Efficient mutual magic and magic capacity with matrix product states

• URL: http://arxiv.org/abs/2504.07230v1
• Date: Wed, 09 Apr 2025 19:12:26 GMT
• Title: Efficient mutual magic and magic capacity with matrix product states
• Authors: Poetri Sonya Tarabunga, Tobias Haug,
• Abstract summary: We introduce the mutual von-Neumann SRE and magic capacity, which can be efficiently computed in time.<n>We find that mutual SRE characterizes the critical point of ground states of the transverse-field Ising model.<n>The magic capacity characterizes transitions in the ground state of the Heisenberg and Ising model, randomness of Clifford+T circuits, and distinguishes typical and atypical states.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Stabilizer R\'enyi entropies (SREs) probe the non-stabilizerness (or magic) of many-body systems and quantum computers. Here, we introduce the mutual von-Neumann SRE and magic capacity, which can be efficiently computed in time $O(N\chi^3)$ for matrix product states (MPSs) of bond dimension $\chi$. We find that mutual SRE characterizes the critical point of ground states of the transverse-field Ising model, independently of the chosen local basis. Then, we relate the magic capacity to the anti-flatness of the Pauli spectrum, which quantifies the complexity of computing SREs. The magic capacity characterizes transitions in the ground state of the Heisenberg and Ising model, randomness of Clifford+T circuits, and distinguishes typical and atypical states. Finally, we make progress on numerical techniques: we design two improved Monte-Carlo algorithms to compute the mutual $2$-SRE, overcoming limitations of previous approaches based on local update. We also give improved statevector simulation methods for Bell sampling and SREs with $O(8^{N/2})$ time and $O(2^N)$ memory, which we demonstrate for $24$ qubits. Our work uncovers improved approaches to study the complexity of quantum many-body systems.

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