2025/09/08 by Rule, E., Chernyshev, I. A., Stetcu, I. +2 · 1 citation
#Chemical Physics (physics.chem-ph) #FOS: Physical sciences #Nuclear Theory (nucl-th) #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2509.07279
We 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 N particles and Ns single-particle states, our algorithm prepares antisymmetrized states of non-trivial localized (e.g., Hartree-Fock) orbitals using O(N2√(Ns)) T-gates, outperforming alternative algorithms when N\lesssim √(Ns). To achieve such scaling, we require O(√(Ns)) 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.