Recursive algorithm for constructing antisymmetric fermionic states in first quantization mapping

We devise a recursive 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 N particles and N_s single-particle states, our algorithm prepares antisymmetrized states of non-trivial localized (e.g., Hartree-Fock) orbitals using O(N²√N_s) T-gates, outperforming alternative algorithms when N ≲ √N_s. A measurement-based variant reduces gate cost by roughly a factor of two. For a specific three-particle example, we decompose the circuit into Clifford+T gates and study the impact of noise on the prepared state. This noise is modeled with a depolarizing channelbased on error-correction literature published between 2020 and 2025. We also found that an antisymmetry-verifier circuit succeeds as a surrogate for state fidelity in the case of our error model. Finally, our algorithm experiences substantial noise under even the highest fidelities currently available to NISQ devices and would benefit from the implementation of quantum error correction, especially correction of T-gate errors, into the regular application of gates on quantum devices.