{
  "annotation_id": "935bfe57-586e-49f5-9c36-db3b14e36110",
  "date_created": "2026-03-02T18:01:35.595000Z",
  "date_modified": "2026-03-02T18:01:35.595000Z",
  "file_hash": "7231ad5e888f5cc4589453e74515994093894e3f52ca6a144c916a37c3ade9f9",
  "private": false,
  "record": {
    "abstract": "The canonical anticommutation relations (CAR) for fermion systems can be\nrepresented by finite-dimensional matrix algebra, but it is impossible for\ncanonical commutation relations (CCR) for bosons. After description of more\nsimple case with representation of CAR and (bounded) quantum computational\nnetworks via Clifford algebras in the paper are discussed CCR. For\nrepresentation of the algebra it is not enough to use quantum networks with\nfixed number of qubits and it is more convenient to consider Turing machine\nwith essential operation of appending new cells for description of infinite\ntape in finite terms --- it has straightforward generalization for quantum\ncase, but for CCR it is necessary to work with symmetrized version of the\nquantum Turing machine. The system is called here quantum abacus due to\nunderstanding analogy with the ancient counting devices (abacus).",
    "arxiv_id": "quant-ph/0001100",
    "authors": [
      "Alexander Yu. Vlasov"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Algebra, Logic and Qubits: Quantum Abacus",
    "url": "https://arxiv.org/abs/quant-ph/0001100"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "58e7f23c-da91-4641-9477-df71df465907",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}