131886 20241125101139.0 doi 10.21468/SciPostPhys.15.5.186 sideral 137069 ART-2023-137069 eng Roca-Jerat, Sebastián Circuit Complexity through phase transitions: Consequences in quantum state preparation 2023 Access copy available to the general public Unrestricted In this paper, we analyze the circuit complexity for preparing ground states of quantum many-body systems. In particular, how this complexity grows as the ground state approaches a quantum phase transition. We discuss different definitions of complexity, namely the one following the Fubini-Study metric or the Nielsen complexity. We also explore different models: Ising, ZZXZ or Dicke. In addition, different forms of state preparation are investigated: analytic or exact diagonalization techniques, adiabatic algorithms (with and without shortcuts), and Quantum Variational Eigensolvers. We find that the divergence (or lack thereof) of the complexity near a phase transition depends on the non-local character of the operations used to reach the ground state. For Fubini-Study based complexity, we extract the universal properties and their critical exponents. In practical algorithms, we find that the complexity depends crucially on whether or not the system passes close to a quantum critical point when preparing the state. For both VQE and Adiabatic algorithms, we provide explicit expressions and bound the growth of complexity with respect to the system size and the execution time, respectively. info:eu-repo/semantics/openAccess by http://creativecommons.org/licenses/by/3.0/es/ 4.6 2023 PHYSICS, MULTIDISCIPLINARY 21 / 112 = 0.188 2023 Q1 T1 1.623 2023 Physics and Astronomy (miscellaneous) 2023 Q1 8.2 2023 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Sancho-Lorente, Teresa Román-Roche, Juan (orcid)0000-0003-2995-6615 Zueco, David (orcid)0000-0003-4478-1948 15, 5 (2023), [30 pp.] SciPost physics 2542-4653 570027 http://zaguan.unizar.es/record/131886/files/texto_completo.pdf Versión publicada 2049948 http://zaguan.unizar.es/record/131886/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:131886 articulos driver 2024-11-22-12:01:54 ARTICLE