Many-Body Magic Via Pauli-Markov Chains-From Criticality to Gauge Theories

Year: 2023

Authors: Tarabunga PS., Tirrito E., Chanda T., Dalmonte M.

Autors Affiliation: Abdus Salam Int Ctr Theoret Phys ICTP, Str Costiera 11, I-34151 Trieste, Italy; SISSA, Via Bonomea 265, I-34136 Trieste, 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, I-38123 Trento, Italy; Indian Inst Technol Indore, Dept Phys, Khandwa Rd, Indore 453552, India.

Abstract: We introduce a method to measure many-body magic in quantum systems based on a statistical exploration of Pauli strings via Markov chains. We demonstrate that sampling such Pauli-Markov chains gives ample flexibility in terms of partitions where to sample from: in particular, it enables the efficient extraction of the magic contained in the correlations between widely separated subsystems, which characterizes the nonlocality of magic. Our method can be implemented in a variety of situations. We describe an efficient sampling procedure using tree tensor networks, that exploit their hierarchical structure leading to a modest O(log N) computational scaling with system size. To showcase the applicability and efficiency of our method, we demonstrate the importance of magic in many-body systems via the following discoveries: (a) for one-dimensional systems, we show that long-range magic displays strong signatures of conformal quantum criticality (Ising, Potts, and Gaussian), overcoming the limitations of full state magic; (b) in two-dimensional Z2 lattice gauge theories, we provide conclusive evidence that magic is able to identify the confinement-deconfinement transition, and displays critical scaling behavior even at relatively modest volumes. Finally, we discuss an experimental implementation of the method, which relies only on measurements of Pauli observables.

Journal/Review: PRX QUANTUM

Volume: 4 (4)      Pages from: 40317-1  to: 40317-19

More Information: We are indebted to M. Collura, A. Hamma, G. Lami, L. Leone, and S.F.E. Oliviero for fruitful discussions and collaborations on related topics. We thank G. Magnifico, S. Montangero, S. Notarnicola, and P. Silvi for discussions on tree tensor networks. We thank L. Piroli and C. Castelnovo for comments on the manuscript. P.S.T. acknowledges support from the Simons Foundation through Award No. 284558FY19 to the ICTP. M.D. and E.T. acknowledge support from the MIUR Programme FARE (MEPH), and from QUANTERA DYNAMITE PCI2022-132919. M.D.’s work was also supported by the PNRR MUR Project PE0000023-NQSTI, and by the EU-Fla gship programme Pasquans2. E.T. is also funded by the European Union under Horizon Europe Programme-Grant Agreement No. 101080086-NeQST. Our TTN codes have been implemented using C++ Itensor library [110].
KeyWords: Mutual Information; Quantum; Entanglement; Efficient; Entropy; State
DOI: 10.1103/PRXQuantum.4.040317

Citations: 13
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