- vices are subject to considerable noise and short coherence time. Consequently, it is critical to minimize circuit execution latency. Traditionally, each basis gate of a transpiled circuit is decoded into a fixed episode of the device control pulses. Recently, people started to investigate merged pulse generation for customized gates through quantum optimal control (QOC). However, existing QOC approaches face the challenges of (i) restricted search space due to prohibitive compilation overhead; (ii) suboptimal end-to-end performance due to aggressive local optimization and falsely introduced dependency among the customized gates; (iii) inadequate adaptivity towards system calibration, which is critical for NISQ devices. In this work, we propose PAQOC, a novel QOC framework that can (i) automatically detect frequently encountered gate patterns in the logical circuit by modeling the problem as a subgraph mining process and reuse these patterns to enable much larger search space exploration (i.e., program aware); (ii) systemically construct customized gate-set based on the impact to the overall program latency (i.e., criticality-aware); and (iii) quickly adapt to system re-calibration thanks to the small-scale pattern-based gate generation (i.e., adaptivity-aware). PAQOC achieves a good tradeoff between circuit performance and compilation time, allowing fully automatic, single stop, ad- hoc customized pulse generation for more efficient execution of user programs on NISQ devices. Evaluations using fifteen applications show that PAQOC can achieve on average 1.95× speedup of the circuit latency and achieve on average 36.7% reduction in compilation overhead. With PAQOC, circuits can run faster with reduced noise, allowing deeper circuits to be tested within the coherence time of present NISQ platforms.

Chen, Yanhao↗
DOE OSTI2024

The crucial role of diagnostics in achieving ignition on the National Ignition Facility (NIF)

Well over 100 diagnostics can operate on the National Ignition Facility (NIF) as a result of several decades of development on NIF, and before that on Nova, OMEGA, and earlier LLNL lasers. A subset of these have guided the approach to achieving ignition on the NIF in 2022 [H. Abu-Shawareb et al. (Indirect Drive ICF Collaboration), Phys. Rev. Lett. 129(7), 075001 (2022)]. Achieving ignition on NIF has required many types of experiments with this core set of diagnostics, some constraining known unknowns and some revealing surprises—arguably unknown unknowns. Early design work realized that the extreme precision required for ignition on NIF would require fine-tuning by experiment, that is, measuring and adjusting known unknowns. Many examples are given where the use of the core set of ignition diagnostics in experimental arrangements called platforms demonstrated control of the key theoretical parameters defined as shape, adiabat, velocity, and mix. The direction of the adjustments to input conditions is found either by trend analysis or, in many cases, by observing from the diagnostic data the direction to make an adjustment. In addition, diagnostics have revealed some unexpected or neglected known issues, which degrade performance, or unexpected issues, unknown unknowns. Some of these factors had been previously considered, but underestimated or difficult to calculate at the time. The overall methodology can be described as a variant of Popper's falsifiability philosophy [K. Popper, The Logic of Scientific Discovery (Hutchinson, 1974)]. This paper summarizes the role of ignition diagnostics in terms of falsification or validation of theory or experimental setup as well as uncovering unexpected issues. The journey to ignition started in the seventies with a 1-µm wavelength laser producing disastrous results. Diagnostics have guided us to the recent multi-decadal goal of demonstrating ignition and burn in the laboratory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

MFANS 2024 - Formally Proving Characteristics of Cyber-Physical Systems

Cyber-physical systems (CPS) are engineered systems that rely on the smooth integration of computational algorithms and physical elements. This integration presents new challenges for verifying that systems will behave as expected. The goal of this presentation is to present current challenges and potential solutions for the formal verification of cyber-physical systems. For cyber systems, formal methods refer to systematically rigorous mathematical techniques employed in the specification, development, analysis, and verification of both software and hardware systems. Recent advancements in computer science have yielded sophisticated tools specifically designed to address challenges associated with formal methods in complex systems. These tools leverage various foundational concepts such as logic, formal languages, program semantics, type systems, type theory, and automata theory. A notable achievement in the application of formal methods is the seL4 microkernel, claimed to be the first general-purpose operating-system kernel to be verified. Its proof implies the absence of bugs and guarantees that the kernel meets specifications. For physical systems, dynamic and control theory has a history of using rigorous analytic techniques to prove functional correctness. Lyapunov, optimal, classical, modern, and robust control theories all provide rigorous mathematical methods both to analyze system performance and to design controller that can be guaranteed to meet certain objectives. Recent computational techniques like level set theory and reachability analysis provide assertions that a system's state will avoid unsafe regions. Even though success has been independently achieved for cyber systems and physical systems, the integration of such systems creates new challenges. In particular, there is an obvious discrepancy between finite-state machines and infinite-state systems, resulting in different approaches for modeling and analyzing these system. While it is possible to simulate hybrid systems, this provides only a demonstration of a performance and not proof. For hybrid systems, current formal methods and system analysis approaches typically require a workarounds to work on hybrid systems like CPS. This paper will outline the state of the art and limits of current practice for formally verifying CPS and will identify possible research directions that require attention.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Integration of Control Methods and Digital Twins for Advanced Nuclear Reactors

Advanced nuclear reactors offer a new set of features to energy generation, due to their ability to adapt to variable energy demand, operate autonomously, be deployed in rural locations and monitored remotely, afford compact size and lower power ratings, and rely on novel technologies to achieve safer operations. Thus, a requirement for the success of these reactors is the use of intelligent forms of control to track changing power demands, make autonomous decisions, and reduce the need for human involvement. Regulatory requirements pertaining to control of nuclear reactors could be met via historical means of control; however, these are not expected to enable the level of highly autonomous operations desired in advanced nuclear reactors. Historical control methods rely on both logical and high-performance (HP) control. These two types of control are usually used separately, with a human element being introduced whenever decisions are cascaded from one science to another. AI/ML control, on the other hand, can replace the human element in the current U.S. fleet of nuclear power plants (NPPs) by acting as a supervisory optimizer that understands the plant internal/external variables in order to make control decisions, and can easily handle non-linear and multi-input/multi out (MIMO) decisions—another requirement for advanced nuclear reactors that could be difficult to handle via logical and HP control. Because of the harsh operating environments produced in advanced reactors, resulting in the frequent failure of sensors and other types of equipment, and considering the lack of operating history for advanced nuclear reactors, control of advanced nuclear reactors would necessitate relying on a model that can track and adapt to the actual process (i.e., a digital twin). This digital twin can make approximations when knowledge and data are unavailable and would evolve as more knowledge is gained. The reactor control must also be risk-informed to account for the high-consequence nature of advanced reactors. This report introduces a high-level (i.e., not method- or process-specific) integration of the three different control and digital twinning methods able to meet the requirements for advanced nuclear reactors. These methods could be applied during both the operational and design stages of these reactors. The aim is to demonstrate how each method interfaces with and highlights enabling solutions necessitated by the unique features of advanced nuclear reactors.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

Geometric Structure and Transversal Logic of Quantum Reed–Muller Codes

Designing efficient and noise-tolerant quantum computation protocols generally begins with an understanding of quantum error-correcting codes and their native logical operations. The simplest class of native operations are transversal gates, which are naturally fault-tolerant. Here, in this paper, we aim to characterize the transversal gates of quantum Reed–Muller (RM) codes by exploiting the well-studied properties of their classical counterparts. We start our work by establishing a new geometric characterization of quantum RM codes via the Boolean hypercube and its associated subcube complex. More specifically, a set of stabilizer generators for a quantum RM code can be described via transversal X and Z operators acting on subcubes of particular dimensions. This characterization leads us to define subcube operators composed of single-qubit π/2 k Z -rotations that act on subcubes of given dimensions. We first characterize the action of subcube operators on the code space: depending on the dimension of the subcube, these operators either (1) act as a logical identity on the code space, (2) implement non-trivial logic, or (3) rotate a state away from the code space. Second, and more remarkably, we uncover that the logic implemented by these operators corresponds to circuits of multi-controlled-Z gates that have an explicit and simple combinatorial description. Overall, this suite of results yields a comprehensive understanding of a class of natural transversal operators for quantum RM codes.

Reed–Muller (RM) codes↗
DOE OSTI2024

Integrate Latimer Controls' Solution into RTAC (CRADA Final Report, CRD-23-24672)

Latimer Controls, Inc. was awarded two vouchers under the Department of Energy's American-Made Solar Prize Round 6 to conduct collaborative research at a national laboratory. The National Renewable Energy Laboratory (NREL) was selected as a partner to assist Latimer Controls in the performance evaluation of its photovoltaic (PV) control software. This collaboration focuses on developing a hardware-in-the-loop (HIL) testbed at NREL, which will be used to test and validate the Latimer PV control technology in a realistic yet de-risked environment. Both Latimer and NREL teams will work together to analyze the collected test data, derive insights, and disseminate the scientific findings. Recent studies underscore the potential of solar energy as a zero-marginal-cost and zero-emission flexibility resource within the bulk power system, particularly when integrated with advanced control systems. To enhance the performance of such systems, Latimer Controls has developed leading-edge technologies, including machine learning (ML) algorithms and hierarchical inverter set-point allocation methods. These innovations are designed to estimate the operational headroom of large PV plants for grid integration and control. However, comprehensive validation under real-world conditions remains necessary. To address this gap, the concurrent CRADA project proposes the real-world application and validation of the Latimer Control solution within a HIL environment. Initially, the Latimer algorithm was developed and tested within MATLAB Simulink, a platform suitable for research-level simulations and iterative development. However, transitioning this technology to a real solar site as an industry-ready solution necessitates implementation in a format compatible with widely used solar power plant controllers. In this additional CRADA work, the MATLAB Simulink-based logic will be translated into Structured Text, a programming language compliant with IEC 61131 standards, which is commonly used for custom logic implementations in industry-leading programmable logic controllers (PLCs), such as the Schweitzer SEL real-time automation controller (RTAC). This transition will facilitate the deployment of the Latimer Control solution in real-world solar power plants, thereby advancing the technology towards commercialization.

14 SOLAR ENERGY↗
DOE OSTI2022

Independent temperature and humidity control of a precooled desiccant air cooling system with proportional and fuzzy logic + proportional based controllers

Providing room comfort quickly by using less energy in cooling systems is important both in terms of efficiency and environment. In this study, independent temperature/humidity control strategies are designed for precooled desiccant based evaporative cooling system to provide room comfort quickly with less energy. Therefore, the speed controls of the system's actuators become important depending on the room, cooler and atmosphere conditions. The mathematical models are obtained to determine the relation between voltages of actuators and the variations in the room's temperature and humidity. After that, new control strategies are developed based on Proportional and Fuzzy+Proportional techniques and the control performance is increased by adding extra modes to the operation of the actuators. The effects of the control techniques on the cooling performance and energy consumption were investigated for different cases. It has been observed that the room temperature and relative humidity reach the set values in a short time for both techniques and are successfully kept at these values under the disturbances. By using Fuzzy+Proportional controller, the robustness of the cooler increases due to more precisely adjustment of controller's parameter depending the system conditions. Finally, both control strategies provide more than 20% energy savings compared to the traditional ON/OFF control.

42 ENGINEERING↗
DOE OSTI2024

Engineering 3D Floquet Codes by Rewinding

Floquet codes are a novel class of quantum error-correcting codes with dynamically generated logical qubits arising from a periodic schedule of noncommuting measurements. We utilize the interpretation of measurements in terms of condensation of topological excitations and the rewinding of measurement sequences to engineer new examples of Floquet codes. In particular, rewinding is advantageous for obtaining a desired set of instantaneous stabilizer groups on both toric and planar layouts. Our first example is a Floquet code with instantaneous stabilizer codes that have the same topological order as the three-dimensional (3D) toric code(s). This Floquet code also exhibits a splitting of the topological order of the 3D toric code under the associated sequence of measurements, i.e., an instantaneous stabilizer group of a single copy of the 3D toric code in one round transforms into an instantaneous stabilizer group of two copies of the 3D toric code up to nonlocal stabilizers in the following round. We further construct boundaries for this 3D code and argue that stacking it with two copies of the 3D subsystem toric code allows for a transversal implementation of the logical non-Clifford controlled-controlled- Z gate. We also show that the coupled-layer construction of the X-cube Floquet code can be modified by a rewinding schedule such that each of the instantaneous stabilizer codes is finite depth equivalent to the X-cube model up to toric codes; the X-cube Floquet code exhibits a splitting of the X-cube model into a copy of the X-cube model and toric codes under the measurement sequence. Our final 3D example is a generalization of the 2D Floquet toric code on the honeycomb lattice to three dimensions, which has instantaneous stabilizer codes with the same topological order as the 3D fermionic toric code. Published by the American Physical Society2024

Physics↗
DOE OSTI2023

A nanocryotron memory and logic family

The development of superconducting electronics based on nanocryotrons has been limited so far to few device circuits, in part due to the lack of standard and robust logic cells. Here, we introduce and experimentally demonstrate designs for a set of nanocryotron-based building blocks that can be configured and combined to implement memory and logic functions. The devices were fabricated by patterning a single superconducting layer of niobium nitride and measured in liquid helium on a wide range of operating points. The tests show 10 - 4 bit error rates with above ± 20 % margins up to 50 MHz and the possibility of operating under the effect of an out-of-plane 36 mT magnetic field, with ± 30 % margins at 10 MHz. Additionally, we designed and measured an equivalent delay-flip-flop made of two memory cells to show the possibility of combining multiple building blocks to make larger circuits. These blocks may constitute a solid foundation for the development of nanocryotron logic circuits and finite-state machines with potential applications in the integrated processing and control of superconducting nanowire single-photon detectors.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

JTAG-based PLC memory acquisition framework for industrial control systems

In industrial control systems (ICS), programmable logic controllers (PLC) are the embedded devices that directly control and monitor critical industrial infrastructure processes such as nuclear plants and power grid stations. Cyberattacks often target PLCs to sabotage a physical process. A memory forensic analysis of a suspect PLC can answer questions about an attack, including compromised firmware and manipulation of PLC control logic code and I/O devices. Given physical access to a PLC, collecting forensic information from the PLC memory at the hardware-level is risky and challenging. It may cause the PLC to crash or hang since PLCs have proprietary, legacy hardware with heterogeneous architecture. This paper addresses this research problem and proposes a novel JTAG (Joint Test Action Group)-based framework, Kyros, for reliable PLC memory acquisition. Kyros systematically creates a JTAG profile of a PLC through hardware assessment, JTAG pins identification, memory map creation, and optimizing acquisition parameters. It also facilitates the community of interest (such as ICS owners, operators, and vendors) to develop the JTAG profiles of PLCs. Further, we present a case study of Kyros implementation over Allen-Bradley 1756-A10/B to help understand the framework's application on a real-world PLC used in industry settings. The sample PLC memory dumps are shared with the research community to facilitate further research.

Rais, Muhammad Haris↗
DOE OSTI2024

Enhancing quantum annealing accuracy through replication-based error mitigation *

Abstract Quantum annealers like those manufactured by D-Wave Systems are designed to find high quality solutions to optimization problems that are typically hard for classical computers. They utilize quantum effects like tunneling to evolve toward low-energy states representing solutions to optimization problems. However, their analog nature and limited control functionalities present challenges to correcting or mitigating hardware errors. As quantum computing advances towards applications, effective error suppression is an important research goal. We propose a new approach called replication based mitigation (RBM) based on parallel quantum annealing (QA). In RBM, physical qubits representing the same logical qubit are dispersed across different copies of the problem embedded in the hardware. This mitigates hardware biases, is compatible with limited qubit connectivity in current annealers, and is well-suited for currently available noisy intermediate-scale quantum annealers. Our experimental analysis shows that RBM provides solution quality on par with previous methods while being more flexible and compatible with a wider range of hardware connectivity patterns. In comparisons against standard QA without error mitigation on larger problem instances that could not be handled by previous methods, RBM consistently gets better energies and ground state probabilities across parameterized problem sets.

Djidjev, Hristo N. (ORCID:0000000192868824)↗
DOE OSTI2024

Fox Trails

1. This software utilizes python pandas to pull data from P6 databases or XER files. The software transforms the datasets into multiple main tables by joining, filtering, iteratively flattening hierarchical structured data, and pivoting datasets to give simple flat output tables. The activity table includes all of the information related to an activity including activity codes, global, EPS, and project codes, UDFs, and WBS information as separate columns. This includes the code id, code value and sequence number for all levels in hierarchical codes. The resource table is similar to the activity table and includes all of the information related to resources on activities including UPFs and resource codes. The resource time phased table takes the resource information and time phases it for the budget, forecast, late, and actual dates/units/costs that closely matches P6's user interface's values as it implements the resource curve and calendars. The wbs table contains the WBS structure broken out by levels and includes UDFs, codes, and notebook topics. The final P6 data table is the relationships table which simply contains the relationships. 2. When a user updates the tool with data (via giving it P6 project names with database username/password information or XER files) the system creates the data in #1, then creates a networkx graph with the activity data imbedded in the node data and the relationships added as edges. Each edge also has it's float calculated (working time distance between the predecessor and successor) and attached to the edge. Activities are also tagged as a potential start of a path based on their constraints, constraint dates, remaining start date, and activity status. When a user enters an activity ID into the UI, it runs a shortest path calculation on the network graph between each node tagged as potential start to the entered activity id based on the float tagged on the edge. Each path returned by the algorithm contains all of the nodes on the path in order, as well as the total float of the edges that make the path. This data is then collected and returned to the user in the form of a gantt chart with groupings for each path that includes the total float for each group. 3. Similar to 2, if the user passes through a reference dataset each activity set in the path is checked to see if it had a path in the reference dataset, if that path was the primary path between the start and end activities, and what has changed regarding logic and durations. These changes are color coded and summarized before sent to the user to be displayed by the UI for simple discovery. 4. Utilizing the data from #1, the user can submit desired grouping code(s) and filters to the system. The system will then pull the activities, resources, and relationships and create a gantt chart based on the groupings sent and filtered based on the filters sent. 5. The system will produce a gantt chart in a similar method to #4, but allows interactivity with the data. As the user interacts with the gantt chart, the software captures the changes and stores it with the user making the change so that project controls and implement those changes in P6.

Fox, Ben↗
DOE OSTI2024

Efficient Unitary Designs from Random Sums and Permutations

A unitary k-design is an ensemble of unitaries that matches the first k moments of the Haar measure. In this work, we provide two efficient constructions of k-designs on n-qubits using new random matrix theory techniques. Our first construction is based on exponentiating sums of random i.i.d. Hermitian matrices and uses O(k2n2)-many gates. In the spirit of central limit theorems, we show that this random sum approximates the Gaussian Unitary Ensemble (GUE). We then show that the product of just two exponentiated GUE matrices is already approximately Haar random. Our second construction is based on products of exponentiated sums of random permutations and uses Õ(k poly (n)) many gates. The k dependence is optimal (up to polylogarithmic factors) and is inherited from the efficiency of existing k-wise independent permutations. Furthermore, replacing random permutations with quantum-secure pseudorandom permutations (PRPs), we also obtain a pseudorandom unitary (PRU) ensemble that is secure under nonadaptive queries. A central feature of both proofs is a new connection between the polynomial method in quantum query complexity and the large-dimension (N) expansion in random matrix theory. In particular, the first construction uses the polynomial method to control high moments of certain random matrix ensembles without requiring delicate Weingarten calculations. In doing so, we define and solve a moment problem on the unit circle, asking whether a finite number of equally weighted points can reproduce a given set of moments. In our second construction, the key step is to exhibit an orthonormal basis for irreducible representations of the partition algebra that has a low-degree large-N expansion. This allows us to show that the distinguishing probability is a low-degree rational polynomial of the dimension N.

algebra↗
DOE OSTI2020

Parallel-in-Time Simulation of Lindblad's Equation

Constructing fast quantum logic gates is critical to building a scalable quantum computer. We consider a qudit, a quantum version of a bit that can take an arbitrary number of states, coupled with a cavity. In this project, we wish to force the qudit to reach the 0-state, for any possible initial state. The coupled system changes in time according to Lindblad’s equation, an ordinary differential equation on the density matrix of the quantum system. Lindblad’s equation contains some parameters that we can control, so-called control functions. We seek control functions which force the qudit to the 0-state within 2 microseconds, which is much faster than what is currently done in practice. The search method is gradient descent, a numerical optimization method that uses gradient information to iteratively improve the control parameters. My contribution to this project is an attempt to speed up the computation of the gradient. It currently takes about 40 seconds to compute the gradient which involves solving a set of ODEs sequentially. Current supercomputers have thousands of cores, but sequential computations can only make use of 1 core at a time. We wish to divide up the work better, so that we can use many more cores at once. To this end, we have implemented the Multigrid Reduction in Time (MGRIT) algorithm. We perform a systematic parameter search on how to best apply this algorithm. Results indicate a 25 percent speed up for solving Lindblad’s equation and determining how close the final state is the 0-state.

97 MATHEMATICS AND COMPUTING↗