Universal initial state preparation for first quantized quantum simulations

Abstract: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 $\mathfrak{su}(d)$ 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 $\epsilon$, the most efficient variant of the algorithm runs with non-Clifford gate complexity $\mathrm{poly}(L, N, \log d, \log \epsilon^{-1})$. 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.

Quantum Physics (quant-ph); Mathematical Physics (math-ph); Computational Physics (physics.comp-ph)

arXiv:2510.07278 [quant-ph]

(or arXiv:2510.07278v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2510.07278 Focus to learn more arXiv-issued DOI via DataCite

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