{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,5]],"date-time":"2026-03-05T05:49:37Z","timestamp":1772689777873,"version":"3.50.1"},"reference-count":83,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2021,6,26]],"date-time":"2021-06-26T00:00:00Z","timestamp":1624665600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>This article aims to bring quantum computing to robotics. A quantum algorithm is developed to minimize the distance traveled in warehouses and distribution centers where order picking is applied. For this, a proof of concept is proposed through a Raspberry Pi 4, generating a quantum combinatorial optimization algorithm that saves the distance travelled and the batch of orders to be made. In case of computational need, the robot will be able to parallelize part of the operations in hybrid computing (quantum + classical), accessing CPUs and QPUs distributed in a public or private cloud. We developed a stable environment (ARM64) inside the robot (Raspberry) to run gradient operations and other quantum algorithms on IBMQ, Amazon Braket (D-Wave), and Pennylane locally or remotely. The proof of concept, when run in the above stated quantum environments, showed the execution time of our algorithm with different public access simulators on the market, computational results of our picking and batching algorithm, and analyze the quantum real-time execution. Our findings are that the behavior of the Amazon Braket D-Wave is better than Gate-based Quantum Computing over 20 qubits, and that AWS-Braket has better time performance than Qiskit or Pennylane.<\/jats:p>","DOI":"10.3390\/a14070194","type":"journal-article","created":{"date-parts":[[2021,6,27]],"date-time":"2021-06-27T22:24:57Z","timestamp":1624832697000},"page":"194","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":33,"title":["qRobot: A Quantum Computing Approach in Mobile Robot Order Picking and Batching Problem Solver Optimization"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2725-277X","authenticated-orcid":false,"given":"Parfait","family":"Atchade-Adelomou","sequence":"first","affiliation":[{"name":"Research Group on Data Science for the Digital Society, La Salle, Universitat Ramon Llull, Carrer de Sant Joan de La Salle, 42, 08022 Barcelona, Spain"},{"name":"Lighthouse Disruptive Innovation Group, LLC., 7 Broadway Terrace, Apt. 1, Cambridge, MA 02139, USA"}]},{"given":"Guillermo","family":"Alonso-Linaje","sequence":"additional","affiliation":[{"name":"Facultad de Ciencias, Campus Miguel Delibes, Universidad de Valladolid, C\/Plaza de Santa Cruz, 8, 47002 Valladolid, Spain"}]},{"given":"Jordi","family":"Albo-Canals","sequence":"additional","affiliation":[{"name":"Lighthouse Disruptive Innovation Group, LLC., 7 Broadway Terrace, Apt. 1, Cambridge, MA 02139, USA"}]},{"given":"Daniel","family":"Casado-Fauli","sequence":"additional","affiliation":[{"name":"Research Group on Data Science for the Digital Society, La Salle, Universitat Ramon Llull, Carrer de Sant Joan de La Salle, 42, 08022 Barcelona, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,26]]},"reference":[{"key":"ref_1","first-page":"413","article-title":"New technology trends and their transformative impact on logistics and supply chain processes","volume":"5","author":"Angeleanu","year":"2015","journal-title":"Int. J. Econ. Pract. Theor."},{"key":"ref_2","first-page":"491","article-title":"Benchmarking in omni-channel logistics","volume":"5","year":"2015","journal-title":"Res. Logist. Prod."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1287\/trsc.2016.0675","article-title":"50th anniversary invited article\u2014City logistics: Challenges and opportunities","volume":"50","author":"Savelsbergh","year":"2016","journal-title":"Transp. Sci."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"769","DOI":"10.1177\/0042098020917790","article-title":"Urban robotic experimentation: San Francisco, Tokyo and Dubai","volume":"58","author":"While","year":"2021","journal-title":"Urban Stud."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Van der Aalst, W.M., Bichler, M., and Heinzl, A. (2018). Robotic Process Automation, Springer.","DOI":"10.1007\/s12599-018-0542-4"},{"key":"ref_6","first-page":"21","article-title":"Robotic Process Automation\u2014A driver of digital transformation?","volume":"12","author":"Siderska","year":"2020","journal-title":"Eng. Manag. Prod. Serv."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Agostinelli, S., Marrella, A., and Mecella, M. (2020). Towards intelligent robotic process automation for BPMers. arXiv.","DOI":"10.1007\/978-3-030-37453-2_2"},{"key":"ref_8","unstructured":"Tompkins, J.A., White, J.A., Bozer, Y.A., and Tanchoco, J.M.A. (2010). Facilities Planning, John Wiley and Sons."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"024003","DOI":"10.1088\/2058-9565\/ab7559","article-title":"A quantum-classical cloud platform optimized for variational hybrid algorithms","volume":"5","author":"Karalekas","year":"2020","journal-title":"Quantum Sci. Technol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1145\/3457356.3457358","article-title":"Overview of Quantum Technologies, Standards, and their Applications in Mobile Devices","volume":"24","author":"Cornet","year":"2021","journal-title":"GetMobile Mob. Comput. Commun."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"115","DOI":"10.3322\/caac.21338","article-title":"Cancer statistics in China, 2015","volume":"66","author":"Chen","year":"2016","journal-title":"CA Cancer J. Clin."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/j.jenvman.2015.07.008","article-title":"Slaughterhouse wastewater characteristics, treatment, and management in the meat processing industry: A review on trends and advances","volume":"161","author":"Mehrvar","year":"2015","journal-title":"J. Environ. Manag."},{"key":"ref_13","first-page":"131","article-title":"A grouping genetic algorithm for the order batching problem in distribution warehouses","volume":"86","author":"Koch","year":"2016","journal-title":"J. Bus. Econ."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1356","DOI":"10.1016\/j.cor.2008.02.010","article-title":"The multi-period incremental service facility location problem","volume":"36","author":"Hinojosa","year":"2009","journal-title":"Comput. Oper. Res."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1007\/s10845-016-1248-4","article-title":"Order batching operations: An overview of classification, solution techniques, and future research","volume":"30","author":"Cergibozan","year":"2019","journal-title":"J. Intell. Manuf."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"246578","DOI":"10.1155\/2013\/246578","article-title":"Order batching in warehouses by minimizing total tardiness: A hybrid approach of weighted association rule mining and genetic algorithms","volume":"2013","author":"Azadnia","year":"2013","journal-title":"Sci. World J."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ejor.2017.09.002","article-title":"Designing efficient order picking systems by combining planning problems: State-of-the-art classification and review","volume":"267","year":"2018","journal-title":"Eur. J. Oper. Res."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/j.proeng.2014.12.098","article-title":"Path planning with modified a star algorithm for a mobile robot","volume":"96","author":"Babinec","year":"2014","journal-title":"Procedia Eng."},{"key":"ref_19","first-page":"293","article-title":"Rapidly-exploring random trees: Progress and prospects","volume":"5","author":"LaValle","year":"2001","journal-title":"Algorithmic Comput. Robot. New Dir."},{"key":"ref_20","unstructured":"LaValle, S.M. (2021, May 10). Rapidly-Exploring Random Trees: A New Tool for Path Planning. Available online: https:\/\/www.cs.csustan.edu\/~xliang\/Courses\/CS4710-21S\/Papers\/06%20RRT.pdf."},{"key":"ref_21","unstructured":"Cheng, P., and LaValle, S.M. (2002, January 11\u201315). Resolution complete rapidly-exploring random trees. Proceedings of the 2002 IEEE International Conference on Robotics and Automation, Washington, DC, USA."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1071\/EG05341","article-title":"The fast marching method: An effective tool for tomographic imaging and tracking multiple phases in complex layered media","volume":"36","author":"Rawlinson","year":"2005","journal-title":"Explor. Geophys."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1080\/07408170590516917","article-title":"Order Batching to Minimize Total Travel Time in a parallel-aisle warehouse","volume":"37","author":"Gademann","year":"2005","journal-title":"IIE Trans."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1037\/1076-8998.6.1.64","article-title":"Incivility in the workplace: Incidence and impact","volume":"6","author":"Cortina","year":"2001","journal-title":"J. Occup. Health Psychol."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/j.compind.2004.06.001","article-title":"Batching orders in warehouses by minimizing travel distance with genetic algorithms","volume":"56","author":"Hsu","year":"2005","journal-title":"Comput. Ind."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"6533","DOI":"10.1080\/00207540701441947","article-title":"Using a multiple-GA method to solve the batch picking problem: Considering travel distance and order due time","volume":"46","author":"Tsai","year":"2008","journal-title":"Int. J. Prod. Res."},{"key":"ref_27","unstructured":"Tsang, E. (2014). Foundations of Constraint Satisfaction: The Classic Text, BoD\u2013Books on Demand."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1007\/s10878-014-9734-0","article-title":"The unconstrained binary quadratic programming problem: A survey","volume":"28","author":"Kochenberger","year":"2014","journal-title":"J. Comb. Optim."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1112\/plms\/s2-42.1.230","article-title":"On computable numbers, with an application to the Entscheidungsproblem","volume":"2","author":"Turing","year":"1937","journal-title":"Proc. Lond. Math. Soc."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1007\/BF02650179","article-title":"Simulating physics with computers","volume":"21","author":"Feynman","year":"1982","journal-title":"Int. J. Theor. Phys"},{"key":"ref_31","first-page":"97","article-title":"Quantum theory, the Church\u2013Turing principle and the universal quantum computer","volume":"400","author":"Deutsch","year":"1985","journal-title":"Proc. R. Soc. Lond. Math. Phys. Sci."},{"key":"ref_32","unstructured":"Shor, P. (1994, January 20\u201322). Algorithms for quantum computation: Discrete logarithms and factoring. Proceedings of the 35th Annual Symposium on Foundations of Computer Science, Santa Fe, NM, USA."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Grover, L.K. (1996, January 22\u201324). A fast quantum mechanical algorithm for database search. Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing\u2014STOC \u201996, New York, NY, USA.","DOI":"10.1145\/237814.237866"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"79","DOI":"10.22331\/q-2018-08-06-79","article-title":"Quantum Computing in the NISQ era and beyond","volume":"2","author":"Preskill","year":"2018","journal-title":"Quantum"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Wang, D., Higgott, O., and Brierley, S. (2019). Accelerated Variational Quantum Eigensolver. Phys. Rev. Lett., 122.","DOI":"10.1103\/PhysRevLett.122.140504"},{"key":"ref_36","unstructured":"Farhi, E., Goldstone, J., and Gutmann, S. (2014). A Quantum Approximate Optimization Algorithm. arXiv."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1080\/00107514.2014.964942","article-title":"An introduction to quantum machine learning","volume":"56","author":"Schuld","year":"2014","journal-title":"Contemp. Phys."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1038\/nature23474","article-title":"Quantum machine learning","volume":"549","author":"Biamonte","year":"2017","journal-title":"Nature"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"226","DOI":"10.22331\/q-2020-02-06-226","article-title":"Data re-uploading for a universal quantum classifier","volume":"4","author":"Latorre","year":"2020","journal-title":"Quantum"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Atchade-Adelomou, P., Golobardes-Ribe, E., and Vilasis-Cardona, X. (2020). Using the Parameterized Quantum Circuit combined with Variational-Quantum-Eigensolver (VQE) to create an Intelligent social workers\u2019 schedule problem solver. arXiv.","DOI":"10.1007\/978-3-030-61705-9_21"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Atchade-Adelomou, P., Casado-Fauli, D., Golobardes-Ribe, E., and Vilasis-Cardona, X. (2021). quantum Case-Based Reasoning (qCBR). arXiv.","DOI":"10.1007\/s10462-022-10238-w"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Atchade-Adelomou, P., and Alonso-Linaje, G. (2021). Quantum Enhanced Filter: QFilter. arXiv.","DOI":"10.21203\/rs.3.rs-405334\/v1"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"20190143","DOI":"10.1098\/rsfs.2019.0143","article-title":"Quantum computing using continuous-time evolution","volume":"10","author":"Kendon","year":"2020","journal-title":"Interface Focus"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/978-3-031-02518-1","article-title":"Adiabatic Quantum Computation and Quantum Annealing Theory and Practice","volume":"5","author":"McGeoch","year":"2014","journal-title":"Synth. Lect. Quantum Comput."},{"key":"ref_45","unstructured":"McDonald, K.T. (2021, May 10). Ph410 Physics of Quantum Computation1. Available online: https:\/\/www.physics.princeton.edu\/~mcdonald\/examples\/ph410problems.pdf."},{"key":"ref_46","unstructured":"Landauer, E.O.W.R. (2021, May 10). Fundamental concepts of Hamiltonian Pauli Terms Quantum Computation. Available online: https:\/\/core.ac.uk\/download\/pdf\/25212354.pdf."},{"key":"ref_47","unstructured":"Harrow, A.W., and Farhi, E. (2021, May 10). Quantum Supremacy through the Quantum Approximate Optimization Algorithm. Available online: https:\/\/arxiv.org\/pdf\/1602.07674.pdf."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"5355","DOI":"10.1103\/PhysRevE.58.5355","article-title":"Quantum Annealing in the Transverse Ising Model","volume":"58","author":"Kadowaki","year":"1998","journal-title":"Phys. Rev. E"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1016\/0377-2217(92)90192-C","article-title":"The Vehicle Routing Problem: An Overview of Exact and Approximate Algorithm","volume":"59","author":"Laporte","year":"1992","journal-title":"Eur. J. Oper. Res."},{"key":"ref_50","unstructured":"Sarkar, K.B.A., Mouedenne, A., Hubregtsen, A.Y.T., and Krol, I.A.A. (2020, January 9\u201313). Quantum Computer Architecture: Towards Full-Stack Quantum Accelerators. Proceedings of the Design, Automation & Test in Europe Conference & Exhibition (DATE), Grenoble, France."},{"key":"ref_51","first-page":"17","article-title":"Multi-objective Genetic Algorithms for Vehicle Routing Problem with Time Windows","volume":"24","author":"Ross","year":"2004","journal-title":"Appl. Intell."},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Peruzzo, A., McClean, J., Shadbolt, P., Yung, M.H., Zhou, X.Q., Love, P.J., Aspuru-Guzik, A., and O\u2019Brien, J.L. (2014). A variational eigenvalue solver on a photonic quantum processor. Nat. Commun., 5.","DOI":"10.1038\/ncomms5213"},{"key":"ref_53","first-page":"1","article-title":"QAOA for Max-Cut Requires Hundreds of Qubits for Quantum Speed-up","volume":"9","author":"Matsuura","year":"2019","journal-title":"Sci. Rep."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"042318","DOI":"10.1103\/PhysRevA.68.042318","article-title":"The Clifford Group, Stabilizer States, and Linear and Quadratic Operations over GF(2)","volume":"68","author":"Moor","year":"2003","journal-title":"Phys. Rev. A"},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Rebentrost, P., Schuld, M., Wossnig, L., Petruccione, F., and Lloyd, S. (2018). Quantum gradient descent and Newton\u2019s method for constrained polynomial optimization. arXiv.","DOI":"10.1088\/1367-2630\/ab2a9e"},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"Vyskocil, T., and Djidjev, H. (2019). Embedding Equality Constraints of Optimization Problems into a Quantum Annealer. Algorithms, 12.","DOI":"10.3390\/a12040077"},{"key":"ref_57","doi-asserted-by":"crossref","unstructured":"Anuradha Mahasinghe Michael, J., and Dinneen, R.H. (2019, January 29\u201331). Solving the Hamiltonian Cycle Problem using a Quantum Computer. Proceedings of the Australasian Computer Science Week Multiconference, Sydney, NSW, Australia.","DOI":"10.1145\/3290688.3290703"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"5","DOI":"10.3389\/fphy.2014.00005","article-title":"Ising formulations of many NP problems","volume":"2","author":"Lucas","year":"2014","journal-title":"Front. Phys."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"13","DOI":"10.3389\/fict.2019.00013","article-title":"A Hybrid Solution Method for the Capacitated Vehicle Routing Problem Using a Quantum Annealer","volume":"6","author":"Roch","year":"2019","journal-title":"Front. ICT"},{"key":"ref_60","unstructured":"Braket, A. (2021, May 05). Amazon Braket Services. Available online: https:\/\/aws.amazon.com\/braket\/?nc1=h_ls."},{"key":"ref_61","unstructured":"Xie, L., Li, H., and Luttmann, L. (2021). Formulating and solving integrated order batching and routing in multi-depot AGV-assisted mixed-shelves warehouses. arXiv."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1088\/1126-6708\/2004\/10\/016","article-title":"Bethe Ansatz for Quantum Strings","volume":"2004","author":"Arutyunov","year":"2004","journal-title":"J. High Energy Phys."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"1900070","DOI":"10.1002\/qute.201900070","article-title":"Expressibility and Entangling Capability of Parameterized Quantum Circuits for Hybrid Quantum-Classical Algorithms","volume":"2","author":"Sim","year":"2019","journal-title":"Adv. Quantum Technol."},{"key":"ref_64","doi-asserted-by":"crossref","unstructured":"Atchade-Adelomou, P., Golobardes-Rib\u00e9, E., and Vilas\u00eds-cardona, X. (2020, January 11\u201313). Using the Variational-Quantum-Eigensolver (VQE) to Create an Intelligent Social Workers Schedule Problem Solver. Proceedings of the International Conference on Hybrid Artificial Intelligence Systems, Gij\u00f3n, Spain.","DOI":"10.1007\/978-3-030-61705-9_21"},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/j.laa.2004.12.014","article-title":"On Rayleigh\u2013Ritz ratios of a generalized Laplacian matrix of directed graphs","volume":"402","author":"Wu","year":"2005","journal-title":"Linear Algebra Its Appl."},{"key":"ref_66","unstructured":"Foundation, R.P. (2021, May 10). Raspberry Pi 4. Available online: https:\/\/www.raspberrypi.org\/products\/raspberry-pi-4-model-b\/."},{"key":"ref_67","first-page":"9","article-title":"ARM architecture and systems","volume":"17","author":"Jaggar","year":"1997","journal-title":"IEEE Ann. Hist. Comput."},{"key":"ref_68","doi-asserted-by":"crossref","unstructured":"Jiang, Q., Lee, Y.C., and Zomaya, A.Y. (2020, January 11\u201314). The Power of ARM64 in Public Clouds. Proceedings of the 2020 20th IEEE\/ACM International Symposium on Cluster, Cloud and Internet Computing (CCGRID), Melbourne, Australia.","DOI":"10.1109\/CCGrid49817.2020.00-47"},{"key":"ref_69","doi-asserted-by":"crossref","unstructured":"Wille, R., Van Meter, R., and Naveh, Y. (2019, January 25\u201329). IBM\u2019s Qiskit Tool Chain: Working with and Developing for Real Quantum Computers. Proceedings of the 2019 Design, Automation & Test in Europe Conference & Exhibition (DATE), Florence, Italy.","DOI":"10.23919\/DATE.2019.8715261"},{"key":"ref_70","unstructured":"IBM (2021, May 10). DOcplex Python Modeling API. Available online: https:\/\/www.ibm.com\/docs\/en\/icos\/12.9.0?topic=docplex-python-modeling-api."},{"key":"ref_71","unstructured":"Eisberg, R., and Resnick, R. (2021, May 10). Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles. Available online: https:\/\/ui.adsabs.harvard.edu\/abs\/1985qpam.book.....E\/abstract."},{"key":"ref_72","unstructured":"Iterate (2021, May 10). Cyberduck\u2014SSH. Available online: https:\/\/cyberduck.io\/sftp\/."},{"key":"ref_73","unstructured":"The Raspberry Pi Foundation (2021, May 10). Configuration of the Raspberry Pi. Available online: https:\/\/www.raspberrypi.org\/documentation\/configuration\/."},{"key":"ref_74","unstructured":"Bergholm, V., Izaac, J., Schuld, M., Gogolin, C., Alam, M.S., Ahmed, S., Arrazola, J.M., Blank, C., Delgado, A., and Jahangiri, S. (2020). PennyLane: Automatic Differentiation of Hybrid Quantum-Classical Computations. arXiv."},{"key":"ref_75","unstructured":"Braket, A. (2021, February 26). Github Amazon Braket. Available online: https:\/\/github.com\/aws\/amazon-braket-sdk-python."},{"key":"ref_76","doi-asserted-by":"crossref","unstructured":"Sete, E.A., Zeng, W.J., and Rigetti, C.T. (2016, January 17\u201319). A functional architecture for scalable quantum computing. Proceedings of the 2016 IEEE International Conference on Rebooting Computing (ICRC), San Diego, CA, USA.","DOI":"10.1109\/ICRC.2016.7738703"},{"key":"ref_77","unstructured":"McKay, D.C., Alexander, T., Bello, L., Biercuk, M.J., Bishop, L., Chen, J., Chow, J.M., C\u00f3rcoles, A.D., Egger, D., and Filipp, S. (2018). Qiskit backend specifications for openqasm and openpulse experiments. arXiv."},{"key":"ref_78","unstructured":"D-Wave (2021, May 10). D-Wave Computer. Available online: https:\/\/www.dwavesys.com\/quantum-computing."},{"key":"ref_79","unstructured":"PennyLane, A.B. (2021, February 26). PennyLane-Braket Plugin. Available online: https:\/\/amazon-braket-pennylane-plugin-python.readthedocs.io\/en\/latest\/."},{"key":"ref_80","unstructured":"PennyLane, A.B. (2021, March 26). PennyLane-Braket Plugin. Available online: https:\/\/docs.aws.amazon.com\/braket\/latest\/developerguide\/braket-devices.html."},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TQE.2021.3050449","article-title":"Benchmarking Hamiltonian Noise in the D-Wave Quantum Annealer","volume":"2","author":"Zaborniak","year":"2021","journal-title":"IEEE Trans. Quantum Eng."},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"44","DOI":"10.4236\/jcc.2020.811004","article-title":"Formulation of the Social Workers\u2019 Problem in Quadratic Unconstrained Binary Optimization Form and Solve It on a Quantum Computer","volume":"8","year":"2020","journal-title":"J. Comput. Commun."},{"key":"ref_83","unstructured":"Braket, A. (2021, June 26). qRobot Platform. Available online: https:\/\/github.com\/pifparfait\/qRobot_Platform\/blob\/main\/RaspberryPi_ARM64_for_QML.ipynb."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/14\/7\/194\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:24:56Z","timestamp":1760163896000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/14\/7\/194"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,26]]},"references-count":83,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2021,7]]}},"alternative-id":["a14070194"],"URL":"https:\/\/doi.org\/10.3390\/a14070194","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6,26]]}}}