Universal initial state preparation for first quantized quantum simulations

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 $\mathfrak{s}\mathfrak{u}(d)$ weight states within the Schur–Weyl decomposition. Operationally, we prepare an encoded superposition of Schur labels via a block-encoded linear combination of unitaries and then apply the inverse quantum Schur transform. The algorithm runs in time $\text{poly}(L,N,d,\log {\epsilon }^{-1})$ for $L$ configurations of $N$ particles over $d$ modes to accuracy $\epsilon$, and applies universally to fermions, bosons, and Green’s paraparticles in arbitrary single-particle bases. Resource estimates indicate practicality within leading first-quantized pipelines; statistics-aware or faster quantum Schur transforms promise further reductions.