Quantum resources have played a crucial role in our understanding of many-body systems over the past two decades. While entanglement has been extensively studied, the role of other quantum resources—such as magic, which is essential for quantum computational advantage—remains less explored. Understanding the emergence and dynamics of magic is key to advancing quantum simulators and quantum computing architectures.

 

In this talk, I will show how magic serves as a fundamental bridge between quantum information theory and many-body physics. I will begin by reviewing stabilizer Rényi entropies as a powerful measure of magic and its utility in characterizing complex quantum states. Building on this framework, I will explore three key aspects of magic in many-body systems:

 

(a) Magic Growth in Many-Body Dynamics: I will discuss how generic many-body evolution— whether governed by random circuits or Hamiltonian dynamics—rapidly generates magic, highlighting its connections to thermalization and quantum chaos [1-2].

 

(b) Classical Simulability of Quantum Many-Body Systems: I will examine the feasibility of classical simulations that leverage tensor network methods and the stabilizer formalism. Specifically, I will show that Pauli expectation values can be efficiently computed even for deep Clifford circuits doped with T-gates or general phase gates, provided the number of non-Clifford

operations remains comparable to the system size [3].

 

(c) Complexity Transitions in Monitored Quantum Circuits: I will present recent insights into complexity transitions in monitored quantum dynamics, where measurement-induced phase transitions sharply delineate regimes of classical simulability and quantum advantage [4-5].

 

I will conclude by discussing experimental implications, outlining potential avenues for realizing these phenomena in near-term quantum devices, and addressing the challenges in probing and controlling magic in many-body settings.

 

[1] X. Turkeshi, E. Tirrito, P. Sierant, Magic spreading in random quantum circuits arXiv:2407.03929 (2024)

[2] E. Tirrito, X. Turkeshi, P. Sierant, Anticoncentration and magic spreading under ergodic quantum dynamics, arXiv:2412.10229

[3] G. Fux, B. Beri, R. Fazio, E. Tirrito, Disentangling unitary dynamics with classically simulable quantum circuits, arXiv:2410.09001

[4] G. Fux, E. Tirrito, M. Dalmonte, R. Fazio, Measurement-induced phase transition in magic Phys. Rev. Research 6, L042030 (2024)

[5] P.S. Tarabunga, E. Tirrito, Magic transition in measurement-only circuits arXiv:2407.15939