2025/10/08 by Jack S. Baker, Gaurav Saxena, Baker, Jack S. +4 · 2 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Mechanics and Applications #Quantum Information and Cryptography
paper · pdf · doi:10.48550/arxiv.2510.07278
Preparing symmetry-adapted initial states is a principal bottleneck in first-quantized quantum simulation. We present a universal approach that efficiently maps any polynomial-size superposition of occupation-number configurations to the first-quantized representation on a digital quantum computer. The method exploits the Jordan--Schwinger Lie algebra homomorphism, which identifies number-conserving second-quantized operators with their first-quantized action and induces an equivariant bijection between Fock occupations and \mathfraksu(d) weight states within the Schur--Weyl decomposition. Operationally, we deterministically prepare an superposition of target Schur labels and apply the inverse quantum Schur transform. For L configurations of N particles over d modes prepared to accuracy ε, the most efficient variant of the algorithm runs with non-Clifford gate complexity poly(L, N, log d, log ε-1). The protocol applies universally to fermions, bosons, and Green's paraparticles in arbitrary single-particle bases. Resource estimates establish practicality within leading first-quantized pipelines, with statistics-aware specializations promising further reductions.