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arXiv · 2312.02039

Entanglement-magic separation in hybrid quantum circuits

Gerald E. Fux·Emanuele Tirrito·Marcello Dalmonte·Rosario Fazio
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Abstract

Magic describes the distance of a quantum state to its closest stabilizer state. It is -- like entanglement -- a necessary resource for a potential quantum advantage over classical computing. We study magic, 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 (sub)-extensive and area law scaling of magic 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 potential quantum advantage, hybrid circuits can host multiple distinct transitions where not only entanglement, but also other non-linear properties of the density matrix come into play.

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Gerald E. Fux, Emanuele Tirrito, Marcello Dalmonte, Rosario Fazio. 2023-12-04. Entanglement-magic separation in hybrid quantum circuits. https://doi.org/10.1103/physrevresearch.6.l042030

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