Home | Jefferson Lab - Abstract · Web viewThe goal of a tracking algorithm is connecting the detected hits to form tracks. In this approach each neuron corresponds to the connection

PROPOSAL FOR FY2021 LABORATORY DIRECTED RESEARCH AND DEVELOPMENT FUNDS

TITLE: _QPU-BASED NEAR REAL TIME DATA PROCESSING_________TOPIC: ___QUANTUM INFORMATION SCIENCE___

LEAD SCIENTIST OR ENGINEER:

MARCO BATTAGLIERI

Phone: 757-269-6002

Email: [email protected]

Date: 05/31/2020

Department/Division: Physics

Other Personnel: Cristiano Fanelli (co-PI, MIT/JLab), William Phelps (co-PI, CNU/JLab), Andru Quiroga (CNU), Evaristo Cisbani (INFN/ISS Roma1), Alessio Del Dotto (INFN/LNF), Mariangela Bondi’ (INFN/Ge), Luca Marsicano (INFN/Ge)

Mentor (if needed)

Proposal Term: From: 11/2020Through: 10/2021The proposed duration of this project is expected to be 2 years.

Division Budget Analyst Susan Brown

Phone: 757-236-7668

Email: [email protected]

This document and the material and data contained herein were developed under the sponsorship of the United States Government. Neither the United States nor the Department of Energy, nor the Thomas Jefferson National Accelerator Facility, nor their employees, makes any warranty, express or implied, or assumes any liability or responsibility for accuracy, completeness or usefulness of any information, apparatus, product or process disclosed, or represents that its use will not infringe privately owned rights. Mention of any product, its manufacturer, or suppliers shall not, nor is it intended to imply approval, disapproval, or fitness for any particular use. A royalty-free, non-exclusive right to use and disseminate the same for any purpose whatsoever, is expressly reserved to the United States and the Thomas Jefferson National Accelerator Facility.

2 of 20 JLab LDRD Proposal

THOMAS JEFFERSON NATIONAL ACCELERATOR FACILITY

AbstractQuantum computing is an emerging technology which is gaining computational power at a doubly exponential rate according to Neven’s law and could fundamentally change how we solve problems by allowing the simultaneous evaluation of a very large number of states. In October 2019 a Sycamore programmable superconducting processor claimed to have quantum supremacy, which is demonstrating that a quantum device can solve a problem that no classical computer can feasibly solve. Within experimental nuclear physics there is a paradigm shift in how data acquisition (DAQ) systems operate due to the need to support processing large volumes of data in near real-time. New approaches like streaming readout will further the integration of online and offline analyses leading to better data quality control during data taking and allowing shorter analysis cycles. Streaming readout is an enormous challenge for the current computational power available with traditional computing resources and in the next few years advances in quantum computing could be a competing alternative to the present computational paradigms. The goal of this project is to investigate the feasibility of current and future quantum computing technology for near real-time data processing in streaming readout systems. This project will utilize a prototype environment for streaming readout currently being tested at Jefferson Lab; these data will be processed with algorithms implemented on QPU resources to evaluate the reconstruction performance.A project like this has a tremendous potential to revolutionize DAQ systems and could be applicable to experiments with more complex readout systems such as SOLID and the future Electron Ion Collider.



Summary of ProposalDescription of Project

“Will experimental nuclear physics take advantage of Quantum Computing to solve Big Data problems in near real-time?”

The development of streaming readout (SRO) for the nuclear physics (NP) community is driven by the Streaming Grand Challenge at JLab [1], which aims to determine novel approaches to further the convergence of online and offline analysis leading to better data quality control during data taking and shorter analysis cycles. Moving the event building and high-level (HL) selection on computing farms has different advantages, e.g., deploying software algorithms that can access all detector information to efficiently select interesting signals. While NP experiments are considering using AI with accelerated hardware to solve several tasks [2], we also observe the unprecedented growth of computational power of quantum computers (QC) which are: (i) able to operate rapidly through certain problems that no classical computer could solve in any feasible amount of time (remarkably quantum supremacy has been claimed in 2019 [3]); (ii) capable in perspective to manage larger datasets. Real-world applications on QC started emerging recently (see, e.g., [4,5]) contributing to the development of cutting-edge machine learning implementations on QC which in turn fostered QPU-based applications for high energy physics (see, e.g., [6–9] described later).

For this project, a collaboration of experts in experimental NP, streaming readout, and in reconstruction algorithms implemented on both conventional CPUs/GPUs and on QPUs, is required. The project will leverage on the synergy between Experimental NP and Quantum Information Science (QIS). Motivated by the challenges presented by SRO, the ultimate goal is demonstrating the potential of real-time data processing with HL-QC algorithms. The planned activities will develop algorithms for the most compute-intensive parts of the data processing of every experiment, like (i) tracking and (ii) clustering. As a first step, we will test the QC approach offline, relying on future technological advances that will allow us to access QC with minimal latency time. The reconstruction performance determined in a prototype experimental environment for SRO will be projected according to the computing power (e.g. number of qubits) expected to be available in the next years and scaled to a more complex scenario (larger data



volumes) of a whole experiment like the SOLID experiment or the Electron Ion Collider (EIC) in a full streaming mode.

Expected Results Tests will be performed in a prototype environment within a SRO framework using real data collected by the CLAS12 Forward-Tagger (FT) sub-detector during February 2020 tests, which represents an ideal data reconstruction pipeline based on QC: (i) clustering for the calorimeter; (ii) tracks finding; and (iii) decision trees for HL-event selection. The observed reconstruction and time performance will be projected to the computing power available in the next years and scaled to a larger experiment like SOLID or EIC in a full SRO mode. Notice that the FT-tracker does not currently support SRO, and given the complexity of this task we have to focus first on developing procedures applicable to data collected in triggered mode.

These results can be vital for the Streaming Grand Challenge in individuating new cutting-edge computing resources for data processing.

The activity labeled (i) is anticipated for the first year. Activity (ii) will start in parallel in the first year, and will take advantage of an already existing tracking algorithm based on quantum annealing and implemented on D-Wave by the personnel of this project. Activity (iii) is anticipated for the second year. All the activities will be compared to machine learning applications already developed (see, e.g., the ML algorithms [10] already developed for streaming readout). We will write a document showing performance and projections based on real data. We also anticipate the creation and maintenance of a dedicated repository for the developed software.



Proposal NarrativePurpose/GoalsThe idea that a quantum computer can potentially compute things that a classicalcomputer cannot was expressed for the first time by Richard Feynman in the early1980s. In the recent years advances in both (i) artificial intelligence—with an un-precedented growth of neural networks applications1—and (ii) quantum computing—with the increasing computational power of QPUs—contributed to the rise of an emerging interdisciplinary research area also known as quantum machine learning (QML). The rapidly growing availability of QC in the cloud2 as well as prototypes in the industry and academia settings, ranging from quantum annealers (QAs) (see, e.g., D-Wave [4]) to gate-based quantum processors using several technologies [11], and the ability of quantum algorithms to tackle global optimization problems (e.g., using Hopfield neural networks), are promoting real-world applications (e.g., the traffic control system developed by Volkswagen [5]). Noticeably, as of today quantum annealing scales up to an order of magnitude more qubits than gate methods, see Fig. 1.Real-time data filtering/processing are among the main challenges in present experiments in nuclear physics and in future high energy facilities (EIC) and high intensity experiments (SOLID). The consolidated usage of high level algorithms based on machine learning for reducing tracks at the HLT1 [12] and of the topological trigger at the HLT2 in LHCb [13,14,15] is pushing the development of new GPU-based software applications to process events in real time [16]. Machine learning based algorithms—in particular boosted decision trees (BDT), random forests and decision rule ensembles due to their simpler parallelization—have been also implemented on FPGA, see for example the usage of BDT in the CMS Level-1 muon endcap trigger for track finding [17].

1 Y. Benjo, G. Hinton and Y. LeCun have received the Turing Award on 2018 for their break-throughs in the development of deep networks.

2 A new quantum computer, a 5000 qubit system named Advantage, will be made available foron-premise deployments and in D-Wave’s Leap cloud service in mid-2020.



While FPGAs are more suitable for prompt solutions and simple algorithms, quantum computing on the other hand can be used in the future to cope with complex problems and large volumes of data. We recently observed a plenitude of potential QPU-based applications which could result in a substantial change in the way we approach data processing. Different groups started developing new quantum architectures, e.g.: (i) in preparation of the HL-LHC upgrade, the authors in [6,7] studied a track finding algorithm capable of improving the reconstruction time of the Kalman filter; (ii) for the CMS experiment case, the authors in [8] used a D-Wave QA to perform track clustering on certain event topologies; (iii) QA has been used by [9] to solve a Higgs-signal-versus-background problem; (iv) quantum algorithms have been recently used for jet clustering [18].In this context and motivated by the challenges presented by streaming readout as discussed in the previous sections, we will develop novel custom high-level reconstruction algorithms based on QA. Since this could be a technology suitable for near real-time processing, we need to do our tests with a detector system compatible with the SRO. This will be done offline in a framework equivalent to streaming in order to use the existing technology available on the cloud for quantum computing. The CLAS12 FT sub-detector constitutes a simplified (with a relatively small number of channels) but realistic template for testing different reconstruction algorithms on beam data taken in SRO mode. In particular, the FT-tagger is made by:(1) the FT- Cal, a PbWO4 calorimeter used to measure the scattered electron energy with good accuracy. Multi cluster identification provides access to final states with a π0 γγ in the FT-Cal acceptance. ➝ (2) MicroMega FT-Tracker covering very forward polar angles (between 2.5° to 5°) around the beam line, which is overwhelmed by hadro-production background and the identification of the tracks corresponding to a good low-Q2 scattered electron is challenging. (3) the FT-Hodo, a plastic-scintillator-tiles made hodoscope located in front of the FT-Cal, will be correlated to the calorimeter information to distinguish between charged (electron) and neutral (gamma) clusters. Notice that tests in SRO mode have been already performed with the FT-Cal, and tests are planned for next year for the FT-Hodo. The current readout of the FT tracker is not streaming compatible, and therefore we will not be able to test QC-based tracking



algorithms on SRO data. On the other hand, due to the complexity of the tracking algorithms, we have to focus first on developing procedures applicable to data collected in triggered mode. If an upgrade of the front-end electronics could make the FT-Tracker readout streaming-compatible, we will apply the same methodology to SRO data. The ultimate goal is demonstrating the potential of near real-time processing of data with quantum computing, that is providing a detailed characterization of the performance both in terms of reconstruction efficiency and time, with useful projections obtained by scaling the results to future available QPU resources and more complex experimental environments such as the Electron Ion Collider.

Figure 1: Number of qubits as a function of time for annealing and circuit-based processors. Numbers are taken from [19].

Approach/MethodsQuantum annealing [20] (see also representation sketched in Fig. 2 (left)), is a process to find the global minimum of an objective quadratic function over binary variables. This is also known as a



QUBO3 problem type traditionally used in computer science, see Eq. (1), that can be implemented in a D-Wave system [4]:4

f(x) = Σij Qij xi xj + Σi Qii xi (1)

In Eq. (1) Q is an N x N upper-triangular matrix of real weights, and x, a vector of binary variables. Notice the analogy with Hopfield networks [21, 22], a form of recurrent artificial neural network popularized by John Hopfield in 1982, which constitutes an interesting class of algorithms that can be mapped onto a problem of finding the ground state of a QUBO problem:

E = - 1/2 Σi,j wi,j si sj + Σi θi si (2)

In Eq. (2) the quantity called energy (E) is a Lyapunov function that either decreases or stays the same upon network units being updated and the ith spin has been dubbed si, the other terms being weights and parameters.As previously mentioned, this simple and elegant formulation allows to embed and solve a plethora of problems; in particular, we are interested here in applications useful for fast reconstruction of events detected in the forward tagger in Hall B CLAS12; the FT consists of an electromagnetic calorimeter (FT-Cal) to accurately measure the energy of the electron, of a tracker (FT-Trk) to precisely determine its scattering angle and of a scintillating hodoscope (FT-Hodo) to distinguish electrons from photons. Consequently we are focused on fast applications based on Eqs. (1), (2) regarding:

(i) A fast clustering (see, Fig. 2 (right)) for the FT- Cal, where multi-cluster identification provides access to final states with a π0 γγ in ➝the FT-Cal acceptance. Notice that different approaches [23] can be explored for clustering. (ii) A fast track finding algorithm (see, e.g., Fig. 2 (center)) from hits detected in the MicroMega FT-Tracker will be developed starting from an existing algorithm based on the work of [24] that has been already implemented by the same authors on D-Wave. The goal of a

3 Quadratic Unconstrained Binary Optimization.

4 It is worth mentioning tools like qbsolv based on an iterative hybrid classical/quantum approach with multiple trials developed to solve larger and more densely connected QUBOs [26].



tracking algorithm is connecting the detected hits to form tracks. In this approach each neuron corresponds to the connection of two hits. The model used for the Hamiltonian is flexible enough to be modified and ported to the case of CLAS12 FT. (iii) A fast particle identification algorithm inspired by topological triggers [13, 14] based on decision trees [9, 25, 26]. The hits from the FT-Hodo will be correlated to the calorimeter information to distinguish between charged (electron) and neutral (gamma) clusters.

Figure 2: (left) Heuristic representation of quantum annealing to search for the global optimum via quantum processes. See text and references therein for more details; (center) Results from [29] showing the reconstruction of tracks as a function of the sweep cycles using the Denby-Peterson model implemented on a classical computer. Ideally the final sweep cycle in the classical approach corresponds to the global solution found by the quantum annealer; (right) example of clustering that can be tackled with quantum annealing, image taken from [23] where the reader can find more details.

A comparison with classical ML approaches will be provided for each algorithm, e.g. for (i) we will compare to the ML clustering already implemented in JANA2 [27] and used for the SRO activities [10]; for (ii) we will compare to the tracking implementation on CPU/GPUs. The physics applications (i), (ii), (iii) share a common methodology

structured as follows:● Data pre (post)-processing, which can play an important role in

the algorithm performance.● Test different data volume and embedding in D-Wave

architecture with possible partition of data (e.g. detector sectors/subregions) to improve global reconstruction.

● Using different hamiltonians and optimization of hyperparameters (e.g., using Bayesian Optimization [28]



maximizing some figure of merit (FoM) which encodes the reconstruction performance).

● Validation of results with different datasets (e.g., toy model, simulation, real data) and under different experimental physics conditions (streaming readout and triggered modes).

● Provide projected performance and timing studies on QPU with a comparison to ‘classical’ methods (e.g. ML on CPU/GPU).

An important goal of this project is to assess quantum advantage in deploying these algorithms on QPU. This implies a comparison with other methods implemented on classical processing units. Another aspect that will be covered is the optimization of the total reconstruction time (see Fig. 3 (right)), that is trying to minimize the programming, anneal and readout times on the QPU. A detailed study of the internet latency and total service time (see Fig. 3 (left)) is also needed to address the feasibility of near real-time deployment of these reconstruction algorithms.

Figure 3: (left) overview of execution of a single quantum machine instruction, starting from a client system; (right) Detail of the QPU access time. Images taken from [30].

In the following a breakdown of the anticipated activities and goals for FY2021 and FY2022 is presented.

Goals for FY2021CLAS12-FT data collection: the FT-Cal and the FT-Hodo will be operated in streaming mode while the FT-Trk will be triggered in a traditional way. The resulting data sample will be used to test the QC algorithms. Considering the current pandemic, our work plan is structured in such a way to take advantage of the data already collected in 2020 in SRO mode to start testing the clustering



algorithms on QC. We will use minimum bias triggered data to start testing tracking on QC. By FY2022 we anticipate to have collected other data in SRO mode that will be used in this project (for FT-Cal and FT-Hodo).

● Quarter 1○ Port algorithms to QC architecture

▪ Re-adapt existing tracking algorithm for FT-Trk.

▪ Create clustering algorithm for FT-Cal.



● Quarter 2○ Test algorithms with simulated data.

▪ Test different data volumes.

▪Hyperparameter tuning.

● Quarter 3○ Test algorithms with experimental data.

▪ Optimization of reconstruction time.

▪ Compare results with traditional/AI-based algorithms (see, [10]).

● Quarter 4○ Analyze the performance.

▪ Document methods, results and projections.

▪ Compile the first year final report.

Goals for FY2022We anticipate that, based on the results obtained during the first year of activity, we will extend this study to include PID and apply clustering and tracking algorithms to more complex and realistic data-sets, expected by future experiments and facilities.

Among the other activities we expect to:● Develop quantum decision trees algorithm for PID with the FT-

Hodo. ● Extend tracking algorithms for more complex experimental

setups.● Test (clustering, tracking, decision trees) with CLAS12

simulated and possibly experimental data. ● Extrapolate algorithms performance for future experiments and

facilities (SOLID, EIC).● Compile the final report.

Required Resources The major resources needed for this project are:



● Accelerator beam time: ○ This will be a part of the ongoing streaming readout

activities and tests in Hall B at JLab; no additional beam time will be requested for this project.

● Quantum computing resources from D-Wave System. The activities outlined in this project imply deployment of standard machine learning and deep learning algorithms for benchmarking performance of quantum computing algorithms. Other resources are detailed in the budget explanation.

Anticipated Outcomes/ResultsThis work will assess the possible quantum advantage of high-level reconstruction algorithms (clustering, tracking and PID) implemented on a quantum computer for fast large-volume data processing of future experiments that will run in streaming readout mode.We anticipate to create and maintain a repository for reconstruction algorithms based on QC as well as report in a final document the reconstruction efficiency and time performance of these novel architectures. These results will be based on the optimization of the reconstruction time on QPU, and projected to future available QPU resources, scaling the performance to more complex environments for data acquisition in experiments like SOLID and the EIC.The obtained performance will be benchmarked against classical approaches implemented on standard processing units and will be reported in the final reports.

Budget Explanation

Purchase/Procurements:● We anticipate $20k for purchasing quantum computing

resources from D-Wave Systems. All the accounts of the personnel involved in the proposal will be granted access to the allocated computing time.

● We require a mobile deep learning workstation (e.g., Dell Precision 7740, Intel Xeon E2286M, 8 Core Xeon, Nvidia Quadro RTX 5000, 96GB, 2x16GB/2x32GB, DDR4 2666MHz ECC Memory) (anticipated total cost of $9.5k). A portable workstation allows for smart working during the COVID-19 pandemic. This workstation has important features that allow us



to work interactively using a hybrid framework (e.g, optimization with machine learning combined to quantum annealing on D-Wave systems). It will also facilitate access and sharing of resources among the JLab and external collaborators of this project.



Personnel:● Staff: Dr. M. Battaglieri, PI, JLab (0.05 FTE); Dr. Cristiano

Fanelli, co-PI, MIT/JLab (0.25 FTE), Dr. William Phelps, co-PI, CNU/JLab (0.15 FTE); MIT postdoc (0.60 FTE); JLab postdoc (0.85 FTE); CNU undergrad (0.15 FTE). A detailed description is provided below.

This project will take advantage of the interaction with MIT (whose physics and engineering departments have world-leading groups in quantum computing) and will create synergies between experimental nuclear physics, quantum information science and artificial intelligence. We will use real data collected by the CLAS12 experiment in Hall B and develop custom solutions based on quantum computing to test the feasibility for the streaming readout challenge.

● Dr. Marco Battaglieri (0.05 FTE) is the Hall B leader at JLab. He is a streaming readout expert (co-PI of eRD-23 Streaming readout for EIC detectors) and leader of the CLAS12 FT project. He will be responsible for running CLAS12 FT SRO tests and providing experimental data.

● Dr. Cristiano Fanelli (0.25 FTE) holds a position at MIT and is working off-campus at JLab. Among his activities, he is involved in the streaming readout project at JLab where he is developing high-level algorithms based on AI and he is leading a quantum computing project on tracking at ORNL. A subcontract to MIT (under a MOU between JLab/MIT) will cover 25% of Cristiano's salary as Research Scientist at MIT and to let him hire a postdoc from MIT that will work 0.60 FTE. The subcontract includes MIT overhead costs and the procurement of the workstation. Details on the MOU will be worked out with JLab before the beginning of the LDRD project, to facilitate the recruitment of MIT personnel in this project if approved.

● Dr. William Phelps (0.15 FTE) holds a joint position as a JLab Staff Scientist at JLab and is an Assistant Professor at CNU. Among his activities, he is involved in AI research and an active member of the CLAS12 experiment as well as a core member of the software group. He also collaborates in the quantum computing project of the other co-PI with his undergraduate research assistant Andru Quiroga.

● MIT postdoc (0.60 FTE): the ideal candidate to hire will have experience in quantum computing (optimization of data volume and reconstruction time on QPU, algorithm development and embedding on D-Wave architecture) and is expected to spend time at JLab to work closely with the other collaborators. In case the project may not be funded through the full duration of



the candidate’s position, the person’s salary will be covered by MIT. MIT uses the NIH guidelines for minimum salaries.

● JLab-Postdoc (0.85 FTE): we plan to hire at 0.85 FTE another postdoc who is currently employed at JLab (full or part of his salary covered by JLab). Since we will use data from JLab experiments and will benchmark our results from quantum annealing against AI-based algorithms, the postdoc is not expected to have previous experience on quantum computing but rather she/he has to be experienced in analysis of JLab data and possibly AI-based techniques.

● Andru Quiroga (0.15 FTE) is an undergraduate research assistant majoring in computer engineering at CNU. He is already involved in the tracking quantum computing project of Dr. Fanelli and he is developing a computationally efficient data preprocessing which contributes to the total programming time.

● Other personnel: Dr. Evaristo Cisbani (INFN/Roma1), Dr Alessio Del Dotto (LNF/INFN), Dr. Mariangela Bondi’ (INFN/Ge), Dr. Luca Marsicano (INFN/Ge). The collaborators listed as other personnel will not have salaries under the LDRD, but only travel/visits costs. Dr Cisbani and Del Dotto are already involved in the tracking quantum computing project. Dr Bondi’ and Dr Marsicano have experience with the CLAS12 forward tagger.

Travel:● We anticipate $20k: to attend a workshop on the topic of the

proposal and cover travel costs, registration, accommodation and per diem; to cover costs and per diem of the following travels: from/to MIT to/from JLab; to cover travel costs overseas of other personnel.



References

[1] Streaming Readout V Workshop, Nov 2019: https://www.bnl.gov/srv2019/.

[2] A.I. for Nuclear Physics Workshop, 2020.

[3] F. Arute et al. Quantum supremacy using a programmable superconducting processor. Nature, 574(7779):505–510, 2019.

[4] D-wave systems: https://www.dwavesys.com.

[5] F. Neukart et al. Traffic flow optimization using a quantum annealer. Frontiers in ICT, 4:29, 2017.

[6] F. Bapst et al. A pattern recognition algorithm for quantum annealers. Computing and Software for Big Science, 4(1):1, 2020.

[7] C. Tuysuz et al. Particle Track Reconstruction with Quantum Algorithms. arXiv preprint arXiv:2003.08126, 2020.

[8] S. Das et al. Track clustering with a quantum annealer for primary vertex reconstruction at hadron colliders. arXiv preprint arXiv:1903.08879, 2019.

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[10] C. Fanelli, AI-supported algorithms for streaming readout, 2020, Streaming Readout VI Workshop, 2020.

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[17] D. Acosta, A. Brinkerhoff, E. Busch, A Carnes, I Furic et al. Boosted decision trees in the level-1 muon endcap trigger at CMS. In Journal of Physics: Conference Series, volume 1085, page 042042. IOP Publishing, 2018.[18] A. Y. Wei, P. Naik, A. W. Harrow, and J. Thaler Phys. Rev. D 101, 094015 – Published 14 May 2020[19] https://en.wikipedia.org/wiki/List_of_quantum_processors[20] SE Venegas-Andraca et al. A cross-disciplinary introduction to quantum annealing-based algorithms. Contemp. Phys., 59(2):174–197, 2018[21] DJC MacKay. Information theory, inference and learning algorithms. Cambridge university press, 2003[22] RJ Glauber. Time-dependent statistics of the Ising model. J. Math. Phys., 4(2):294–307, 1963.

[23] H. Ushijima-Mwesigwa et al. Graph partitioning using quantum annealing on the D-Wave system. In Proceedings of the Second International Workshop on Post Moores Era Supercomputing, pages 22–29, 2017.

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[26] H. Neven et al. QBoost: Large Scale Classifier Training with Adiabatic Quantum Optimization. In ACML, pages 333–348, 2012.

[27] D. Lawrence et al. JANA2: C++ framework for multi-threaded HENP (HighEnergy and Nuclear Physics), 2020.

[28] J. Snoek, H. Larochelle, and RP Adams. Practical bayesian optimization of machine learning algorithms. In Adv. Neural Inf. Process. Syst., pages 2951–2959, (2012).

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[30] https://docs.dwavesys.com/docs/latest/c_timing_1.html


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Home | Jefferson Lab - Abstract · Web viewThe goal of a tracking algorithm is connecting the detected hits to form tracks. In this approach each neuron corresponds to the connection