{
  "id": "1908.07958",
  "version": "v1",
  "published": "2019-08-21T16:05:12.000Z",
  "updated": "2019-08-21T16:05:12.000Z",
  "title": "Efficient Encoding of Matrix Product States into Quantum Circuits of One- and Two-Qubit Gates",
  "authors": [
    "Shi-Ju Ran"
  ],
  "comment": "6 pages, 5 figures",
  "categories": [
    "quant-ph",
    "cond-mat.str-el"
  ],
  "abstract": "Matrix product state (MPS) belongs to the most important mathematical models in, for example, condensed matter physics and quantum information sciences. However, to realize an $N$-qubit MPS with large $N$ and large entanglement on a quantum platform is extremely challenging, since it requires high-level qudits or multi-body gates of two-level qubits to carry the entanglement. In this work, an efficient method that accurately encodes a given MPS into a quantum circuit with only one- and two-qubit gates is proposed. The idea is to construct the unitary matrix product operators that optimally disentangle the MPS to a product state. These matrix product operators form the quantum circuit that evolves a product state to the targeted MPS with a high fidelity. Our benchmark on the ground-state MPS's of the strongly-correlated spin models show that the constructed quantum circuits can encode the MPS's with much fewer qubits than the sizes of the MPS's themselves. This method paves a feasible and efficient path to realizing quantum many-body states and other MPS-based models as quantum circuits on the near-term quantum platforms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-21T16:05:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum circuit",
      "matrix product state",
      "two-qubit gates",
      "efficient encoding",
      "quantum platform"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}