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At least 595 records · Page 33

A Suppression-based STDP Rule Resilient to Jitter Noise in Spike Patterns for Neuromorphic Computing

Multi-spike models of synaptic plasticity, such as the triplet and suppression spike-timing-dependent plasticity (STDP) rules, exhibit better alignment with neurophysiological data in the brain compared to the pair-based STDP rule. Previous studies have empirically shown that the pair-based STDP rule can detect spatiotemporal spike patterns hidden in equally dense distractor spike trains in an unsupervised manner. However, it fails to detect spike patterns influenced by jitter noise. Given that spiking neural networks (SNNs) exhibit variability in generated spike trains in response to the same inputs, it becomes imperative to have learning rules capable of detecting spike patterns even in the presence of jitter noise. In this study, we introduce a simplified suppression-based STDP rule that demonstrates significantly enhanced tolerance to jitter in spike patterns compared to the pair-based STDP rule. Unlike the ideal suppression STDP rule, characterized by an exponential learning window and requiring high-resolution synapses, the simplified rule limits the synaptic efficacy update to a single bit at any given instant. Moreover, it employs 4-bit fixed-point synapses, facilitating straightforward implementation in neuromorphic hardware.

Gautam, Ashish [ORNL]↗

Real-Time Inertia Estimation Tool Implementation Based on Probing Signals

As renewable energy penetration increases and the traditional generators retire in power grids, system inertia decreases and exhibits significant daily fluctuations. Furthermore, fast frequency responses (FFRs) provided by the inverter-based resources (IBRs) begin to playa very critical role and bring new challenges to real-time system inertia monitoring due to the difficulties of quantifying its artificial inertia contribution. Thus, necessitating an accurate real-time inertia estimation tool will not only benefit the secure power grid operations, but also provide insights on assessing the artificial inertia contribution from the IBRs. This paper presents a probing-based real-time inertia estimation tool that has been validated through a power-hardware-in-the-Ioop (PHIL) test system using identical hardware battery energy storage system (BESS) and control in an actual power grid. Preliminary results indicate high estimation accuracy of the developed tool and pave the way for the field test and deployment.

inverter-based resources↗

Electric Drive Technologies Research: ELT223 Component Modeling, Co-Optimization, and Trade-Space Evaluation Annual Report

This project is intended to support the development of new traction drive systems that meet the targets of 100 kW/L for power electronics and 50 kW/L for electric machines with reliable operation to 300,000 miles. To meet these goals, new designs must be identified that make use of state-of-the-art and next-generation electronic materials and design methods. Designs must exploit synergies between components, for example converters designed for high-frequency switching using wide band gap (WBG) devices and ceramic capacitors. This project included: (1) a survey of available technologies; (2) investigating new technologies, that for example, reduce volume of thermal management or magnetic components; (3) the development of computer aided design tools that consider the converter volume, reliability, and electrical performance; (4) exercising the design software to evaluate performance gaps and predict the impact of certain technologies and design approaches, i.e. GaN semiconductors, ceramic capacitors, ceramic thermal management components, and select topologies; (5) building and testing hardware prototypes to validate models and concepts. The design tools enable co-optimization of the power module and passive elements and provide some design guidance. At the end of the project, new advanced computing methods, such as machine learning approaches, were considered.

33 ADVANCED PROPULSION SYSTEMS↗

Binary operations on neuromorphic hardware with application to linear algebraic operations and stochastic equations

Abstract Non-von Neumann computational hardware, based on neuron-inspired, non-linear elements connected via linear, weighted synapses—so-called neuromorphic systems—is a viable computational substrate. Since neuromorphic systems have been shown to use less power than CPUs for many applications, they are of potential use in autonomous systems such as robots, drones, and satellites, for which power resources are at a premium. The power used by neuromorphic systems is approximately proportional to the number of spiking events produced by neurons on-chip. However, typical information encoding on these chips is in the form of firing rates that unarily encode information. That is, the number of spikes generated by a neuron is meant to be proportional to an encoded value used in a computation or algorithm. Unary encoding is less efficient (produces more spikes) than binary encoding. For this reason, here we present neuromorphic computational mechanisms for implementing binary two’s complement operations. We use the mechanisms to construct a neuromorphic, binary matrix multiplication algorithm that may be used as a primitive for linear differential equation integration, deep networks, and other standard calculations. We also construct a random walk circuit and apply it in Brownian motion simulations. We study how both algorithms scale in circuit size and iteration time.

97 MATHEMATICS AND COMPUTING↗

Dynamically robust coordinated set point tracking of distributed DERs at point of common coupling

Low-inertia operation of small-scale power systems, such as a microgrid or a portion of a long feeder, requires careful coordination of the controller performance of the constituting devices. This challenge is exacerbated in microgrids serving the functionalities of a conventional synchronous-based generation unit while comprised of smaller DERs operating mainly interfaced through power electronics converters. This paper builds on the idea of set point modulation and proposes a two-level control strategy that aims to achieve superior performance at the point of common coupling (PCC) of microgrids by combining a local control level with a distributed and coordinated level. Several case studies on both AC and DC systems, the CIGRE low-voltage benchmark system as the AC system and a test DC microgrid, validate the performance of the proposed approach. The real-world applicability of the approach is established via a high-fidelity power hardware-in-the-loop (PHIL) experimental setup and an application case study on grid frequency regulation. The proposed approach enables a microgrid to participate in ancillary service provisions where speed and quality of regulation are critical.

24 POWER TRANSMISSION AND DISTRIBUTION↗

A survey of techniques for optimizing transformer inference

Recent years have seen a phenomenal rise in the performance and applications of transformer neural networks. The family of transformer networks, including Bidirectional Encoder Representations from Transformer (BERT), Generative Pretrained Transformer (GPT) and Vision Transformer (ViT), have shown their effectiveness across Natural Language Processing (NLP) and Computer Vision (CV) domains. Transformer-based networks such as ChatGPT have impacted the lives of common men. However, the quest for high predictive performance has led to an exponential increase in transformers' memory and compute footprint. Researchers have proposed techniques to optimize transformer inference at all levels of abstraction. Further, this paper presents a comprehensive survey of techniques for optimizing the inference phase of transformer networks. We survey techniques such as knowledge distillation, pruning, quantization, neural architecture search and lightweight network design at the algorithmic level. We further review hardware-level optimization techniques and the design of novel hardware accelerators for transformers. We summarize the quantitative results on the number of parameters/FLOPs and the accuracy of several models/techniques to showcase the tradeoff exercised by them. We also outline future directions in this rapidly evolving field of research. We believe that this survey will educate both novice and seasoned researchers and also spark a plethora of research efforts in this field.

97 MATHEMATICS AND COMPUTING↗

Multiphysics Modeling of Hydrokinetic Turbine Energy Conversion System

Hydrokinetic turbines (HKTs) hold great promise as a renewable energy source, but high maintenance costs and limited energy output hinder their widespread adoption. The lack of comprehensive research on HKT drivetrain designs creates a knowledge gap in enhancing generation efficiency and cost reduction. A model of the HKT system with a focus on electric drivetrains and power converters is required to address this knowledge gap. This paper first introduces a MATLAB-averaged model integrating electrical-mechanical-thermal domains and aging behaviors within multi-time frames. Then a PLECS model, which incorporates maximum power point tracking and dq reference framed control for AC-DC-AC power converters, is enriched by a dynamic thermal model to predict fast transients accurately. These models optimize the design at the component level, resulting in improved integrated system performance. Furthermore, the validation of the models is carried out through hardware experiments for the averaged model and hardware-in-the-loop testing for the dynamic model.

ADVANCED PROPULSION SYSTEMS,HYDRO ENERGY↗

Transient Stability-Enhancing Method for Grid-Forming Inverters Under Current Limiting

The primary controller of a grid-forming (GFM) inverter governs the internal reference voltage and angle, which enables the inverter to naturally synchronize and share power with the connected grid; however, during disturbances on the grid caused by, e.g., line faults, overloading, or frequency and phase shifts, a GFM inverter can be pushed into a current-limited operation to protect the device against thermal damage. This can lead to a windup of the internal reference frequency generated by the primary controller and cause a total loss of synchronism with the grid. Here, to make the primary controller of GFM inverters more robust against transient instability, this paper proposes a method that manipulates the reference signals governed by the primary controller by introducing the concept of fictitious power. The fictitious power counteracts the integrator windup in the primary controller, which enables the current-limited inverter to conceive a stable operating point. This method is benchmarked against five state-of-the-art GFM inverter stabilization methods to evaluate its stability-enhancing performance. Full-order electromagnetic-transient simulations and experimental results of a hardware inverter test setup validate the benefits of the method to improve the transient stability of GFM inverters in the face of grid disturbances.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Performance Portable Graphics Processing Unit Acceleration of a High-Order Finite Element Multiphysics Application

The Lawrence Livermore National Laboratory (LLNL) will soon have in place the El Capitan exascale supercomputer, based on advanced micro devices (AMD) graphics processing units (GPUs). As part of a multiyear effort under the National Nuclear Security Administration (NNSA) Advanced Simulation and Computing (ASC) program, we have been developing marbl, a next generation, performance portable multiphysics application based on high-order finite elements. In previous years, we successfully ported the Arbitrary Lagrangian–Eulerian (ALE), multimaterial, compressible flow capabilities of marbl to nvidia GPUs as described in Vargas et al. Here, in this paper, we describe our ongoing effort in extending marbl's GPU capabilities with additional physics, including multigroup radiation diffusion and thermonuclear burn for high energy density physics (HEDP) and fusion modeling. We also describe how our portability abstraction approach based on the raja Portability Suite and the mfem finite element discretization library has enabled us to achieve high performance on AMD based GPUs with minimal effort in hardware-specific porting. Throughout this work, we highlight numerical and algorithmic developments that were required to achieve GPU performance.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Coupling between interfacial charge and mechanical deformation at high temperatures in ceramics. Final report

Basic research, under this project, has led to new fundamental discoveries in the effect of electric field (and temperature) on diffusion kinetics, electroluminescence and electronic conductivity in ceramic materials. For example, yttria stabilized zirconia sinters in just seconds well below 1000°C, while, at the same time, exhibiting a highly non-linear rise in conductivity, and intense electroluminescence. The phenomenon has been shown to occur in nearly all ceramics whether they are ionic or electronic conductors, or insulators. The rise in conductivity leads to Joule heating but in-situ measurements with a platinum standard at APS and Brookhaven (NSLS-II) have shown that the temperatures are much below what would have been needed to sinter in a few seconds. We have explored the hypothesis that huge concentrations of Frenkel pairs of vacancies and interstitials are produced. While these point defects accelerate sintering (by the interstitials being transported to the pores and the vacancies to the grain boundaries), they may also produce electron-hole pairs which can impart high electrical conductivity or recombine to emit photons. Many measurements, including in-situ measurements of lattice expansion are consistent with this hypothesis. However, the energy barrier for generating Frenkels in zirconia for example is much larger than can be expected at temperature and electrical fields in these experiments. Most recent work suggests that short wavelength phonons play a critical role in the genesis of the “flash” phenomenon. For example, the Debye temperature has been shown to be the lower bound for initiating flash. Molecular dynamics simulations have shown that large concentrations of Frenkel pairs can form under the proliferation of “optical” phonons at the edge of the Brillouin zone, that is with a wavelength at or below the lattice parameter. This project has led to the development of new experimental techniques as well as a software hardware interface for process and control and data analysis in real time, with a time scale of less than one second. This approach spells a new paradigm in materials science research. It potential impact on high rate manufacturing is self evident.

36 MATERIALS SCIENCE↗

Turboexpander for Direct Cooling in Hydrogen Vehicle Fueling Infrastructure

Hydrogen fuel cell electric vehicles (FCEVs) have been identified as one of a few options for zero carbon emissions transportation. A major advantage of FCEVs is that they can fuel quickly and follow a familiar fueling behavior to hydrocarbon-fueled vehicles. Whether light duty or heavy duty, the goal for a hydrogen dispenser is to fuel a vehicle in the same amount of time as the fossil fuel equivalent. When hydrogen is dispensed into the vehicle storage system, however, the temperature rises due to the Joule-Thomson effect and the heat of compression. Typically, vehicles store the compressed hydrogen in composite overwrapped pressure vessels that have a polymer liner with an operational temperature limit of 85°C. This temperature limit can be exceeded during fast fueling if hydrogen is not precooled. Precooling allows for a dispenser to fuel a vehicle at a faster flow rate by preventing the storage tank on the vehicle from overheating. Fueling protocols and requirements are presented in SAE J2601 Fueling Protocols for Light Duty Gaseous Hydrogen Surface Vehicles [1]. A heavy-duty equivalent is under development with similar requirements for precooling. Currently, conventional precooling for light-duty vehicle refueling uses a heat exchanger and chiller to cool the hydrogen gas to -40°C before entering the vehicle. The precooling system represents a significant part of the station capital and operating costs, so if the cost of the precooling system can be reduced by improving its efficiency, the overall station capital and operating cost can be reduced. In this project, National Renewable Energy Laboratory (NREL) and Sandia National Laboratories (SNL) researchers teamed up to investigate the turboexpander precooling application. A turboexpander is a device that places a turbine in a flow path where a pressure differential can be attained. This expansion device will extract work and lower the temperature of the fluid as the pressure reduces. While initial calculations based on established principles showed potential for a turboexpander to generate cooled gas, much work needs to be done to prove the concept. Turboexpanders typically work best under steady state conditions, while the dispenser is a very dynamic flow system. Dynamic turboexpander systems have been proven, such as a turbocharger on a gasoline vehicle. The inlet pressure at a dispenser is also much higher than any other known turboexpander system but should behave similarly to higher density fluids at lower pressures. Having both performed initial calculations, NREL and SNL researchers teamed up to investigate the turboexpander precooling application further. A project was soon built around the idea with SNL performing system modeling using previously proven capabilities and NREL performing hardware characterization with established station capabilities. Creare LLC was contracted as the turbomachinery expert to design and build the concept device. Part way through the project, however, contracting issues with the funding partner caused the project to terminate early before building and characterizing the concept device. While the project could not continue, many key findings were already learned. This paper is a summary of those findings.

08 HYDROGEN↗

The Psyche Gamma-Ray and Neutron Spectrometer

A Gamma-Ray and Neutron Spectrometer (GRNS) instrument has been developed as part of the science payload for NASA’s Discovery Program Psyche mission to the M-class asteroid (16) Psyche. The GRNS instrument is designed to measure the elemental composition of Psyche with the goal to understand the origin of this mysterious, potentially metal-rich planetary body. The GRNS will measure the near-surface abundances for the elements Ni, Fe, Si, K, S, Al, and Ca, as well as the spatial distribution of Psyche’s metal-to-silicate fraction (or metal fraction). These measurements address three of the five Psyche mission science objectives: determine if Psyche is a core; determine whether small metal bodies incorporate light elements into the metal phase; and determine whether Psyche was formed under reducing conditions. The Gamma-Ray Spectrometer (GRS) uses a cryocooled, high-purity Ge (HPGe) sensor to detect cosmic-ray generated gamma rays in the 60 to 9000-keV energy range. The HPGe sensor is surrounded by a borated plastic anticoincidence shield that provides three functions: active background rejection from charged particle interactions in the HPGe sensor; fast neutron measurements; and direct measurements of the incident galactic cosmic ray flux. The Neutron Spectrometer (NS) uses three 3 He gas proportional sensors, each with different material wraps to measure thermal (<0.4 eV), low-energy epithermal (0.4 eV to 1 keV), and high-energy epithermal (up to 100 keV) neutrons. This paper provides an overview of the Psyche GRNS, including: its science and measurement objectives; the design of the instrument hardware, software, and operation; pre-launch performance measurements and its initial performance in space; and an overview of its data products and expected operation for different Psyche mission phases.

Engineering - Instrumentation related to nuclear s↗

The Exploitation of Data Reduction for Visualization

The disparity between the computational speed and storage bandwidth, as demonstrated in Figure 1, is a well known problem that grows with each successive generation. The visualization community is principally responding to this issue by using in situ to reduce which data must be written to storage. However, other communities are taking different, possibly complementary approaches. In particular, data compression is a common general approach to reduce storage demands. Data compression technologies are typically not designed with post processing in mind. The principal metrics measured are compression ratio, the improved bandwidth to storage, and the error introduced. It is assumed that data is inflated to its full size before any post processing can happen. Although when talking about bandwidth disparities, HPC’s dirty little secret is that no part of the memory nor interconnect hardware is increasing at the rate of computation. For example, the Summit supercomputer has a peak computation rate almost 10 times its predecessor, Titan, but only about 4 times the memory, less than twice the aggregate memory bandwidth, and almost no improvement in the interconnect bisection bandwidth. Naively inflating data for post processing does not help with limitations in the memory and interconnect systems.

97 MATHEMATICS AND COMPUTING↗

Development of Hydrogen Burner for FT4000® Aeroderivative Engine - Final Report

This report details an effort to develop a retrofittable fuel/air injector for the FT4000® aeroderivative gas turbine that enables use of hydrogen as a carbon-free fuel for efficient power generation. The FT4000 engine’s low-NOx combustor was developed by Pratt & Whitney and RTX Technology Research Center with core technology from the Pratt & Whitney PW4000 turbofan aircraft engine. The current FT4000 production engine operates on either natural gas or No. 2 fuel oil with water injection to achieve high thermal efficiency and low emissions. This engine is fielded by Mitsubishi Power Aero and delivers 70 MW of power with a simple-cycle efficiency of over 41% when operating with wet compression. The work reported here advances the technology readiness level of the FT4000 combustor for operation with hydrogen, starting with an experimental assessment of the current production hardware with increasing hydrogen content mixed with natural gas and ending with improved nozzle concepts for fully robust operation with 100% hydrogen. High-pressure single-sector combustor rig tests have been completed, demonstrating the ability for the dual fuel nozzle to operate an FT4000 combustor on 100% hydrogen with low nitrogen oxide (NOx) emissions. Metal temperature measurements and video images of the flame structure from zero to 100% hydrogen highlight opportunities to improve the fuel nozzle robustness for high hydrogen conditions. The design of new fuel/air mixer concepts to improve durability and operability with high hydrogen levels was also completed. A total of eleven new concepts were developed and analyzed, ranging from modifications to the bill-of-materials nozzle to fully clean sheet designs. The concepts were evaluated with non-reacting and reacting flow evaluations to assess the performance of the new hardware designs. Non-reacting tests included Phase Doppler Particle Analysis (PDPA) for droplet size and velocity, mechanical patternation for liquid water flux, and planar laser induced fluorescence (PLIF) with acetone-seeding for gaseous fuel/air mixing characterization. Five scaled candidate fuel nozzle designs, in addition to a scaled bill-of-materials nozzle, were then successfully evaluated in an atmospheric pressure burner rig. The nozzles were evaluated for performance with natural gas, hydrogen/natural gas blends, and pure hydrogen. For 100% hydrogen, the nozzles were evaluated with and without water injection. Optical and infrared imaging of the flame and fuel nozzle was captured. NOx emissions were sampled from fixed emissions probes. The results show measurable differences between the various designs, and the data was used to down-select the two most promising designs to advance to future full pressure rig testing. Results from this study have cleared the current production FT4000 engines with dual fuel nozzles to operate at baseload power on blends of hydrogen mixed with natural gas and water. Two promising nozzle designs have been developed to enable fully robust operation with up to 100% hydrogen. These nozzles require validation at full baseload operating conditions before they can be introduced to the field.

03 NATURAL GAS↗

Microgrid Fast Charging Station (MFCS) Design Platform Project (Summary Report)

This report documents the important steps and outcomes of the Microgrid Fast Charging Station (MFCS) Design Platform project, executed by XENDEE Corporation and its testing and validation by Idaho National Laboratory (INL). This final summary report builds on the first summary released on April 30th, 2021 and adds the final results from the Hardware in the Loop (HIL) simulations and tests, which have been completed July 14th 2021. With this report XENDEE Corporation and Idaho National Laboratory conclude the first version of the Microgrid Fast Charging Station (MFCS) Design Platform as well as all related tests and validations for two in-depth case studies for islanded and non-islanded operation. The platform itself utilizes XENDEE’s advanced modeling systems and INL’s HIL system to ensure project viability and technical feasibility. It also intelligently maps all cables, transformers, and distributed technology interactions to anticipate and mitigate problems during peak usage or adverse conditions. Finally, the system is designed to optimize dispatch and generation at each time step of the day allowing the Microgrid to take advantage of energy sales to the utility and best manage the charging of an electrical fleet. This allows operators to reliably build bankable Microgrid systems and to operate them to reach the maximum efficiency even under the dynamic needs of electric vehicle fast charging

24 POWER TRANSMISSION AND DISTRIBUTION↗

Comparative Study of Quasi-Particle Burst Events in Transmon Qubits made with Different Materials and Geometries

Superconducting qubits are susceptible to various noise sources, including cosmic rays. ambient gamma and infrared radiation, which can significantly impact their performance. High-energy radiations deposit energy into the qubit substrate, generating high-energy phonons that disrupt Cooper pairs and create quasi-particles (QPs). Infrared photons, on the other hand can directly create QPs. The tunneling of these quasi-particles across Josephson junctions leads to qubit de-excitation and causes relaxation errors. In this study, we utilize a fast feedback mechanism for qubit reset to detect QP burst events with high time resolution [1]. We investigate transmon qubits fabricated with different encapsulations [2], geometries, and substrates at the above-ground laboratory of the Superconducting Quantum Materials and Systems (SQMS) center at Fermilab. Our preliminary results are presented, with discussions on their implications for the performance of modern quantum hardware. [1] Dominicis and Roy et al.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Hierarchical Power Flow Control in Smart Grids: Enhancing Rotor Angle and Frequency Stability with Demand-Side Flexibility

Large-scale integration of renewables in power systems gives rise to new challenges for keeping synchronization and frequency stability in volatile and uncertain power flow states. To ensure the safety of operation, the system must maintain adequate disturbance rejection capability at the time scales of both rotor angle and system frequency dynamics. This calls for flexibility to be exploited on both the generation and demand sides, compensating volatility and ensuring stability at the two separate time scales. This article proposes a hierarchical power flow control architecture that involves both transmission and distribution networks as well as individual buildings to enhance both small-signal rotor angle stability and frequency stability of the transmission network. The proposed architecture consists of a transmission-level optimizer enhancing system damping ratios, a distribution-level controller following transmission commands and providing frequency support, and a building-level scheduler accounting for quality of service and following the distribution-level targets. Furthermore, we validate the feasibility and performance of the whole control architecture through real-time hardware-in-loop tests involving real-world transmission and distribution network models along with real devices at the Stone Edge Farm Microgrid.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Promise of Graph Sparsification and Decomposition for Noise Reduction in QAOA: Analysis for Trapped-Ion Compilations

We develop new approximate compilation schemes that significantly reduce the expense of compiling the Quantum Approximate Optimization Algorithm (QAOA) for solving the Max-Cut problem. Our main focus is on compilation with trapped-ion simulators using Pauli-X operations and all-to-all Ising Hamiltonian HIsing evolution generated by Molmer-Sorensen or optical dipole force interactions, though some of our results also apply to standard gate-based compilations. Our results are based on principles of graph sparsification and decomposition; the former reduces the number of edges in a graph while maintaining its cut structure, while the latter breaks a weighted graph into a small number of unweighted graphs. Though these techniques have been used as heuristics in various hybrid quantum algorithms, there have been no guarantees on their performance, to the best of our knowledge. This work provides the first provable guarantees using sparsification and decomposition to improve quantum noise resilience and reduce quantum circuit complexity. For quantum hardware that uses edge-by-edge QAOA compilations, sparsification leads to a direct reduction in circuit complexity. For trapped-ion quantum simulators implementing all-to-all HIsing pulses, we show that for a (1−ϵ) factor loss in the Max-Cut approximation (ϵ>0), our compilations improve the (worst-case) number of HIsing pulses from O(n2) to O(nlog(n/ϵ)) and the (worst-case) number of Pauli-X bit flips from O(n2) to O(nlog(n/ϵ)ϵ2) for n-node graphs. This is an asymptotic improvement for any constant ϵ>0. We demonstrate that significant improvements to the approximation ratio are obtained using decomposition in simulated trapped-ion experiments with dephasing noise. We further present a generic argument showing that sparsification results in an exponentially improved circuit fidelity lower bound in digital computing schemes based on one- and two-qubit gates, which are relevant to a wide variety of hardwares such as superconducting qubits and certain neutral atom or trapped ion setups, and more sophisticated noise models. We anticipate these approximate compilation techniques will be useful tools in a variety of future quantum computing experiments.

Moondra, Jai [Georgia Institute of Technology]↗