{
  "id": "2307.01696",
  "version": "v1",
  "published": "2023-07-04T13:05:29.000Z",
  "updated": "2023-07-04T13:05:29.000Z",
  "title": "Preparation of matrix product states with log-depth quantum circuits",
  "authors": [
    "Daniel Malz",
    "Georgios Styliaris",
    "Zhi-Yuan Wei",
    "J. Ignacio Cirac"
  ],
  "categories": [
    "quant-ph",
    "cond-mat.stat-mech",
    "cond-mat.str-el"
  ],
  "abstract": "We consider preparation of matrix product states (MPS) via quantum circuits of local gates. We first prove that faithfully preparing translation-invariant normal MPS of $N$ sites requires a circuit depth $T=\\Omega(\\log N)$. We then introduce an algorithm based on the renormalization-group transformation to prepare normal MPS with an error $\\epsilon$ in depth $T=O(\\log (N/\\epsilon))$, which is optimal. We also show that measurement and feedback leads to an exponential speed-up of the algorithm, to $T=O(\\log\\log (N/\\epsilon))$. Measurements also allow one to prepare arbitrary translation-invariant MPS, including long-range non-normal ones, in the same depth. Finally, the algorithm naturally extends to inhomogeneous MPS.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-04T13:05:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "matrix product states",
      "log-depth quantum circuits",
      "preparing translation-invariant normal mps",
      "preparation",
      "prepare arbitrary translation-invariant mps"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}