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At least 397 records · Page 22

Viscoelastic Modeling of Polymers in ALEGRA with the GAP Model

The Glassy Amorphous Polymer (GAP) model is a viscoelastic/plastic model developed at Los Alamos National Laboratory to accurately model a variety of polymers across a wide range of conditions and loading rates, including shock loading. In the present report we introduce and assess this model, newly implemented in the ALEGRA shock and multiphysics code, using a series of verification and application-related validation problems. We describe the mathematical and theoretical formulation of the model, as well as its implementation in ALEGRA, in detail. We provide verification results that assess the model implementation against published computational results, as well as validation results which we compare to existing experimental results when possible. These comparisons instill confidence in the implementation and indicate that the addition of the GAP model to the ALEGRA code provides users with a high-fidelity polymer modeling capability that is capable of recreating complex polymer phenomena.

36 MATERIALS SCIENCE↗

The Essence of Cryptol: A Denotational Cryptol Interpreter in Coq for Foundational Assurances for Quantum Resistant Cryptosystems

Systems of the utmost consequence need a means to establish authenticity of software and data. Cryptosystems implement authentication, but can be vulnerable to cryptographic and implementation attacks. With the threat of quantum cryptographic attacks, “post-quantum” cryptosystems (PQCs) must be henceforth used in these systems. However, the new cryptography needs new ways to, rigorously and machine-checkably, prove systems free of vulnerabilities. We propose a retargetable capability to rapidly instantiate proven correct postquantum cryptosystems through novel proof-carrying synthesis and proof-automation technique, extending those proven successful on existing systems. This capability is crucial to meeting the cryptographic requirements for future high-consequence systems. Since specifications for high consequence cryptography are presently captured in a domain specific language known as Cryptol. While this can enable convenient fully automated reasoning about Cryptol specificaitons and implementations via the Software Analysis Workbench (SAW), Cryptol has expressivity gaps, so that cryptosystems with probabilistic programming features like Falcon cannot be fully expressed in the language. Moreover, SAW’s automation fails for programs and specificaitons with inductive and recursive structure, as in the Sphincs+ PQC. Finally, Cryptol and SAW together represent some 200,000 lines of unverified Haskell, so that the any guarantees about high consequence cryptography are presently contingent on a large, unverified, yet trusted computing base. The first step of the larger project of agile, assured crpytography is therefore to provide a formal, mechanized semantics for Cryptol, so that the specifications expressed by cryptographers in Cryptol can be reasoned about and compiled into performant implementations with a foundational, machine checkable certificate of correctness. This report describes our work on this first step, culminating in the design of a certified denotational interpreter, in Coq, for core Cryptol.

97 MATHEMATICS AND COMPUTING↗

Terra-Populus v0.1: A Python Library for LandScan High-Definition Population Analysis and Modeling

The terra-populus library is designed for use by the LandScan HD technical team, offering a streamlined set of tools for generating and updating LandScan HD datasets from foundational building-level data, referred to as 'molecules,' provided by the building-level attribution team. This document serves as the primary technical documentation for terra-populus. Version 0.1 of the library includes the core modeling components necessary for LandScan HD production. It enables the generation of the LandScan HD Baseline dataset as well as corresponding confidence measures for the occupancy rates used. Parameters have been included for incorporating damaged building indicators and changes in population, to faciliate the creation of rapid updates for LandScan HD. Future iterations of terra-populus will introduce tools for creating a confidence index, and quantifying and propagating uncertainty, facilitating the creation of probabilistic LandScan HD outputs. This report provides an overview of the tools available in the library and the corresponding code implementations. One of the key advancements implemented in terra-populus is a redefinition of the atomic modeling unit for LandScan HD. Traditionally, the LandScan HD vector analytical framework has generated population estimates at the building sub-component (molecule) level. However, terra-populus adopts a building-level modeling approach. This shift is an operational decision aimed at aligning LandScan HD outputs with confidence measures, which are computed and validated at the building level (confidence measures are not included in this version of terra-populus, aside from those associated with the occupancy rates). Additional advancements to the LandScan HD modeling, as implemented by terra-populus, include a minimum population value parameter and an auto assignment of building floor counts. The population minimum value was implemented to prevent buildings and subsequent LandScan HD pixels that contained small values that may not rasterize in production. An 'auto' value has been included as a method for dealing with buildings lacking floor count information, where it is the average floor count of all other buildings with a residential building use type tag. The logic behind this is to remain consistent with the current logic employed for dealing with building use type null instances, where a null use type is defaulted to residential since it is the most common building type. The auto logic is intended to apply the most common building floor count of the most common type of buildings. The tools provided in terra-populus represent a significant step forward in improving the efficiency, reproducibility, and transparency of the LandScan HD modeling process. As the library evolves, it will continue to serve as a foundational resource for high-resolution population modeling.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗

Performance Assurance Planning Guide for Utility Energy Service Contracts: 2025 Edition

Administered by the U.S. Department of Energy's (DOE) Federal Energy Management Program (FEMP), the Utility Program has fostered collaboration among federal agencies and their serving utilities for more than 25 years. The Utility Program supports agencies using Utility Energy Service Contracts (UESCs), a well-developed, effective contracting vehicle that enable the latest approaches to cost-effective energy management at federal sites. Federal agencies have successfully used UESCs to award over 2,000 energy and water efficiency and renewable energy projects, investing approximately $\$$2.8 billion in furthering the Federal Government's efforts to reduce energy intensity. Authorized by 42 U.S. Code section 8256 (10 U.S. Code section 2913 for the Department of Defense), a UESC is a limited-source acquisition between a federal agency and an eligible serving utility for energy management services that generate savings from the implementation of energy- and water -conservation measures (collectively referred to as ECMs), with 42 U.S. Code section 8287 (Defense Federal Acquisition Regulation Supplement, Part 241), providing the term of a UESC, which may extend up to 25 years. Through a UESC, the utility partner assesses designs, and implements the desired ECMs - which can range from lighting retrofits and renewable energy systems, to combined heat and power plants or other technologies and strategies, and may provide financing for the project. The agency may use any combination of appropriations and third-party financing to pay for the project, providing useful flexibility. There is no limit to the project size, big or small, that can be implemented using a UESC. To assist agencies implementing a UESC, FEMP has developed a Utility Energy Service Contract Guide and this companion guidance document to help agencies and their utility partners better understand the best practices for to ensure UESCs continue to perform and generate savings throughout their performance period. These best practices utilize a combination of effective project management, communication, documentation, and a detailed Performance Assurance Plan. This plan is a project specific set of actionable protocols that define important tasks and responsibilities throughout the contract term and reflects the site conditions, complexities, agency capabilities, and operating and maintaining planned ECMs.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Capability Building Progression of an Insider Threat Mitigation Program at International Nuclear Power Plant

With threats to nuclear facilities continuously evolving, the development and implementation of insider threat mitigation programs is increasingly important. The Office of International Nuclear Security within the U.S. Department of Energy’s National Nuclear Security Administration (DOE/NNSA’s) developed the “Insider Threat Mitigation Program: Facility Implementation Handbook” to assist organizations to be better positioned to minimize the risks posed by malicious insiders. The handbook identified eight elements that contribute to the development and implementation of insider threat mitigation programs. This report outlines the development of a capability building progression of an insider threat mitigation program at international nuclear power plants. This information can be stand-alone or be accompanied by a technical exchange with subject matter experts to support development and implementation of programs with interested international partners.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Frequency and time multiplexing for multiphoton state generation

One of the primary challenges with photonic quantum information processing is that single-photon states are created and heralded probabilistically, rather than being created on demand. One solution to this problem is multiplexing , which is attempting probabilistic generation of a single photon at multiple locations, times, or frequencies, and switching one successfully generated photon into an output mode. Motivated by the development of frequency-based photonic quantum information processing, we consider multiplexing using frequency and time as our options to use to get many photon generation opportunities. We devise an approach for generating multiphoton states, with photons populating multiple frequency modes in the same spatiotemporal mode. This method uses a variable-length optical delays to manipulate the temporal mode of the photons, and spaced fiber Bragg grating (FBG) reflectors to jointly manipulate the frequency and temporal modes of the photons. Experimental progress toward implementing this multiplexing scheme is proceeding along 2 fronts, each with different ways to achieve the variable-length optical delay. First, we will implement this scheme using a free-space optical quantum memory with multiple discretely adjustable free-space delays. For this implementation method, I calculate multiphoton generation rates, accounting for loss, that are realistically achievable with commercially available hardware. This work will appear in a theory paper, currently in preparation. Second, we will implement this multiplexing scheme in an integrated manner: the variable-length optical delay will happen on-chip using a long-lifetime Q-switchable Fabry-Perot cavity. The joint manipulation of the frequency and temporal modes of the photons will still happen off-chip in fiber with FBG reflectors. I report on experimental progress in constructing integrated Q-switchable Fabry-Perot cavities.

97 MATHEMATICS AND COMPUTING↗

Graphical User Interface for a Biasing Board for the PSEC6

The PSEC6 is an application-specific integrated circuit (ASIC) designed for a readout system for a large area picosecond photodetector (LAPPD). The PSEC6 is currently in fabrication and pending testing. The testing system for the PSEC5, the previous iteration of the ASIC, required expensive and non-portable equipment, because the ASIC needs twelve adjustable reference voltages. The new testing system consists of an low-cost, open-source, cross-platform graphical user interface (GUI), a digital system, and a biasing board. The digital system is the interface between the GUI and biasing board, and can be implemented on a microcontroller or field-programmable gate array (FPGA). The biasing board contains twelve digital-to-analog converters (DACs) that are configurable via the GUI, which gives users the ability to write voltage values to all or specific DACs. The GUI was developed in C on Linux using the widget library GTK4 and cross-compiled for Windows compatibility. I2C and SPI protocols were implemented on an Adafruit Feather ESP32-S3 microcontroller to write commands to the DACs and PSEC6. A hardware implementation of the I2C protocol is in development on an FPGA. Since LAPPDs will be used by the Accelerator Neutrino Neutron Interaction Experiment (ANNIE) at Fermilab, the PSEC6 testing system in this internship project can potentially benefit future neutrino research. The project is relevant to the Department of Energy’s microelectronics mission, because the PSEC6 is an ASIC that will handle fast time signals arriving from the detector for readout. It also provided experience with building a cross-platform user interface, practicing digital design and implementation in hardware description language (HDL), and using simulations to inform new design iterations.

Guerrero, Sasha Camila [North Central Coll.]↗

Are Deep Energy Retrofits in Commercial Buildings Including Window Upgrades?

U.S. Commercial buildings account for about 20% of total U.S. energy consumption. Because the thermal performance of windows significantly affects building energy efficiency and HVAC system performance, best practice guidance often includes window and envelope improvements in conjunction with HVAC upgrades to optimize energy use and improve occupant comfort. It is an open question, however, regarding how often these best practices are implemented in the field. This paper aims to address that gap by conducting a literature review and a series of interviews with commercial building auditing and management professionals to explore the factors that drive window retrofits in commercial buildings. The paper explores a range of case studies from deep energy retrofits across the globe, comparing projects with and without window retrofits. The primary goals of this review are to: (1) provide data from real-world case studies illustrating the role of windows in deep energy renovations and HVAC upgrades, (2) conduct retrofit cost analyses for windows and high-performance HVAC systems and (3) offer insights into how window upgrade decisions are made and when they are implemented as part of deep energy retrofits. Most of the retrofit studies focused exclusively on high performance HVAC upgrades without considering how window upgrades might further enhance the overall energy efficiency of commercial buildings. Interviews with building industry experts shed light on the key factors influencing deep energy retrofit decisions and what factors tip the scales in favor of including window measures with more comprehensive retrofit projects.

Cort, Katherine↗

Solar Pathways in Federal Energy Assistance Programs: Expanding Low Income Home Energy Assistance Program (LIHEAP) and Weatherization Assistance Program (WAP)

How can solar best fit within your LIHEAP or WAP activities? Come join NREL and learn about the various pathways and new resources available to help implement solar in low-income programs. Panelists will share results from a multi-year research project, including survey results on LIHEAP and WAP solar adoption across the United States. This session will highlight case studies from early implementers, key lessons learned and resources developed based on stakeholder feedback for interested organizations. Attendees can expect gain a better understanding of the perceived barriers and opportunities to solar implementation, including the importance of partner coordination and complementary funding sources, and the next steps for how to get started. Additionally, attendees will hear from a local implementer of solar in WAP about their program and process.

Colorado↗

Leveraging FPGA Advantages for Quicker Data Processing for LBNF

The Long Baseline Neutrino Facility (LBNF) will deliver a 2.4 MW muon neutrino beam from Fermilab to the Deep Underground Neutrino Experiment (DUNE), requiring unprecedented precision in beamline alignment to achieve DUNE's neutrino oscillation measurement goals. Vertical misalignments of beamline components as small as 0.5 mm can contribute 6-7\% uncertainty in predicted neutrino flux, necessitating sub-0.1 mm alignment monitoring capabilities. The Horn Location Sensor (HLS) system employs frequency sweep interferometry (FSI) in a distributed hydrostatic leveling network to achieve the required precision under harsh radiation conditions up to 5000 kRad/year. Traditional FSI implementations suffer from laser sweep nonlinearities that degrade resolution and require computationally intensive post-processing corrections using gas reference cells. This work presents a real-time FPGA-based implementation of the HLS data acquisition and processing system using a sweep tracker interferometer for dynamic sweep linearization. The system utilizes a PYNQ-Z2 FPGA with programmable logic implementing parallel 16k-point FFT processing across four channels, synchronized by the sweep tracker signal to eliminate post-processing requirements. Spectral performance testing demonstrates significant improvements in peak sharpness compared to traditional fixed-frequency digitization. The FPGA implementation enables real-time displacement monitoring with processing speeds orders of magnitude faster than software-based approaches, essential for the operational requirements of LBNF's eventual distributed sensor network. This advancement in real-time FSI processing directly supports DUNE's precision neutrino physics program by providing the rapid feedback necessary for maintaining stringent beamline alignment tolerances during high-power beam operations.

Rossel, Jacob↗

Digitizing Today’s Buildings in the Real World: Lessons from Field Demonstrations

Digital twins, created by generating a virtual replica of a building, enable safe evaluation of operational scenarios and applications like fault detection and diagnosis and advanced controls. However, a prerequisite is the creation of a machine-readable digital representation of a building, currently hindered by fragmented information scattered across mechanical drawings, point lists, and natural language sequences. As a result, digital twin development remains labor-intensive, error-prone, and difficult to validate. To address these challenges, two efforts from ASHRAE aim to support the digitalization of buildings. ASHRAE s223 establishes a semantic model of buildings, representing system components, configuration, and data sources. ASHRAE s231 defines a vendor-neutral programming language for expressing their control logic. As the industry evaluates implementing them in their products, understanding the challenges that vendors and implementers may face is crucial. In this paper, we present findings and lessons learned from field demonstrations in five buildings that implemented control applications using ASHRAE s223 and s231. The demonstrations highlight how semantic modeling and formalized control descriptions can significantly reduce software development time, manual point mapping, and hard-coding. Beyond time efficiency, they enable reliable automation by minimizing human interpretation and providing a means for consistency across projects. We describe the processes and best practices for model creation and model usage, from translating heterogeneous building documentation into semantic representations to implementing control logic in real-world systems. Finally, we discuss the challenges that persist, including integration with legacy software environments, gaps in interoperability, and the level of expertise still required to effectively leverage semantic models.

Prakash, Anand Krishnan↗

Graphical User Interface for a Biasing Board for the PSEC6

The PSEC6 is an application-specific integrated circuit (ASIC) designed for a readout system for a large area picosecond photodetector (LAPPD). The PSEC6 is currently in fabrication and pending testing. The testing system for the PSEC5, the previous iteration of the ASIC, required expensive and non-portable equipment, because the ASIC needs twelve adjustable reference voltages. The new testing system consists of an low-cost, open-source, cross-platform graphical user interface (GUI), a digital system, and a biasing board. The digital system is the interface between the GUI and biasing board, and can be implemented on a microcontroller or field-programmable gate array (FPGA). The biasing board contains twelve digital-to-analog converters (DACs) that are configurable via the GUI, which gives users the ability to write voltage values to all or specific DACs. The GUI was developed in C on Linux using the widget library GTK4 and cross-compiled for Windows compatibility. I2C and SPI protocols were implemented on an Adafruit Feather ESP32-S3 microcontroller to write commands to the DACs and PSEC6. A hardware implementation of the I2C protocol is in development on an FPGA. Since LAPPDs will be used by the Accelerator Neutrino Neutron Interaction Experiment (ANNIE) at Fermilab, the PSEC6 testing system in this internship project can potentially benefit future neutrino research. The project is relevant to the Department of Energy’s microelectronics mission, because the PSEC6 is an ASIC that will handle fast time signals arriving from the detector for readout. It also provided experience with building a cross-platform user interface, practicing digital design and implementation in hardware description language (HDL), and using simulations to inform new design iterations.

Guerrero, Sasha Camila [North Central Coll.]↗

Open‐Source Anaerobic Digestion Modeling Platform, Anaerobic Digestion Model No. 1 Fast (ADM1F)

An open‐source modeling platform, called Anaerobic Digestion Model No. 1 Fast (ADM1F), is introduced to achieve fast and numerically stable simulations of anaerobic digestion processes. ADM1F is compatible with an iPython interface to facilitate model configuration, simulation, data analysis, and visualization. Faster simulations and more stable results are accomplished by implementing an advanced open‐source library of numerical methods called Portable Extensive Toolkit for Scientific Computation (PETSc) to solve the ADM1 system of equations. Leveraging PETSc, ADM1F can consistently complete a steady‐state simulation under 0.2 s, over 99% faster than a benchmark ADM1 model implemented with MATLAB while achieving agreement of model outputs within 1% of those obtained with the benchmark model. For dynamic simulations, however, ADM1F has a computational speed advantage only when the influent characteristics update more frequently than every 4 h. The ability of ADM1F to be useful as a tool to study anaerobic digestion systems is demonstrated through two example implementations of ADM1F: (1) a two‐phase co‐digestion scenario evaluating the impact of the organic loading rate and the substrate composition on reactor performance and stability, and (2) a conventional digester scenario assessing the effectiveness of recovery strategies after disruptions that led to instability. These examples demonstrate how the high simulation speed and the convenience of the iPython interface allow ADM1F to complete complex analyses within minutes, much faster than computational strategies currently reported in the literature.

anaerobic co-digestion↗

Identifying preferential flow from soil moisture time series: Review of methodologies

Abstract Identifying and quantifying preferential flow (PF) through soil—the rapid movement of water through spatially distinct pathways in the subsurface—is vital to understanding how the hydrologic cycle responds to climate, land cover, and anthropogenic changes. In recent decades, methods have been developed that use measured soil moisture time series to identify PF. Because they allow for continuous monitoring and are relatively easy to implement, these methods have become an important tool for recognizing when, where, and under what conditions PF occurs. The methods seek to identify a pattern or quantification that indicates the occurrence of PF. Most commonly, the chosen signature is either (1) a nonsequential response to infiltrated water, in which soil moisture responses do not occur in order of shallowest to deepest, or (2) a velocity criterion, in which newly infiltrated water is detected at depth earlier than is possible by nonpreferential flow processes. Alternative signatures have also been developed that have certain advantages but are less commonly utilized. Choosing among these possible signatures requires attention to their pertinent characteristics, including susceptibility to errors, possible bias toward false negatives or false positives, reliance on subjective judgments, and possible requirements for additional types of data. We review 77 studies that have applied such methods to highlight important information for readers who want to identify PF from soil moisture data and to inform those who aim to develop new methods or improve existing ones. Core Ideas Soil moisture data can be used to identify the occurrence of preferential flow (PF) and its initiating conditions. Various data‐analysis methods to identify PF differ in susceptibility to error, bias, and subjectivity. These methods can utilize vast amounts of data from soil moisture monitoring networks to develop understanding of when, where, and under what conditions PF occurs. Newly developed methods may lead to better accuracy and reliability, and reduce the need for subjective judgments. Plain Language Summary Preferential flow through soil occurs when a large amount of water is suddenly available, as during an intense storm. This type of flow moves rapidly through the soil in distinct narrow pathways rather than moving evenly throughout the body of soil, with major consequences for groundwater resources, ecosystems, spreading of contaminants, and other vital concerns. Methods of detecting preferential flow have been developed that utilize measurements of soil water content made by sensors installed at various depths. This measurement technology has been widely implemented, many locations now having datasets years in length, and various methods have been developed for using these to identify preferential flow. The various methods are based on different features in the soil moisture records and vary in their advantages and shortcomings. In this review, we explain and evaluate these methods, highlighting important information for their implementation to identify preferential flow from soil moisture data and for efforts to develop new methods or improve existing ones.

Nimmo, John R↗

Entanglement Renormalization for Quantum Field Theories with Discrete Wavelet Transforms

We propose an adaptation of Entanglement Renormalization for quantum field theories that, through the use of discrete wavelet transforms, strongly parallels the tensor network architecture of the Multiscale Entanglement Renormalization Ansatz (a.k.a. MERA). Our approach, called wMERA, has several advantages of over previous attempts to adapt MERA to continuum systems. In particular, (i) wMERA is formulated directly in position space, hence preserving the quasi-locality and sparsity of entanglers; and (ii) it enables a built-in RG flow in the implementation of real-time evolution and in computations of correlation functions, which is key for efficient numerical implementations. As examples, we describe in detail two concrete implementations of our wMERA algorithm for free scalar and fermionic theories in (1+1) spacetime dimensions. Possible avenues for constructing wMERAs for interacting field theories are also discussed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Efficient Quantum Gibbs Samplers with Kubo–Martin–Schwinger Detailed Balance Condition

Lindblad dynamics and other open-system dynamics provide a promising path towards efficient Gibbs sampling on quantum computers. In these proposals, the Lindbladian is obtained via an algorithmic construction akin to designing an artificial thermostat in classical Monte Carlo or molecular dynamics methods, rather than being treated as an approximation to weakly coupled system-bath unitary dynamics. Recently, Chen, Kastoryano, and Gilyén (arXiv:2311.09207) introduced the first efficiently implementable Lindbladian satisfying the Kubo–Martin–Schwinger (KMS) detailed balance condition, which ensures that the Gibbs state is a fixed point of the dynamics and is applicable to non-commuting Hamiltonians. This Gibbs sampler uses a continuously parameterized set of jump operators, and the energy resolution required for implementing each jump operator depends only logarithmically on the precision and the mixing time. In this work, we build upon the structural characterization of KMS detailed balanced Lindbladians by Fagnola and Umanità, and develop a family of efficient quantum Gibbs samplers using a finite set of jump operators (the number can be as few as one), akin to the classical Markov chain-based sampling algorithm. Compared to the existing works, our quantum Gibbs samplers have a comparable quantum simulation cost but with greater design flexibility and a much simpler implementation and error analysis. Moreover, it encompasses the construction of Chen, Kastoryano, and Gilyén as a special instance.

97 MATHEMATICS AND COMPUTING↗

Spatiotemporal pattern detection, generation, and computation with circuits

Abstract Implementations of neurons, delays, and synapse circuits are presented with simulations. These neural elements are used to create two small spiking neural networks, the Rate-Window and Order-Biased clusters, which are capable of detecting simple two-spike spatiotemporal patterns. A simple pattern detecting network (SPDN) is created by combining the Rate-Window and Order-Biased clusters, where clusters are small spiking neural networks, and its simple pattern detection ability is demonstrated in simulation. The SPDN is used to implement a complex pattern detecting network (CPDN) and its complex pattern detection ability is demonstrated in simulation. Methods for generating arbitrary spatiotemporal patterns are presented. The CPDN and spatiotemporal pattern generation methods are then used to implement a novel spatiotemporal computing paradigm based on detecting and responding to spatiotemporal symbols. A simulation of a spatiotemporal half adder is presented to demonstrate the computing paradigm.

97 - MATHEMATICS AND COMPUTING↗

Performance evaluations of signed and unsigned noisy approximate quantum Fourier arithmetic

The Quantum Fourier Transform (QFT) grants competitive advantages, especially in resource usage and circuit approximation, for performing arithmetic operations on quantum computers, and offers a potential route toward a numerical quantum-computational paradigm. In this paper, we utilize efficient techniques to implement QFT-based integer addition and multiplications. These operations are fundamental to various quantum applications including Shor’s algorithm, weighted-sum optimization problems in data processing and machine learning, and quantum algorithms requiring inner products. We carry out performance evaluations of these implementations based on IBM’s superconducting-qubit architecture using different compatible noise models. We isolate the sensitivity of the component quantum circuits on both one-/two-qubit gate error rates, and the number of the arithmetic operands’ superposed integer states. We analyze performance and identify the most effective approximation depths for unsigned quantum addition and quantum multiplication within the given context. We then perform a similar analysis of signed addition and compare to the unsigned results. We observe significant dependency of the optimal approximation depth on the degree of machine noise and the number of superposed states in certain performance regimes. Finally, we elaborate on the algorithmic challenges—relevant to signed, unsigned, modular and non-modular versions—that could also be applied to current implementations of QFT-based subtraction, division, exponentiation, and their potential tensor extensions. Here, we analyze the performance trends in our results and speculate on possible future developments within this computational paradigm.

Computational models↗