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  • Letter
  • Open Access

Entanglement – nonstabilizerness separation in hybrid quantum circuits

Gerald E. Fux1, Emanuele Tirrito1,2, Marcello Dalmonte1,3, and Rosario Fazio1,4

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Phys. Rev. Research 6, L042030 – Published 30 October, 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.L042030

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.

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Phys. Rev. Research 6, L042030– Published 30 October, 2024
  • Received 9 December 2023
  • Accepted 17 September 2024
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