{
  "annotation_id": "d0ddb5cb-0a9d-498e-b814-70b6f5e04168",
  "date_created": "2026-02-17T05:53:19.907000Z",
  "date_modified": "2026-02-17T05:53:19.907000Z",
  "file_hash": "49d4524d48998db99fdb378d4e56ae2143ac7085fc2f3d1a9a21c7fc75b0bbf7",
  "private": false,
  "record": {
    "abstract": "The preparation of quantum states is one of the most fundamental tasks in quantum computing, and a key primitive in many quantum algorithms. Of particular interest to areas such as quantum simulation and linear-system solvers are sparse quantum states, which contain only a small number $s$ of non-zero computational basis states compared to a generic state. In this work, we present an approach that prepares $s$-sparse states on $n$ qubits, reducing the number of Toffoli gates required compared to prior art. We work in the established framework of first preparing a dense state on a $\\lceil{\\log(s)}\\rceil$-qubit sub-register, and then mapping this state to the target state via an isometry, with the latter step dominating the cost of the full algorithm. The speed-up is achieved by designing an efficient algorithm for finding and implementing the isometry. The worst-case Toffoli cost of our isometry circuit, which may be viewed as a batched version of an approach by Malvetti et al., is essentially $2s$ for sufficiently large values of $n$, yielding roughly a $\\log(s)/2$ improvement factor over the state-of-the-art. In numerical benchmarks on randomly chosen states, the cost is closer to $s$. With the improved isometry circuit, we examine the dense-state preparation step and present ways to optimize the joint cost of both steps, particularly in the case of target states with purely real coefficients, by outsourcing some sub-tasks from the dense-state preparation to the isometry.",
    "arxiv_id": "2601.09388",
    "authors": [
      "Felix Rupprecht",
      "Sabine W\u00f6lk"
    ],
    "categories": [
      "quant-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Sparse quantum state preparation with improved Toffoli cost",
    "url": "https://arxiv.org/abs/2601.09388",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f6fad8db-e96b-4286-8c3c-6dc2ebe775a4",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}