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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Digital Twin Framework for PIP-II Linac: AI-Driven Multi-Scale Modeling from Ion Source to 800 MeV

The PIP-II linac will enable >1.2 MW beam power for DUNE, requiring unprecedented operational reliability across its warm front-end (RFQ, MEBT) and five distinct SRF sections operating at 162.5/325/650 MHz. We present a comprehensive digital twin framework uniquely combining a fully differentiable fast beam transport code with neural network surrogates trained on high-fidelity PIC simulations, capturing space charge and nonlinear dynamics beyond traditional envelope codes while achieving 10⁴ speedup at <1% accuracy. End-to-end differentiability enables gradient-based optimization across 500+ parameters simultaneously previously impossible with conventional tools while the model incorporates static/dynamic errors and serves as a virtual commissioning platform for diverse hardware integration. The framework facilitates reinforcement learning for pulsed/CW mode transitions, predictive maintenance through anomaly detection, and autonomous tuning algorithm development with real-time execution capability. Validation against physics simulations shows excellent agreement for the front-end, with initial results demonstrating potential for 30% commissioning time reduction and proactive fault mitigation, providing a scalable blueprint for operating next-generation high-intensity accelerators.

Pathak, Abhishek [Fermilab] (ORCID:000000021704208↗
DOE OSTI2023

Characterizing and mitigating coherent errors in a trapped ion quantum processor using hidden inverses

Quantum computing testbeds exhibit high-fidelity quantum control over small collections of qubits, enabling performance of precise, repeatable operations followed by measurements. Currently, these noisy intermediate-scale devices can support a sufficient number of sequential operations prior to decoherence such that near term algorithms can be performed with proximate accuracy (like chemical accuracy for quantum chemistry problems). While the results of these algorithms are imperfect, these imperfections can help bootstrap quantum computer testbed development. Demonstrations of these algorithms over the past few years, coupled with the idea that imperfect algorithm performance can be caused by several dominant noise sources in the quantum processor, which can be measured and calibrated during algorithm execution or in post-processing, has led to the use of noise mitigation to improve typical computational results. Conversely, benchmark algorithms coupled with noise mitigation can help diagnose the nature of the noise, whether systematic or purely random. Here, we outline the use of coherent noise mitigation techniques as a characterization tool in trapped-ion testbeds. We perform model-fitting of the noisy data to determine the noise source based on realistic physics focused noise models and demonstrate that systematic noise amplification coupled with error mitigation schemes provides useful data for noise model deduction. Further, in order to connect lower level noise model details with application specific performance of near term algorithms, we experimentally construct the loss landscape of a variational algorithm under various injected noise sources coupled with error mitigation techniques. This type of connection enables application-aware hardware codesign, in which the most important noise sources in specific applications, like quantum chemistry, become foci of improvement in subsequent hardware generations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1977

Hybrid receiver study

The results are presented of a 4 month study to design a hybrid analog/digital receiver for outer planet mission probe communication links. The scope of this study includes functional design of the receiver; comparisons between analog and digital processing; hardware tradeoffs for key components including frequency generators, A/D converters, and digital processors; development and simulation of the processing algorithms for acquisition, tracking, and demodulation; and detailed design of the receiver in order to determine its size, weight, power, reliability, and radiation hardness. In addition, an evaluation was made of the receiver's capabilities to perform accurate measurement of signal strength and frequency for radio science missions.

Stone, M. S.↗
NASA NTRS1976

A realization of the RAM digital filter

The digital filtering algorithm of W. D. Little, which employs a large RAM to obtain high speed, is implemented in a simple hardware configuration. The nonrecursive version of this filter is compared to the counting digital filter and found to be competitive for low-order filters up to order 7 (8 coefficients).

Zohar, S.↗
NASA NTRS1987

The hypercluster: A parallel processing test-bed architecture for computational mechanics applications

The development of numerical methods and software tools for parallel processors can be aided through the use of a hardware test-bed. The test-bed architecture must be flexible enough to support investigations into architecture-algorithm interactions. One way to implement a test-bed is to use a commercial parallel processor. Unfortunately, most commercial parallel processors are fixed in their interconnection and/or processor architecture. In this paper, we describe a modified n cube architecture, called the hypercluster, which is a superset of many other processor and interconnection architectures. The hypercluster is intended to support research into parallel processing of computational fluid and structural mechanics problems which may require a number of different architectural configurations. An example of how a typical partial differential equation solution algorithm maps on to the hypercluster is given.

Blech, Richard A.↗
NASA NTRS1992

Lunar PMAD technology assessment

This report documents an initial set of power conditioning models created to generate 'ballpark' power management and distribution (PMAD) component mass and size estimates. It contains converter, rectifier, inverter, transformer, remote bus isolator (RBI), and remote power controller (RPC) models. These models allow certain studies to be performed; however, additional models are required to assess a full range of PMAD alternatives. The intent is to eventually form a library of PMAD models that will allow system designers to evaluate various power system architectures and distribution techniques quickly and consistently. The models in this report are designed primarily for space exploration initiative (SEI) missions requiring continuous power and supporting manned operations. The mass estimates were developed by identifying the stages in a component and obtaining mass breakdowns for these stages from near term electronic hardware elements. Technology advances were then incorporated to generate hardware masses consistent with the 2000 to 2010 time period. The mass of a complete component is computed by algorithms that calculate the masses of the component stages, control and monitoring, enclosure, and thermal management subsystem.

Metcalf, Kenneth J.↗
NASA NTRS1999

Deep Space Control Challenges of the New Millennium

The exploration of deep space presents a variety of significant control challenges. Long communication delays coupled with challenging new science objectives require high levels of system autonomy and increasingly demanding pointing and control capabilities. Historically, missions based on the use of a large single spacecraft have been successful and popular since the early days of NASA. However, these large spacecraft missions are currently being displaced by more frequent and more focused missions based on the use of smaller and less expensive spacecraft designs. This trend drives the need to design smart software and good algorithms which together with the miniaturization of control components will improve performance while replacing the heavier and more expensive hardware used in the past. NASA's future space exploration will also include mission types that have never been attempted before, posing significant challenges to the underlying control system. This includes controlled landing on small bodies (e.g., asteroids and comets), sample return missions (where samples are brought back from other planets), robotic exploration of planetary surfaces (e.g., intelligent rovers), high precision formation flying, and deep space optical interferometry, While the control of planetary spacecraft for traditional flyby and orbiter missions are based on well-understood methodologies, control approaches for many future missions will be fundamentally different. This paradigm shift will require completely new control system development approaches, system architectures, and much greater levels of system autonomy to meet expected performance in the presence of significant environmental disturbances, and plant uncertainties. This paper will trace the motivation for these changes and will layout the approach taken to meet the new challenges. Emerging missions will be used to explain and illustrate the need for these changes.

Bayard, David S.↗
NASA NTRS2008

Spiking Neurons for Analysis of Patterns

Artificial neural networks comprising spiking neurons of a novel type have been conceived as improved pattern-analysis and pattern-recognition computational systems. These neurons are represented by a mathematical model denoted the state-variable model (SVM), which among other things, exploits a computational parallelism inherent in spiking-neuron geometry. Networks of SVM neurons offer advantages of speed and computational efficiency, relative to traditional artificial neural networks. The SVM also overcomes some of the limitations of prior spiking-neuron models. There are numerous potential pattern-recognition, tracking, and data-reduction (data preprocessing) applications for these SVM neural networks on Earth and in exploration of remote planets. Spiking neurons imitate biological neurons more closely than do the neurons of traditional artificial neural networks. A spiking neuron includes a central cell body (soma) surrounded by a tree-like interconnection network (dendrites). Spiking neurons are so named because they generate trains of output pulses (spikes) in response to inputs received from sensors or from other neurons. They gain their speed advantage over traditional neural networks by using the timing of individual spikes for computation, whereas traditional artificial neurons use averages of activity levels over time. Moreover, spiking neurons use the delays inherent in dendritic processing in order to efficiently encode the information content of incoming signals. Because traditional artificial neurons fail to capture this encoding, they have less processing capability, and so it is necessary to use more gates when implementing traditional artificial neurons in electronic circuitry. Such higher-order functions as dynamic tasking are effected by use of pools (collections) of spiking neurons interconnected by spike-transmitting fibers. The SVM includes adaptive thresholds and submodels of transport of ions (in imitation of such transport in biological neurons). These features enable the neurons to adapt their responses to high-rate inputs from sensors, and to adapt their firing thresholds to mitigate noise or effects of potential sensor failure. The mathematical derivation of the SVM starts from a prior model, known in the art as the point soma model, which captures all of the salient properties of neuronal response while keeping the computational cost low. The point-soma latency time is modified to be an exponentially decaying function of the strength of the applied potential. Choosing computational efficiency over biological fidelity, the dendrites surrounding a neuron are represented by simplified compartmental submodels and there are no dendritic spines. Updates to the dendritic potential, calcium-ion concentrations and conductances, and potassium-ion conductances are done by use of equations similar to those of the point soma. Diffusion processes in dendrites are modeled by averaging among nearest-neighbor compartments. Inputs to each of the dendritic compartments come from sensors. Alternatively or in addition, when an affected neuron is part of a pool, inputs can come from other spiking neurons. At present, SVM neural networks are implemented by computational simulation, using algorithms that encode the SVM and its submodels. However, it should be possible to implement these neural networks in hardware: The differential equations for the dendritic and cellular processes in the SVM model of spiking neurons map to equivalent circuits that can be implemented directly in analog very-large-scale integrated (VLSI) circuits.

Huntsberger, Terrance↗
NASA NTRS2012

Copilot: Monitoring Embedded Systems

Runtime verification (RV) is a natural fit for ultra-critical systems, where correctness is imperative. In ultra-critical systems, even if the software is fault-free, because of the inherent unreliability of commodity hardware and the adversity of operational environments, processing units (and their hosted software) are replicated, and fault-tolerant algorithms are used to compare the outputs. We investigate both software monitoring in distributed fault-tolerant systems, as well as implementing fault-tolerance mechanisms using RV techniques. We describe the Copilot language and compiler, specifically designed for generating monitors for distributed, hard real-time systems. We also describe two case-studies in which we generated Copilot monitors in avionics systems.

Pike, Lee↗
NASA NTRS2017

Intercomparison of Snow Depth Retrievals over Arctic Sea Ice from Radar Data Acquired by Operation IceBridge

Since 2009, the ultra-wideband snow radar on Operation IceBridge (OIB; a NASA airborne mission to survey the polar ice covers) has acquired data in annual campaigns conducted during the Arctic and Antarctic springs. Progressive improvements in radar hardware and data processing methodologies have led to improved data quality for subsequent retrieval of snow depth. Existing retrieval algorithms differ in the way the air-snow (a-s) and snow-ice (s-i) interfaces are detected and localized in the radar returns and in how the system limitations are addressed (e.g., noise, resolution). In 2014, the Snow Thickness On Sea Ice Working Group (STOSIWG) was formed and tasked with investigating how radar data quality affects snow depth retrievals and how retrievals from the various algorithms differ. The goal is to understand the limitations of the estimates and to produce a well-documented, long-term record that can be used for understanding broader changes in the Arctic climate system. Here, we assess five retrieval algorithms by comparisons with field measurements from two groundbased campaigns, including the BRomine, Ozone, and Mercury EXperiment (BROMEX) at Barrow, Alaska; a field program by Environment and Climate Change Canada at Eureka, Nunavut; and available climatology and snowfall from ERA-Interim (ECMWF (European Centre for Medium-Range Weather Forecasts) Re-Analysis) reanalysis. The aim is to examine available algorithms and to use the assessment results to inform the development of future approaches. We present results from these assessments and highlight key considerations for the production of a long-term, calibrated geophysical record of springtime snow thickness over Arctic sea ice.

Operation IceBridge↗
NASA NTRSDate not supplied

Autonomous In-space Construction, Maintenance, and Reconfiguration Using Programmable Meta-Material

NASA ARC's Coded Structures Laboratory (CSL) is developing autonomous construction, maintenance, and reconfiguration technologies to meet long-duration and deep space infrastructure needs, in accordance with long-term NASA goals of "in-space reliance" and "mass-less exploration." We seek to achieve these capabilities by utilizing a "programmable meta-material" approach that integrates emerging advances in materials (mechanical meta-materials), manufacturing (cooperative mobile robotics), and autonomy (multi-agent planning algorithms). Through the ARMADAS project, we have shown assembly of high-performance engineered cellular materials using multiple cooperating mobile robotic assemblers. In this paper, we describe how such a programmable meta-material architecture may shift the paradigm of how we design, build, manufacture, and operate future space infrastructure and assets. The core of a programmable meta-material architecture consists of 3 main technology sub-areas: the structure, the assembly agents, and the assembly algorithms. We co-design these systems to ensure an adaptable system that can create and reconfigure structures from a base set of building block components. From this core technology, we can branch out and expand the capability of the system through additional secondary component types and robotic agents to perform activities such as inspections, maintenance, repair, payload installation, or perform power and communications interconnect. As these technologies mature, future designers will be able to utilize the system to rapidly integrate and operate assets in space or on planetary surfaces from a set of well-tested part library, or create their own modules to integrate into the system. A core trait to the development of this system is the automation approach. Because of the modular and functional discrete (pixel-like) nature of the structural system, a diverse set of powerful algorithms for analysis, planning, and simulation can be adapted and leveraged to optimize construction, maintenance, and dynamic reorganization (as hardware with programmable form and function). With an ability to free the design space from launch vehicle constraints and fundamentally shift how a mission is designed and conducted, we discuss the influence of a programmable meta-material architecture on mission design, build, and operations. For the "design phase", we discuss project lifecycle effects, costs, time, and performance. For the "build phase", we discuss reusability, ISRU, manufacturing, material logistics, and scalability. And for "operations", we discuss autonomy, maintenance and upgrades, reliability, and reconfiguration. Autonomy and modularity are the primary enabling traits of this system. Engineering systems that utilize a modular and reconfiguration building block approach such as digital communication and computation systems, currently lead all other areas of technology in size and complexity scalability. NASA is extending the benefits and flexibility of digital systems to hardware systems, to optimize materials lifecycle management and expand our space exploration mission capabilities.

in space assembly↗
DOE OSTI2025

Digital Twin Framework for PIP-II Linac: AI-Driven Multi-Scale Modeling from Ion Source to 800 MeV

The PIP-II linac will enable >1.2 MW beam power for DUNE, requiring unprecedented operational reliability across its warm front-end (RFQ, MEBT) and five distinct SRF sections operating at 162.5/325/650 MHz. We present a comprehensive digital twin framework uniquely combining a fully differentiable fast beam transport code with neural network surrogates trained on high-fidelity PIC simulations, capturing space charge and nonlinear dynamics beyond traditional envelope codes while achieving 10⁴× speedup at <1% accuracy. End-to-end differentiability enables gradient-based optimization across 500+ parameters simultaneously—previously impossible with conventional tools—while the model incorporates static/dynamic errors and serves as a virtual commissioning platform for diverse hardware integration. The framework facilitates reinforcement learning for pulsed/CW mode transitions, predictive maintenance through anomaly detection, and autonomous tuning algorithm development with real-time execution capability. Validation against physics simulations shows excellent agreement for the front-end, with initial results demonstrating potential for 30% commissioning time reduction and proactive fault mitigation, providing a scalable blueprint for operating next-generation high-intensity accelerators.

Pathak, Abhishek [Fermilab] (ORCID:000000021704208↗
DOE OSTI2025

Digital quantum simulation of cavity quantum electrodynamics: insights from superconducting and trapped ion quantum testbeds

We explore the potential for hybrid development of quantum hardware where currently available quantum computers simulate open cavity quantum electrodynamical (CQED) systems for applications in optical quantum communication, simulation and computing. Our simulations make use of a recent quantum algorithm that maps the dynamics of a singly excited open Tavis–Cummings model containing N atoms coupled to a lossy cavity. We report the results of executing this algorithm on two noisy intermediate-scale quantum computers: a superconducting processor and a trapped ion processor, to simulate the population dynamics of an open CQED system featuring N = 3 atoms. By applying technology-specific transpilation and error mitigation techniques, we minimize the impact of gate errors, noise, and decoherence in each hardware platform, obtaining results which agree closely with the exact solution of the system. These results can be used as a recipe for efficient and platform-specific quantum simulation of cavity–emitter systems on contemporary and future quantum computers.

cavity QED↗
NASA NTRS2005

Advanced Health Management Algorithms for Crew Exploration Applications

Achieving the goals of the President's Vision for Exploration will require new and innovative ways to achieve reliability increases of key systems and sub-systems. The most prominent approach used in current systems is to maintain hardware redundancy. This imposes constraints to the system and utilizes weight that could be used for payload for extended lunar, Martian, or other deep space missions. A technique to improve reliability while reducing the system weight and constraints is through the use of an Advanced Health Management System (AHMS). This system contains diagnostic algorithms and decision logic to mitigate or minimize the impact of system anomalies on propulsion system performance throughout the powered flight regime. The purposes of the AHMS are to increase the probability of successfully placing the vehicle into the intended orbit (Earth, Lunar, or Martian escape trajectory), increase the probability of being able to safely execute an abort after it has developed anomalous performance during launch or ascent phases of the mission, and to minimize or mitigate anomalies during the cruise portion of the mission. This is accomplished by improving the knowledge of the state of the propulsion system operation at any given turbomachinery vibration protection logic and an overall system analysis algorithm that utilizes an underlying physical model and a wide array of engine system operational parameters to detect and mitigate predefined engine anomalies. These algorithms are generic enough to be utilized on any propulsion system yet can be easily tailored to each application by changing input data and engine specific parameters. The key to the advancement of such a system is the verification of the algorithms. These algorithms will be validated through the use of a database of nominal and anomalous performance from a large propulsion system where data exists for catastrophic and noncatastrophic propulsion sytem failures.

Davidson, Matt↗
DOE OSTI2020

Deep Learning for Automated Identification of Eels in Sonar Data

Freshwater eels, such as the American eel (Anguilla rostrata) present numerous challenges related to safe downstream fish passage at hydroelectric facilities. One of those challenges is effective monitoring of their abundance, movements, and behavior to facilitate design and operation of eel protection and passage facilities. A previous EPRI study documented the ability of human analysts to reliably identify American eels in data obtained with a 1100/1800 kHz, multibeam sonar. This report describes a project to develop deep learning (a subset of artificial intelligence) tools to automate the time-consuming, subjective process of eel identification in multibeam sonar data. The project exploited new data collected in the laboratory and the existing data from the prior EPRI field study to develop and test deep learning and other data analytic tools, including wavelet filtering, differencing for static object removal, and convolutional neural network analysis. The analysis of the laboratory data demonstrated feasibility of the approach, revealed object characteristics observed with the sonar that distinguish eels from similarly sized and shaped acoustic targets, and provided additional data for algorithm selection and training. Deep learning algorithms trained and tested on the laboratory data alone achieved accuracy rates of greater than 98% when classifying acoustic images of eels and similar-sized neutrally buoyant sticks. The algorithm trained and tested on the pre-existing field data alone, and yielded classification accuracy of 9.3% false positives and 13.3% false negatives when distinguishing between eels and sticks/PVC pipes based on video clips (i.e., multiple, consecutive images). This performance is comparable to the classification accuracy achieved by human analysts in the prior study. The deep learning algorithm trained on a combination of video clips obtained in the laboratory and the field and tested on video clips from the field, was able to distinguish eels from sticks and PVC pipes (a river debris analog) of similar size with 100% accuracy. Outreach to the hardware, software, and end-user communities early in the project helped to identify needs and specify the application space. Outreach to those communities at the end of the project communicated project results and opportunities for further development. The project achieved proof of concept for automated identification of eel in multibeam sonar data. Future work should focus on acquisition of additional data for more robust algorithm training and testing; modification of the software tools to accommodate multiple acoustic targets in the acoustic field at a given time; identification of additional object classes; incorporation of motion in the object identification and classification algorithms; operationalizing the software tools, including integration with other existing sonar data analysis tools; and partnering with hardware and software providers for distribution of the software tools with their commercial products.

13 HYDRO ENERGY↗
NASA NTRS2017

A Virtual Laboratory for Aviation and Airspace Prognostics Research

Integration of Unmanned Aerial Vehicles (UAVs), autonomy, spacecraft, and other aviation technologies, in the airspace is becoming more and more complicated, and will continue to do so in the future. Inclusion of new technology and complexity into the airspace increases the importance and difficulty of safety assurance. Additionally, testing new technologies on complex aviation systems and systems of systems can be challenging, expensive, and at times unsafe when implementing real life scenarios. The application of prognostics to aviation and airspace management may produce new tools and insight into these problems. Prognostic methodology provides an estimate of the health and risks of a component, vehicle, or airspace and knowledge of how that will change over time. That measure is especially useful in safety determination, mission planning, and maintenance scheduling. In our research, we develop a live, distributed, hardware- in-the-loop Prognostics Virtual Laboratory testbed for aviation and airspace prognostics. The developed testbed will be used to validate prediction algorithms for the real-time safety monitoring of the National Airspace System (NAS) and the prediction of unsafe events. In our earlier work1 we discussed the initial Prognostics Virtual Laboratory testbed development work and related results for milestones 1 & 2. This paper describes the design, development, and testing of the integrated tested which are part of milestone 3, along with our next steps for validation of this work. Through a framework consisting of software/hardware modules and associated interface clients, the distributed testbed enables safe, accurate, and inexpensive experimentation and research into airspace and vehicle prognosis that would not have been possible otherwise. The testbed modules can be used cohesively to construct complex and relevant airspace scenarios for research. Four modules are key to this research: the virtual aircraft module which uses the X-Plane simulator and X-PlaneConnect toolbox, the live aircraft module which connects fielded aircraft using onboard cellular communications devices, the hardware in the loop (HITL) module which connects laboratory based bench-top hardware testbeds and the research module which contains diagnostics and prognostics tools for analysis of live air traffic situations and vehicle health conditions. The testbed also features other modules for data recording and playback, information visualization, and air traffic generation. Software reliability, safety, and latency are some of the critical design considerations in development of the testbed.

LVC-DE↗
NASA NTRS2005

The Integrated Safety-Critical Advanced Avionics Communication and Control (ISAACC) System Concept: Infrastructure for ISHM

Integrated System Health Management (ISHM) architectures for spacecraft will include hard real-time, critical subsystems and soft real-time monitoring subsystems. Interaction between these subsystems will be necessary and an architecture supporting multiple criticality levels will be required. Demonstration hardware for the Integrated Safety-Critical Advanced Avionics Communication & Control (ISAACC) system has been developed at NASA Marshall Space Flight Center. It is a modular system using a commercially available time-triggered protocol, ?Tp/C, that supports hard real-time distributed control systems independent of the data transmission medium. The protocol is implemented in hardware and provides guaranteed low-latency messaging with inherent fault-tolerance and fault-containment. Interoperability between modules and systems of modules using the TTP/C is guaranteed through definition of messages and the precise message schedule implemented by the master-less Time Division Multiple Access (TDMA) communications protocol. "Plug-and-play" capability for sensors and actuators provides automatically configurable modules supporting sensor recalibration and control algorithm re-tuning without software modification. Modular components of controlled physical system(s) critical to control algorithm tuning, such as pumps or valve components in an engine, can be replaced or upgraded as "plug and play" components without modification to the ISAACC module hardware or software. ISAACC modules can communicate with other vehicle subsystems through time-triggered protocols or other communications protocols implemented over Ethernet, MIL-STD- 1553 and RS-485/422. Other communication bus physical layers and protocols can be included as required. In this way, the ISAACC modules can be part of a system-of-systems in a vehicle with multi-tier subsystems of varying criticality. The goal of the ISAACC architecture development is control and monitoring of safety critical systems of a manned spacecraft. These systems include spacecraft navigation and attitude control, propulsion, automated docking, vehicle health management and life support. ISAACC can integrate local critical subsystem health management with subsystems performing long term health monitoring. The ISAACC system and its relationship to ISHM will be presented.

Gwaltney, David A.↗
NASA NTRS2016

A Quantum-Assisted Algorithm for Sampling Applications in Machine Learning

An increase in the efficiency of sampling from Boltzmann distributions would have a significant impact in deep learning and other machine learning applications. Recently, quantum annealers have been proposed as a potential candidate to speed up this task, but several limitations still bar these state-of-the-art technologies from being used effectively. One of the main limitations is that, while the device may indeed sample from a Boltzmann-like distribution, quantum dynamical arguments suggests it will do so with an instance-dependent effective temperature, different from the physical temperature of the device. Unless this unknown temperature can be unveiled, it might not be possible to effectively use a quantum annealer for Boltzmann sampling. In this talk, we present a strategy to overcome this challenge with a simple effective-temperature estimation algorithm. We provide a systematic study assessing the impact of the effective temperatures in the learning of a kind of restricted Boltzmann machine embedded on quantum hardware, which can serve as a building block for deep learning architectures. We also provide a comparison to k-step contrastive divergence (CD-k) with k up to 100. Although assuming a suitable fixed effective temperature also allows to outperform one step contrastive divergence (CD-1), only when using an instance-dependent effective temperature we find a performance close to that of CD-100 for the case studied here. We discuss generalizations of the algorithm to other more expressive generative models, beyond restricted Boltzmann machines.

Perdomo-Ortiz, Alejandro↗