Magic transition in measurement-only circuits

Year: 2025

Authors: Tarabunga PS., Tirrito E.

Autors Affiliation: Int Sch Adv Studies SISSA, Trieste, Italy; Abdus Salam Int Ctr Theoret Phys ICTP, Trieste, Italy; INFN, Sez Trieste, Trieste, Italy; Univ Trento, Pitaevskii BEC Ctr, CNR INO, Trento, Italy; Univ Trento, Dipartimento Fis, Trento, Italy.

Abstract: Magic, or nonstabilizerness, quantifies the distance of a quantum state from stabilizer states and serves as a resource for quantum computational advantage. Here, we investigate magic transitions in measurement-only quantum circuits comprising competing Clifford and non-Clifford measurements. Remarkably, this circuit can be mapped onto a classical model, enabling efficient large-scale numerical simulations and exact characterization of magic using measures that are additive for tensor products of single-qubit states. We identify a magic transition between two phases exhibiting extensive magic, separated by a critical point where mutual magic displays scaling analogous to entanglement entropy. Additionally, these distinct phases can be distinguished by topological magic. In contrast, with a vanishing rate of non-Clifford measurements, the system exhibits saturation of magic. Our results clarify the nature of magic and its linear combinations in quantum circuits utilizing genuine magic measures, thereby advancing our understanding of quantum complexity in monitored quantum systems.

Journal/Review: NPJ QUANTUM INFORMATION

Volume: 11 (1)      Pages from: 166-1  to: 166-10

More Information: We thank M. Dalmonte, M. Frau, L. Piroli, T. Haug, R. Fazio, X. Turkeshi, and G. Fux for collaboration on related topics. P. S. T. acknowledges support from the Simons Foundation through Award 284558FY19 to the ICTP. E. T. was partly supported by QUANTERA DYNAMITE PCI2022-132919, and by ERC under grant agreement n.101053159 (RAVE). E.T. acknowledges CINECA (Consorzio Interuniversitario per il Calcolo Automatico) award, under the ISCRA initiative and Leonardo early access program, for the availability of high-performance computing resources and support.
KeyWords: Quantum; Entanglement
DOI: 10.1038/s41534-025-01104-y