SciPost Submission Page
Efficient mutual magic and magic capacity with matrix product states
by Poetri Sonya Tarabunga, Tobias Haug
Submission summary
| Authors (as registered SciPost users): | Poetri Sonya Tarabunga |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2504.07230v3 (pdf) |
| Date accepted: | Sept. 10, 2025 |
| Date submitted: | Aug. 15, 2025, 12:17 p.m. |
| Submitted by: | Poetri Sonya Tarabunga |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
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.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
Thank you for managing our submission, and for informing us about the reports provided by the Referees. We appreciated the Referees' comments on our work. We have improved the manuscript according to their comments. We hope that our revised manuscript is suitable for publication in SciPost Physics.
Yours sincerely,
Poetri Sonya Tarabunga and Tobias Haug
List of changes
is now introduced in Sec. II.
• Added Fig.S5 and Fig.S6d to demonstrate determining the critical field of the transverse-
field Ising model
• Added Appendix G to explain fitting procedure for determining critical field
• Expanded Fig.2 into Fig.2 and Fig.3, with more samples to reduce noise, as well as in-
depth study of universal behavior of the C_M and m_1.
• Added new Appendix A to provide proof of marginals for probability distribution $q_\rho$
Published as SciPost Phys. 19, 085 (2025)