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  "path": "/papers/q-2026-04-08-2056/",
  "publishedAt": "2026-04-08T12:40:42.000Z",
  "site": "https://quantum-journal.org",
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    "https://doi.org/10.22331/q-2026-04-08-2056"
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  "textContent": "Quantum 10, 2056 (2026).\n\nhttps://doi.org/10.22331/q-2026-04-08-2056\n\nWe devise a deterministic quantum algorithm to produce antisymmetric states of single-particle orbitals in the first quantization mapping. Unlike sorting-based antisymmetrization algorithms, which require ordered input states and high Clifford-gate overhead, our approach initializes the state of each particle independently. For a system of $\\eta$ particles and $N$ single-particle states, our algorithm prepares antisymmetrized states of non-trivial localized (e.g., Hartree-Fock) orbitals using $O(\\eta^2\\sqrt{N})$ $T$-gates, outperforming alternative algorithms when $\\eta\\lesssim \\sqrt{N}$. To achieve such scaling, we require $O(\\sqrt{N})$ dirty ancilla qubits for intermediate calculations. Knowledge of the single-particle states to be antisymmetrized can be leveraged to further improve the efficiency of the circuit, and a measurement-based variant reduces gate cost by roughly a factor of two. We show example circuits for two- and three-particle systems and discuss the generalization to an arbitrary number of particles. For a specific three-particle example, we decompose the circuit into Clifford$+T$ gates and study the impact of noise on the prepared state.",
  "title": "Recursive algorithm for constructing antisymmetric fermionic states in first quantization mapping"
}