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operations needed to prepare quantum states. It is a

crucial resource for quantum computing and a necessary condition for

quantum advantage.

However, our understanding of magic had been limited to a few qubits due

to a lack of efficient methods to study magic.

Recently, we established efficient methods to compute magic for quantum

computers [1,2] and matrix product states [3,4].This way, we explore the

magic of quantum computers, and determine its fundamental limits for

highly mixed states.

Further, we study the magic of critical many-body systems, as well as

uncover the universal behavior of magic in dynamical systems.

Finally, we discuss how to combine Clifford circuits and matrix product

states to simulate volume-law entanglement and magic at the same time.

Our works provide a powerful tool to probe the computational complexity

of quantum many-body systems.

[1] T. Haug, M.S. Kim, PRX Quantum 4 (2023)

[2] T. Haug, S. Lee, M.S. Kim, Phys. Rev. Lett. 132 (2024)

[3] T. Haug, L. Piroli, Phys. Rev. B 107 (2023)

[4] T. Haug, L. Piroli, Quantum 7 (2023)