000117251 001__ 117251 000117251 005__ 20240319080959.0 000117251 0247_ $$2doi$$a10.1103/PhysRevA.105.042432 000117251 0248_ $$2sideral$$a128753 000117251 037__ $$aART-2022-128753 000117251 041__ $$aeng 000117251 100__ $$aSancho-Lorente, T. 000117251 245__ $$aQuantum kernels to learn the phases of quantum matter 000117251 260__ $$c2022 000117251 5060_ $$aAccess copy available to the general public$$fUnrestricted 000117251 5203_ $$aClassical machine learning has succeeded in the prediction of both classical and quantum phases of matter. Notably, kernel methods stand out for their ability to provide interpretable results, relating the learning process with the physical order parameter explicitly. Here we exploit quantum kernels instead. They are naturally related to the fidelity, and thus it is possible to interpret the learning process with the help of quantum information tools. In particular, we use a support vector machine (with a quantum kernel) to predict and characterize second-order quantum phase transitions. We explain and understand the process of learning when the fidelity per site (rather than the fidelity) is used. The general theory is tested in the Ising chain in transverse field. We show that for small-sized systems, the algorithm gives accurate results, even when trained away from criticality. Besides, for larger sizes we confirm the success of the technique by extracting the correct critical exponent ¿. Finally, we present two algorithms, one based on fidelity and one based on the fidelity per site, to classify the phases of matter in a quantum processor. 000117251 536__ $$9info:eu-repo/grantAgreement/ES/CSIC/PTI-001$$9info:eu-repo/grantAgreement/ES/DGA/E09-17R-Q-MAD$$9info:eu-repo/grantAgreement/EC/H2020/862893/EU/Molecular spin qudits offering new hope for quantum computing/FATMOLS$$9This project has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No H2020 862893-FATMOLS$$9info:eu-repo/grantAgreement/ES/MICINN/PID2020-115221GBC41/AEI/10.13039/501100011033$$9info:eu-repo/grantAgreement/EUR/MOLSPIN-COST/CA15128$$9info:eu-repo/grantAgreement/EUR/QUANTERA/SUMO 000117251 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/ 000117251 590__ $$a2.9$$b2022 000117251 592__ $$a1.11$$b2022 000117251 591__ $$aPHYSICS, ATOMIC, MOLECULAR & CHEMICAL$$b12 / 35 = 0.343$$c2022$$dQ2$$eT2 000117251 593__ $$aAtomic and Molecular Physics, and Optics$$c2022$$dQ1 000117251 591__ $$aOPTICS$$b44 / 99 = 0.444$$c2022$$dQ2$$eT2 000117251 594__ $$a5.4$$b2022 000117251 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000117251 700__ $$0(orcid)0000-0003-2995-6615$$aRoman Roche, J. 000117251 700__ $$0(orcid)0000-0003-4478-1948$$aZueco, D. 000117251 773__ $$g105, 4 (2022), 042432 [9 pp.]$$pPhys. rev., A$$tPhysical Review A$$x2469-9926 000117251 8564_ $$s673949$$uhttps://zaguan.unizar.es/record/117251/files/texto_completo.pdf$$yVersión publicada 000117251 8564_ $$s2874389$$uhttps://zaguan.unizar.es/record/117251/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000117251 909CO $$ooai:zaguan.unizar.es:117251$$particulos$$pdriver 000117251 951__ $$a2024-03-18-13:59:27 000117251 980__ $$aARTICLE