Efficient mutual magic and magic capacity with matrix product states
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arXiv
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| Natura: | Preprint |
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2025
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| _version_ | 1866908579442720768 |
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| author | Tarabunga, Poetri Sonya Haug, Tobias |
| author_facet | Tarabunga, Poetri Sonya Haug, Tobias |
| contents | Stabilizer Rényi 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 $O(Nχ^3)$ for matrix product states (MPSs) of bond dimension $χ$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_07230 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Efficient mutual magic and magic capacity with matrix product states Tarabunga, Poetri Sonya Haug, Tobias Quantum Physics Statistical Mechanics Strongly Correlated Electrons Stabilizer Rényi 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 $O(Nχ^3)$ for matrix product states (MPSs) of bond dimension $χ$. 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. |
| title | Efficient mutual magic and magic capacity with matrix product states |
| topic | Quantum Physics Statistical Mechanics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2504.07230 |