Entanglement – nonstabilizerness separation in hybrid quantum circuits

Year: 2024

Authors: Fux G.E., Tirrito E., Dalmonte M., Fazio R.

Autors Affiliation: Abdus Salam Int Ctr Theoret Phys ICTP, Str Costiera 11, I-34151 Trieste, Italy; Univ Trento, Pitaevskii BEC Ctr, INO, CNR, Via Sommarive 14, I-38123 Trento, Italy; Univ Trento, Dipartimento Fis, Via Sommar 14, I-38123 Trento, Italy; Scuola Int Super Avanzati SISSA, Via Bonomea 265, I-34136 Trieste, Italy; Univ Napoli Federico II, Dipartimento Fis E Pancini, I-80126 Naples, Italy.

Abstract: Nonstabilizerness describes the distance of a quantum state to its closest stabilizer state. It is-like entanglement-a necessary resource for a quantum advantage over classical computing. We study nonstabilizerness, quantified by stabilizer entropy, in a hybrid quantum circuit with projective measurements and a controlled injection of non-Clifford resources. We discover a phase transition between a power law and constant scaling of nonstabilizerness with system size controlled by the rate of measurements. The same circuit also exhibits a phase transition in entanglement that appears, however, at a different critical measurement rate. This mechanism shows how, from the viewpoint of a quantum advantage, hybrid circuits can host multiple distinct transitions where not only entanglement, but also other nonlinear properties of the density matrix come into play.

Journal/Review: PHYSICAL REVIEW RESEARCH

Volume: 6 (4)      Pages from: L042030-1  to: L042030-6

More Information: We thank L. Piroli, X. Turkeshi, C. White, and B. Beri for helpful comments on the manuscript. Also, we thank T. Chanda, M. Collura, P. Sierant, P. Tarabunga, and X. Turkeshi for many insightful discussions. G.E.F. and R.F. acknowledge support from ERC under Grant Agreement No. 101053159 (RAVE) . 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. and R.F. were partly supported by the PNRR MUR project PE0000023-NQSTI. The work of M.D. and R.F. was in part supported by the International Centre for Theoretical Sciences (ICTS) for participating in the following program: Periodicallyr by the International Centre for Theoretical Sciences (ICTS) for participating in the following program: Periodically
KeyWords: Nonlinear optics; Quantum computers; Quantum electronics; Quantum optics
DOI: 10.1103/PhysRevResearch.6.L042030