Nonstabilizerness in U(1) lattice gauge theory
Year: 2025
Authors: Falcao P.R.N., Tarabunga P.S., Frau M., Tirrito E., Zakrzewski J., Dalmonte M.
Autors Affiliation: Uniwersytet Jagiellonski, Szkola Doktorska Nauk Scislych & Przyrodniczych, Lojasiewicza 11, PL-30348 Krakow, Poland; Uniwersytet Jagiellonski, Inst Fizyki Teoretycznej, Wydzial Fizyki Astronomii & Informatyki Stosowanej, Lojasiewicza 11, PL-30348 Krakow, Poland; Abdus Salam Int Ctr Theoret Phys ICTP, Str Costiera 11, I-34151 Trieste, Italy; Int Sch Adv Studies SISSA, Via Bonomea 265, I-34136 Trieste, Italy; INFN, Sez Trieste, via Valerio 2, I-34127 Trieste, Italy; CNR, INO, Pitaevskii BEC Ctr, Via Sommar 14, I-38123 Trento, Italy; Univ Trento, Dipartimento Fis, Via Sommar 14, I-38123 Trento, Italy; Uniwersytet Jagiellonski, Mark Kac Complex Syst Res Ctr, Krakow, Poland.
Abstract: We present a thorough investigation of nonstabilizerness-a fundamental quantum resource that quantifies state complexity within the framework of quantum computing-in a one-dimensional U(1) lattice gauge theory including matter fields. We show how nonstabilizerness is always extensive with volume, and has no direct relation to the presence of critical points. However, its derivatives typically display discontinuities across the latter: This indicates that nonstabilizerness is strongly sensitive to criticality, but in a manner that is very different from entanglement (which, typically, is maximal at the critical point). Our results indicate that error-corrected simulations of lattice gauge theories close to the continuum limit have similar computational costs to those at finite correlation length and provide rigorous lower bounds for quantum resources of such quantum computations.
Journal/Review: PHYSICAL REVIEW B
Volume: 111 (8) Pages from: L081102-1 to: L081102-7
More Information: We thank M. Collura, T. Haug, and P. Hauke for discussions, and A. Paviglianiti for comments on the manuscript. P.R.N.F. thanks A. S. Aramthottil and Konrad Pawlik for valuable discussion on the numerics. Discussions with B. Damski are also appreciated (J.Z.). E.T. acknowledges J. Mildenberger, G. Chandra Santra, and R. Costa de Almeida for insightful discussions. We acknowledge Polish high-performance computing infrastructure PLGrid for awarding this project access to the LUMI supercomputer, owned by the EuroHPC Joint Undertaking, hosted by CSC (Finland) and the LUMI consortium through Grant No. PLL/2023/04/016502. The work of P.R.N.F. and that of J.Z. were funded by the National Science Centre, Poland, Project No. 2021/03/Y/ST2/00186 within the QuantERA II Programme (DYNAMITE) that has received funding from the European Union Horizon 2020 research and innovation program under Grant Agreement No. 101017733. The study was also partially funded by the Research Support Module as part of the Excellence Initiative-Research University program at the Jagiellonian University in Krakow. M.D. and E.T. were partly supported by the QUANTERA DYNAMITE PCI2022-132919. M.D. was also supported by the EU-Flagship program Pasquans2, by PNRR MUR Project No. PE0000023-NQSTI, the PRIN program (project CoQuS), and the ERC Consolidator grant WaveNets. P.S.T. acknowledges support from the Simons Foundation through Award No. 284558FY19 to the ICTP.KeyWords: Quantum; Invariance; Dynamics; ModelsDOI: 10.1103/PhysRevB.111.L081102
