{
  "id": "2504.07230",
  "version": "v2",
  "published": "2025-04-09T19:12:26.000Z",
  "updated": "2025-05-04T21:54:04.000Z",
  "title": "Efficient mutual magic and magic capacity with matrix product states",
  "authors": [
    "Poetri Sonya Tarabunga",
    "Tobias Haug"
  ],
  "comment": "11+8 pages, 5+8 figures",
  "categories": [
    "quant-ph",
    "cond-mat.stat-mech",
    "cond-mat.str-el"
  ],
  "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.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2025-05-04T21:54:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "matrix product states",
      "efficient mutual magic",
      "ground state",
      "magic capacity characterizes transitions",
      "quantum many-body systems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}