Quantum magic dynamics in random circuits
- 1Department of Physics, University of California, Santa Barbara, CA, USA
- 2Institute for Advanced Study, Tsinghua University, Beijing, China
Abstract
Magic refers to the degree of “quantumness” in a system that cannot be fully described by stabilizer states and Clifford operations alone. In quantum computing, stabilizer states and Clifford operations can be efficiently simulated on a classical computer, even though they may appear complicated from the perspective of entanglement. In this sense, magic is a crucial resource for unlocking the unique computational power of quantum computers to address problems that are classically intractable. Magic can be quantified by measures such as Wigner negativity and mana that satisfy fundamental properties such as monotonicity under Clifford operations. In this paper, we generalize the statistical mechanical mapping methods of large- q random circuits to the calculation of Rényi Wigner negativity and mana. Based on this, we find: (1) a precise formula describing the competition between magic and entanglement in many-body states prepared under Haar random circuits; (2) a formula describing the spreading and scrambling of magic in states evolved under random Clifford circuits; (3) a quantitative description of magic “squeezing” and “teleportation” under measurements. Finally, we comment on the relation between coherent information and magic.
Related
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- Complex Quantum Dynamics Versus Classical Simulability of Noisy Random Circuits
- Random quantum circuits, chaos and quantum thermalization
- Rare-History Transitions in Temporally Random Integrable Quantum Circuits
- One Gate at a Time: Complexity Growth in Random Quantum Circuits
BibTeX
@article{zhang2026quantum,
title = {{Quantum magic dynamics in random circuits}},
author = {Yuzhen Zhang and Yingfei Gu},
journal = {npj Quantum Information},
year = {2026},
month = may,
doi = {10.1038/s41534-026-01253-8},
url = {https://doi.org/10.1038/s41534-026-01253-8},
note = {CC BY-NC-ND},
}
RIS
TY - JOUR
TI - Quantum magic dynamics in random circuits
AU - Yuzhen Zhang
AU - Yingfei Gu
PY - 2026
DA - 2026/05/14
JO - npj Quantum Information
DO - 10.1038/s41534-026-01253-8
UR - https://doi.org/10.1038/s41534-026-01253-8
AB - Magic refers to the degree of “quantumness” in a system that cannot be fully described by stabilizer states and Clifford operations alone. In quantum computing, stabilizer states and Clifford operations can be efficiently simulated on a classical computer, even though they may appear complicated from the perspective of entanglement. In this sense, magic is a crucial resource for unlocking the unique computational power of quantum computers to address problems that are classically intractable. Magic can be quantified by measures such as Wigner negativity and mana that satisfy fundamental properties such as monotonicity under Clifford operations. In this paper, we generalize the statistical mechanical mapping methods of large- q random circuits to the calculation of Rényi Wigner negativity and mana. Based on this, we find: (1) a precise formula describing the competition between magic and entanglement in many-body states prepared under Haar random circuits; (2) a formula describing the spreading and scrambling of magic in states evolved under random Clifford circuits; (3) a quantitative description of magic “squeezing” and “teleportation” under measurements. Finally, we comment on the relation between coherent information and magic.
SN - 2056-6387
ER -