{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T20:49:52Z","timestamp":1776286192431,"version":"3.50.1"},"reference-count":59,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,2,5]],"date-time":"2024-02-05T00:00:00Z","timestamp":1707091200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,2,5]],"date-time":"2024-02-05T00:00:00Z","timestamp":1707091200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Consiglio Nazionale Delle Ricerche"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Mach. Intell."],"published-print":{"date-parts":[[2024,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In-depth theoretical and practical research is nowadays being performed on variational quantum algorithms (VQAs), which have the potential to surpass traditional, classical, algorithms on a variety of problems, in physics, chemistry, biology, and optimization. Because they are hybrid quantum-classical algorithms, it takes a certain set of optimal conditions for their full potential to be exploited. For VQAs, the construction of an appropriate ansatz in particular is crucial, since it lays the ground for efficiently solving the particular problem being addressed. To prevent severe negative effects that hamper quantum computation, the substantial noise, together with the structural limitations, characteristic of currently available devices must be also taken into consideration while building the ansatz. In this work the effect of the quantum hardware structure, namely the topological properties emerging from the couplings between the physical qubits and the basis gates of the device itself, on the performances of VQAs is addressed. Specifically, it is here experimentally shown that a complex connectivity in the ansatz, albeit being beneficial for exploring wider sets of solutions, introduces an overhead of gates during the transpilation on a quantum computer that increases the overall error rate, thus undermining the quality of the training. It is hence necessary, when implementing a variation quantum learning algorithm, to find the right balance between a sufficiently parametrized ansatz and a minimal cost in terms of resources during transpilation. Moreover, the experimental finding allows to construct a heuristic metric function, which aids the decision-making process on the best possible ansatz structure to be deployed on a given quantum hardware, thus fostering a more efficient application of VQAs in realistic situations. The experiments are performed on two widely used variational algorithms, the VQE (variational quantum eigensolver) and the VQC (variational quantum classifier), both tested on two different problems, the first on the Markowitz portfolio optimization using real-world financial data, and the latter on a classification task performed on the Iris dataset.<\/jats:p>","DOI":"10.1007\/s42484-024-00144-5","type":"journal-article","created":{"date-parts":[[2024,2,5]],"date-time":"2024-02-05T12:03:48Z","timestamp":1707134628000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["The effects of quantum hardware properties on the performances of variational quantum learning algorithms"],"prefix":"10.1007","volume":"6","author":[{"given":"Giuseppe","family":"Buonaiuto","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Francesco","family":"Gargiulo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Giuseppe","family":"De Pietro","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Massimo","family":"Esposito","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marco","family":"Pota","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,2,5]]},"reference":[{"issue":"6","key":"144_CR1","doi-asserted-by":"publisher","first-page":"403","DOI":"10.1038\/s43588-021-00084-1","volume":"1","author":"A Abbas","year":"2021","unstructured":"Abbas A, Sutter D, Zoufal C, Lucchi A, Figalli A, Woerner S (2021) The power of quantum neural networks. Nat Comput Sci 1(6):403\u2013409","journal-title":"Nat Comput Sci"},{"issue":"20","key":"144_CR2","doi-asserted-by":"publisher","first-page":"13723","DOI":"10.1007\/s00521-021-06009-3","volume":"33","author":"G Acampora","year":"2021","unstructured":"Acampora G, Schiattarella R (2021) Deep neural networks for quantum circuit mapping. Neural Comput Applic 33(20):13723\u201313743. https:\/\/doi.org\/10.1007\/s00521-021-06009-3","journal-title":"Neural Comput Applic"},{"key":"144_CR3","unstructured":"Aleksandrowicz G, Alexander T, Barkoutsos P, Bello L, Ben-Haim Y, Bucher D, Cabrera-Hern\u00e1ndez F, Carballo-Franquis J, Chen A, Chen C et al (2019) Qiskit: An open-source framework for quantum computing. Accessed on: Mar. 16"},{"issue":"11","key":"144_CR4","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/ac2cb3","volume":"23","author":"G-LR Anselmetti","year":"2021","unstructured":"Anselmetti G-LR, Wierichs D, Gogolin C, Parrish RM (2021) Local, expressive, quantum-number-preserving vqe ansatze for fermionic systems. N J Phys 23(11):113010. https:\/\/doi.org\/10.1088\/1367-2630\/ac2cb3","journal-title":"N J Phys"},{"key":"144_CR5","doi-asserted-by":"publisher","unstructured":"Arrasmith A, Cerezo M, Czarnik P, Cincio L, Coles PJ (2021) Effect of barren plateaus on gradient-free optimization. Quantum 5:558. https:\/\/doi.org\/10.22331\/q-2021-10-05-558","DOI":"10.22331\/q-2021-10-05-558"},{"issue":"2","key":"144_CR6","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.98.022322","volume":"98","author":"PK Barkoutsos","year":"2018","unstructured":"Barkoutsos PK, Gonthier JF, Sokolov I, Moll N, Salis G, Fuhrer A, Ganzhorn M, Egger DJ, Troyer M, Mezzacapo A et al (2018) Quantum algorithms for electronic structure calculations: Particle-hole hamiltonian and optimized wave-function expansions. Phys Rev A 98(2):022322","journal-title":"Phys Rev A"},{"issue":"7671","key":"144_CR7","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1038\/nature23474","volume":"549","author":"J Biamonte","year":"2017","unstructured":"Biamonte J, Wittek P, Pancotti N, Rebentrost P, Wiebe N, Lloyd S (2017) Quantum machine learning. Nature 549(7671):195\u2013202. https:\/\/doi.org\/10.1038\/nature23474","journal-title":"Nature"},{"key":"144_CR8","doi-asserted-by":"publisher","unstructured":"Buonaiuto G, Gargiulo F, De\u00a0Pietro G, Esposito M, Pota M (2023) Best practices for portfolio optimization by quantum computing, experimented on real quantum devices. https:\/\/doi.org\/10.1038\/s41598-023-45392-w","DOI":"10.1038\/s41598-023-45392-w"},{"issue":"1","key":"144_CR9","doi-asserted-by":"publisher","first-page":"1791","DOI":"10.1038\/s41467-021-21728-w","volume":"12","author":"M Cerezo","year":"2021","unstructured":"Cerezo M, Sone A, Volkoff T, Cincio L, Coles PJ (2021) Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nat Commun 12(1):1791. https:\/\/doi.org\/10.1038\/s41467-021-21728-w","journal-title":"Nat Commun"},{"issue":"9","key":"144_CR10","doi-asserted-by":"publisher","first-page":"625","DOI":"10.1038\/s42254-021-00348-9","volume":"3","author":"M Cerezo","year":"2021","unstructured":"Cerezo M, Arrasmith A, Babbush R, Benjamin SC, Endo S, Fujii K, McClean JR, Mitarai K, Yuan X, Cincio L, Coles PJ (2021) Variational quantum algorithms. Nature Reviews. Physics. 3(9):625\u2013644. https:\/\/doi.org\/10.1038\/s42254-021-00348-9","journal-title":"Physics."},{"issue":"9","key":"144_CR11","doi-asserted-by":"publisher","first-page":"567","DOI":"10.1038\/s43588-022-00311-3","volume":"2","author":"M Cerezo","year":"2022","unstructured":"Cerezo M, Verdon G, Huang H-Y, Cincio L, Coles PJ (2022) Challenges and opportunities in quantum machine learning. Nat Comput Sci 2(9):567\u2013576. https:\/\/doi.org\/10.1038\/s43588-022-00311-3","journal-title":"Nat Comput Sci"},{"key":"144_CR12","unstructured":"Cheng J, Wang H, Liang Z, Shi Y, Han S, Qian X (2022) Topgen: Topology-aware bottom-up generator for variational quantum circuits. arXiv:2210.08190"},{"issue":"7198","key":"144_CR13","doi-asserted-by":"publisher","first-page":"1031","DOI":"10.1038\/nature07128","volume":"453","author":"J Clarke","year":"2008","unstructured":"Clarke J, Wilhelm FK (2008) Superconducting quantum bits. Nature 453(7198):1031\u20131042","journal-title":"Nature"},{"issue":"6","key":"144_CR14","doi-asserted-by":"publisher","first-page":"389","DOI":"10.1038\/s43588-021-00088-x","volume":"1","author":"PJ Coles","year":"2021","unstructured":"Coles PJ (2021) Seeking quantum advantage for neural networks. Nature Computational Science 1(6):389\u2013390. https:\/\/doi.org\/10.1038\/s43588-021-00088-x","journal-title":"Nature Computational Science"},{"key":"144_CR15","unstructured":"Crooks, G.E.: Gradients of parameterized quantum gates using the parameter-shift rule and gate decomposition. arXiv preprint arXiv:1905.13311. (2019)"},{"key":"144_CR16","unstructured":"Cross AW, Bishop LS, Smolin JA, Gambetta JM (2017) Open quantum assembly language. arXiv:1707.03429"},{"key":"144_CR17","unstructured":"Farhi E, Goldstone J, Gutmann S (2014) A quantum approximate optimization algorithm. arXiv:1411.4028"},{"key":"144_CR18","unstructured":"Global Quantum Computing Market Report (2022) Rising Investments in Quantum Technology Fuel Growth - ResearchAndMarkets.com. https:\/\/www.businesswire.com\/news\/home\/20221129005908\/en\/Global-Quantum-Computing-Market-Report-2022-Rising-Investments-in-Quantum-Technology-Fuel-Growth---ResearchAndMarkets.com"},{"key":"144_CR19","doi-asserted-by":"publisher","unstructured":"Glover, F., Kochenberger, G., Du, Y. (2019) Quantum bridge analytics i: a tutorial on formulating and using qubo models. 4OR 17(4):335\u2013371. https:\/\/doi.org\/10.1007\/s10288-019-00424-y","DOI":"10.1007\/s10288-019-00424-y"},{"issue":"1","key":"144_CR20","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1038\/s41534-018-0116-9","volume":"4","author":"E Grant","year":"2018","unstructured":"Grant E, Benedetti M, Cao S, Hallam A, Lockhart J, Stojevic V, Green AG, Severini S (2018) Hierarchical quantum classifiers. Npj Quantum Inf 4(1):65. https:\/\/doi.org\/10.1038\/s41534-018-0116-9","journal-title":"Hierarchical quantum classifiers. Npj Quantum Inf"},{"issue":"4","key":"144_CR21","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1016\/j.physrep.2008.09.003","volume":"469","author":"H H\u00e4ffner","year":"2008","unstructured":"H\u00e4ffner H, Roos CF, Blatt R (2008) Quantum computing with trapped ions. Phys Rep 469(4):155\u2013203. https:\/\/doi.org\/10.1016\/j.physrep.2008.09.003","journal-title":"Phys Rep"},{"issue":"7747","key":"144_CR22","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1038\/s41586-019-0980-2","volume":"567","author":"V Havlicek","year":"2019","unstructured":"Havlicek V, Corcoles AD, Temme K, Harrow AW, Kandala A, Chow JM, Gambetta JM (2019) Supervised learning with quantum-enhanced feature spaces. Nature. 567(7747):209\u2013212. https:\/\/doi.org\/10.1038\/s41586-019-0980-2","journal-title":"Nature."},{"key":"144_CR23","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.105.052414","volume":"105","author":"Y Huang","year":"2022","unstructured":"Huang Y, Li Q, Hou X, Wu R, Yung M-H, Bayat A, Wang X (2022) Robust resource-efficient quantum variational ansatz through an evolutionary algorithm. Phys Rev A 105:052414. https:\/\/doi.org\/10.1103\/PhysRevA.105.052414","journal-title":"Phys Rev A"},{"key":"144_CR24","unstructured":"IBM quantum. https:\/\/quantum-computing.ibm.com\/"},{"issue":"7\u20138","key":"144_CR25","doi-asserted-by":"publisher","first-page":"1800077","DOI":"10.1002\/qute.201800077","volume":"2","author":"Z-A Jia","year":"2019","unstructured":"Jia Z-A, Yi B, Zhai R, Wu Y-C, Guo G-C, Guo G-P (2019) Quantum neural network states: A brief review of methods and applications. Adv Quantum Technol 2(7\u20138):1800077","journal-title":"Adv Quantum Technol"},{"key":"144_CR26","unstructured":"Kamaka BK (2020) Quantum transpiler optimization: On the development, implementation, and use of a Quantum Research testbed. https:\/\/scholar.afit.edu\/etd\/3590\/"},{"issue":"7671","key":"144_CR27","doi-asserted-by":"publisher","first-page":"242","DOI":"10.1038\/nature23879","volume":"549","author":"A Kandala","year":"2017","unstructured":"Kandala A, Mezzacapo A, Temme K, Takita M, Brink M, Chow JM, Gambetta JM (2017) Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671):242\u2013246","journal-title":"Nature"},{"key":"144_CR28","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.106.052424","volume":"106","author":"J Kim","year":"2022","unstructured":"Kim J, Oz Y (2022) Quantum energy landscape and circuit optimization. Phys Rev A 106:052424. https:\/\/doi.org\/10.1103\/PhysRevA.106.052424","journal-title":"Phys Rev A"},{"key":"144_CR29","doi-asserted-by":"publisher","unstructured":"Li, G., Ding, Y., Xie, Y.: Tackling the Qubit Mapping Problem for NISQ-Era Quantum Devices. arXiv e-prints, 1809\u201302573 (2018) https:\/\/doi.org\/10.48550\/arXiv.1809.02573, arXiv:1809.02573 [cs.ET]","DOI":"10.48550\/arXiv.1809.02573"},{"key":"144_CR30","doi-asserted-by":"publisher","unstructured":"Lucas A (2014) Ising formulations of many np problems. Front Phys 2. https:\/\/doi.org\/10.3389\/fphy.2014.00005","DOI":"10.3389\/fphy.2014.00005"},{"key":"144_CR31","doi-asserted-by":"publisher","first-page":"152","DOI":"10.1007\/11757375_14","volume-title":"Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems","author":"R Marinescu","year":"2006","unstructured":"Marinescu R, Dechter R (2006) And\/or branch-and-bound search for pure 0\/1 integer linear programming problems. In: Beck JC, Smith BM (eds) Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. Springer, Berlin, pp 152\u2013166"},{"key":"144_CR32","doi-asserted-by":"crossref","unstructured":"Markowitz H (1952) Portfolio selection. J Finance 7(1): 77\u201391. Accessed 2022-11-25","DOI":"10.1111\/j.1540-6261.1952.tb01525.x"},{"issue":"1","key":"144_CR33","doi-asserted-by":"publisher","first-page":"4812","DOI":"10.1038\/s41467-018-07090-4","volume":"9","author":"JR McClean","year":"2018","unstructured":"McClean JR, Boixo S, Smelyanskiy VN, Babbush R, Neven H (2018) Barren plateaus in quantum neural network training landscapes. Nat Commun 9(1):4812. https:\/\/doi.org\/10.1038\/s41467-018-07090-4","journal-title":"Nat Commun"},{"issue":"3","key":"144_CR34","doi-asserted-by":"publisher","DOI":"10.1063\/5.0077706","volume":"12","author":"T Miki","year":"2022","unstructured":"Miki T, Okita R, Shimada M, Tsukayama D, Shirakashi J-i (2022) Variational ansatz preparation to avoid cnot-gates on noisy quantum devices for combinatorial optimizations. AIP Adv 12(3):035247. https:\/\/doi.org\/10.1063\/5.0077706","journal-title":"AIP Adv"},{"issue":"3","key":"144_CR35","doi-asserted-by":"publisher","first-page":"1580","DOI":"10.1002\/wcms.1580","volume":"12","author":"M Motta","year":"2022","unstructured":"Motta M, Rice JE (2022) Emerging quantum computing algorithms for quantum chemistry. WIREs Comput Mol Sci 12(3):1580. https:\/\/doi.org\/10.1002\/wcms.1580","journal-title":"WIREs Comput Mol Sci"},{"key":"144_CR36","doi-asserted-by":"publisher","unstructured":"Murali P, Baker JM, Javadi-Abhari A, Chong FT, Martonosi M (2019) Noise-adaptive compiler mappings for noisy intermediate-scale quantum computers. In: Proceedings of the Twenty-Fourth International Conference on Architectural Support for Programming Languages and Operating Systems. ASPLOS 19. ACM, ??? . https:\/\/doi.org\/10.1145\/3297858.3304075","DOI":"10.1145\/3297858.3304075"},{"key":"144_CR37","doi-asserted-by":"publisher","unstructured":"Niu S-f, Wang G-x, Sun X-l (2008) A branch-and-bound algorithm for discrete multi-factor portfolio optimization model. J Shanghai Univ 12:26\u201330. https:\/\/doi.org\/10.1007\/s11741-008-0105-3","DOI":"10.1007\/s11741-008-0105-3"},{"key":"144_CR38","unstructured":"Optimizers\u2013IBM Quantum Documentation \u2014 qiskit.org. https:\/\/qiskit.org\/documentation\/stubs\/qiskit.algorithms.optimizers.html. [Accessed 15-01-2024]"},{"key":"144_CR39","first-page":"2825","volume":"12","author":"F Pedregosa","year":"2011","unstructured":"Pedregosa F, Varoquaux G, Gramfort A, Michel V, Thirion B, Grisel O, Blondel M, Prettenhofer P, Weiss R, Dubourg V, Vanderplas J, Passos A, Cournapeau D, Brucher M, Perrot M, Duchesnay E (2011) Scikit-learn: Machine learning in Python. J Mach Learn Res 12:2825\u20132830","journal-title":"J Mach Learn Res"},{"key":"144_CR40","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/TQE.2022.3184764","volume":"3","author":"E Pelofske","year":"2022","unstructured":"Pelofske E, Brtschi A, Eidenbenz S (2022) Quantum volume in practice: What users can expect from nisq devices. IEEE Trans Quantum Eng 3:1\u201319. https:\/\/doi.org\/10.1109\/TQE.2022.3184764","journal-title":"IEEE Trans Quantum Eng"},{"issue":"1","key":"144_CR41","doi-asserted-by":"publisher","first-page":"4213","DOI":"10.1038\/ncomms5213","volume":"5","author":"A Peruzzo","year":"2014","unstructured":"Peruzzo A, McClean J, Shadbolt P, Yung M-H, Zhou X-Q, Love PJ, Aspuru-Guzik A, O\u2019Brien JL (2014) A variational eigenvalue solver on a photonic quantum processor. Nat Commun 5(1):4213. https:\/\/doi.org\/10.1038\/ncomms5213","journal-title":"Nat Commun"},{"key":"144_CR42","unstructured":"Portfolio Optimization, Qiskit 0.26.2 documentation \u2014 qiskit.org. https:\/\/qiskit.org\/documentation\/stable\/0.26\/tutorials\/finance\/01_portfolio_optimization.html. [Accessed 15-01-2024]"},{"key":"144_CR43","doi-asserted-by":"publisher","unstructured":"Powell MJD (1994) In: Gomez S, Hennart J-P (eds.) A Direct Search Optimization Method That Models the Objective and Constraint Functions by Linear Interpolation, pp. 51\u201367. Springer, Dordrecht. https:\/\/doi.org\/10.1007\/978-94-015-8330-5_4","DOI":"10.1007\/978-94-015-8330-5_4"},{"key":"144_CR44","unstructured":"Quantum computing use cases are getting real-what you need to know \u2014 mckinsey.com. https:\/\/www.mckinsey.com\/capabilities\/mckinsey-digital\/our-insights\/quantum-computing-use-cases-are-getting-real-what-you-need-to-know. [Accessed 09-Mar-2023]"},{"key":"144_CR45","doi-asserted-by":"publisher","unstructured":"Saib W, Wallden P, Akhalwaya I (2021) The effect of noise on the performance of variational algorithms for quantum chemistry. In: 2021 IEEE International Conference on Quantum Computing and Engineering (QCE), pp. 42\u201353. https:\/\/doi.org\/10.1109\/QCE52317.2021.00020","DOI":"10.1109\/QCE52317.2021.00020"},{"issue":"4","key":"144_CR46","doi-asserted-by":"publisher","DOI":"10.1063\/1.5115814","volume":"6","author":"S Slussarenko","year":"2019","unstructured":"Slussarenko S, Pryde GJ (2019) Photonic quantum information processing: A concise review. Applied Phys Rev 6(4):041303. https:\/\/doi.org\/10.1063\/1.5115814","journal-title":"Applied Phys Rev"},{"issue":"12","key":"144_CR47","doi-asserted-by":"publisher","DOI":"10.1063\/1.5141835","volume":"152","author":"IO Sokolov","year":"2020","unstructured":"Sokolov IO, Barkoutsos PK, Ollitrault PJ, Greenberg D, Rice J, Pistoia M, Tavernelli I (2020) Quantum orbital-optimized unitary coupled cluster methods in the strongly correlated regime: Can quantum algorithms outperform their classical equivalents? J Chem Phys 152(12):124107","journal-title":"J Chem Phys"},{"key":"144_CR48","doi-asserted-by":"publisher","unstructured":"Tilly J, Chen H, Cao S, Picozzi D, Setia K, Li Y, Grant E, Wossnig L, Rungger I, Booth GH, Tennyson J (2022) The variational quantum eigensolver: A review of methods and best practices. Phys Rep 986, 1\u2013128. https:\/\/doi.org\/10.1016\/j.physrep.2022.08.003 . The Variational Quantum Eigensolver: a review of methods and best practices","DOI":"10.1016\/j.physrep.2022.08.003"},{"key":"144_CR49","unstructured":"Transpiler \u2013 IBM Quantum Documentation \u2014 docs.quantum.ibm.com. https:\/\/docs.quantum.ibm.com\/api\/qiskit\/transpiler. [Accessed 15-01-2024]"},{"key":"144_CR50","unstructured":"Transpiler (qiskit.transpiler). https:\/\/qiskit.org\/documentation\/apidoc\/transpiler.html"},{"key":"144_CR51","doi-asserted-by":"publisher","unstructured":"Tuysuz C, Clemente G, Crippa A, Hartung T, Kuhn S, Jansen K (2022) Classical Splitting of Parametrized Quantum Circuits. arXiv e-prints, 2206\u201309641. https:\/\/doi.org\/10.48550\/arXiv.2206.09641, arXiv:2206.09641 [quant-ph]","DOI":"10.48550\/arXiv.2206.09641"},{"issue":"1","key":"144_CR52","doi-asserted-by":"publisher","first-page":"6961","DOI":"10.1038\/s41467-021-27045-6","volume":"12","author":"S Wang","year":"2021","unstructured":"Wang S, Fontana E, Cerezo M, Sharma K, Sone A, Cincio L, Coles PJ (2021) Noise-induced barren plateaus in variational quantum algorithms. Nature Communications. 12(1):6961. https:\/\/doi.org\/10.1038\/s41467-021-27045-6","journal-title":"Nature Communications."},{"key":"144_CR53","doi-asserted-by":"publisher","unstructured":"Wierichs, D., Izaac, J., Wang, C., Lin, C.Y.-Y.: General parameter-shift rules for quantum gradients. Quantum 6:677 (2022) https:\/\/doi.org\/10.22331\/q-2022-03-30-677","DOI":"10.22331\/q-2022-03-30-677"},{"key":"144_CR54","unstructured":"Yahoo Finanza - Mercato azionario in tempo reale, quotazioni e notizie di economia e finanza \u2014 it.finance.yahoo.com. https:\/\/it.finance.yahoo.com\/?guccounter=1&guce_referrer=aHR0cHM6Ly93d3cuZ29vZ2xlLmNvbS8&guce_referrer_sig=AQAAAIHdcyeGT4HED4q_5ThVGfe8xfcUwEGfx2gqSvUGHTaH-eGpoUdnNhin27d1jA6rGEe7tq2HLkwDdzJN7rh8yAsN4V07R4Suk7Jv91ApJ5ksWOqS1mTGP_8bxMwYpseCrAjhkJkGqCItNVrKgvm2JjfGTIa8MbAwEQ7fZDzHlkFe. [Accessed 15-01-2024]"},{"key":"144_CR55","doi-asserted-by":"publisher","unstructured":"Younis E, Iancu C (2022) Quantum Circuit Optimization and Transpilation via Parameterized Circuit Instantiation. arXiv e-prints, 2206\u201307885. https:\/\/doi.org\/10.48550\/arXiv.2206.07885. [quant-ph]","DOI":"10.48550\/arXiv.2206.07885"},{"key":"144_CR56","doi-asserted-by":"crossref","unstructured":"Zhang S-X, Hsieh C-Y, Zhang S, Yao H (2021) Neural predictor based quantum architecture search. arXiv:2103.06524","DOI":"10.1088\/2632-2153\/ac28dd"},{"key":"144_CR57","doi-asserted-by":"publisher","unstructured":"Zhao, R., Wang, S.: A review of Quantum Neural Networks: Methods, Models, Dilemma. arXiv e-prints, 2109\u201301840 (2021) https:\/\/doi.org\/10.48550\/arXiv.2109.01840, arXiv:2109.01840 [cs.ET]","DOI":"10.48550\/arXiv.2109.01840"},{"issue":"1","key":"144_CR58","doi-asserted-by":"publisher","first-page":"60","DOI":"10.1038\/s41534-023-00730-8","volume":"9","author":"L Zhao","year":"2023","unstructured":"Zhao L, Goings J, Shin K, Kyoung W, Fuks JI, Kevin Rhee J-K, Rhee YM, Wright K, Nguyen J, Kim J, Johri S (2023) Orbital-optimized pair-correlated electron simulations on trapped-ion quantum computers. Npj Quantum Inf 9(1):60. https:\/\/doi.org\/10.1038\/s41534-023-00730-8","journal-title":"Npj Quantum Inf"},{"key":"144_CR59","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.10.021067","volume":"10","author":"L Zhou","year":"2020","unstructured":"Zhou L, Wang S-T, Choi S, Pichler H, Lukin MD (2020) Quantum approximate optimization algorithm: Performance, mechanism, and implementation on near-term devices. Phys. Rev. X. 10:021067. https:\/\/doi.org\/10.1103\/PhysRevX.10.021067","journal-title":"Phys. Rev. X."}],"container-title":["Quantum Machine Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s42484-024-00144-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s42484-024-00144-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s42484-024-00144-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,24]],"date-time":"2024-06-24T16:20:42Z","timestamp":1719246042000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s42484-024-00144-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,2,5]]},"references-count":59,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,6]]}},"alternative-id":["144"],"URL":"https:\/\/doi.org\/10.1007\/s42484-024-00144-5","relation":{},"ISSN":["2524-4906","2524-4914"],"issn-type":[{"value":"2524-4906","type":"print"},{"value":"2524-4914","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,2,5]]},"assertion":[{"value":"21 May 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 January 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 February 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"9"}}