{
  "id": "1804.05356",
  "version": "v1",
  "published": "2018-04-15T13:18:13.000Z",
  "updated": "2018-04-15T13:18:13.000Z",
  "title": "ZX-Rules for 2-qubit Clifford+T Quantum Circuits",
  "authors": [
    "Bob Coecke",
    "Quanlong Wang"
  ],
  "comment": "16+4 pages",
  "categories": [
    "quant-ph",
    "math.CT"
  ],
  "abstract": "ZX-calculus is a high-level graphical formalism for qubit computation. In this paper we give the ZX-rules that enable one to derive all equations between 2-qubit Clifford+T quantum circuits. Our rule set is only a small extension of the rules of stabilizer ZX-calculus, and substantially less than those needed for the recently achieved universal completeness. One of our rules is new, and we expect it to also have other utilities. These ZX-rules are much simpler than the complete of set Clifford+T circuit equations due to Selinger and Bian, which indicates that ZX-calculus provides a more convenient arena for quantum circuit rewriting than restricting oneself to circuit equations. The reason for this is that ZX-calculus is not constrained by a fixed unitary gate set for performing intermediate computations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-15T13:18:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum circuit",
      "circuit equations",
      "fixed unitary gate set",
      "high-level graphical formalism",
      "rule set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}