Nonstabilizerness via Matrix Product States in the Pauli Basis

Year: 2024

Authors: Tarabunga PS., Tirrito E., Basuls MC., Dalmonte M.

Autors Affiliation: Abdus Salam Int Ctr Theoret Phys ICTP, Str Costiera 11, I-34151 Trieste, Italy; SISSA, Via Bonomea 265, Trieste 34136, Italy; INFN, Sez Trieste, via Valerio 2, I-34127 Trieste, Italy; Univ Trento, Pitaevskii BEC Ctr, CNR INO, Via Sommar 14, I-38123 Trento, Italy; Univ Trento, Dipartimento Fis, Via Sommar 14, Trento, Italy; Max Planck Inst Quantenoptik, Hans Kopfermann Str 1, D-85748 Garching, Germany; Munich Ctr Quantum Sci & Technol MCQST, Schellingstr 4, D-80799 Munich, Germany.

Abstract: Nonstabilizerness, also known as magic, stands as a crucial resource for achieving a potential advantage in quantum computing. Its connection to many-body physical phenomena is poorly understood at present, mostly due to a lack of practical methods to compute it at large scales. We present a novel approach for the evaluation of nonstabilizerness within the framework of matrix product states (MPSs), based on expressing the MPS directly in the Pauli basis. Our framework provides a powerful tool for efficiently calculating various measures of nonstabilizerness, including stabilizer R & eacute;nyi entropies, stabilizer nullity, and Bell magic, and enables the learning of the stabilizer group of an MPS. We showcase the efficacy and versatility of our method in the ground states of Ising and XXZ spin chains, as well as in circuits dynamics that has recently been realized in Rydberg atom arrays, where we provide concrete benchmarks for future experiments on logical qubits up to twice the sizes already realized.

Journal/Review: PHYSICAL REVIEW LETTERS

Volume: 133 (1)      Pages from: 10601-1  to: 10601-7

More Information: We thank M. Collura, M. Frau, A. Hamma, G. Lami, M. Serbyn, and Guo-Yi Zhu for insightful discussions. We especially thank Lorenzo Piroli for pointing out the connection between the stabilizer nullity and the SRE. P. S. T. acknowledges support from the Simons Foundation through Award No. 284558FY19 to the ICTP. M. D. and E. T. were partly supported by the MIUR Programme FARE (MEPH) , by QUANTERA DYNAMITE PCI2022-132919, and by the EU-Flagship programme Pasquans2. M. D. was partly supported by the PNRR MUR Project No. PE0000023-NQSTI. The work of M. D. was in part supported by the International Centre for Theoretical Sciences (ICTS) for participating in the program Periodically and quasi-periodic ally driven com-plex systems (Code No. ICTS/pdcs2023/6) . M. C. B. was partly supported by the DFG (German Research Foundation) under Germany ’ s Excellence Strategy – EXC-2111 – 390814868, and by the EU-QUANTERA project TNiSQ (BA 6059/1-1) .
KeyWords: Renormalization-group; Quantum; Entanglement; Simulation
DOI: 10.1103/PhysRevLett.133.010601

Citations: 3
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