Universal initial state preparation for first quantized quantum simulations

• URL: http://arxiv.org/abs/2510.07278v1
• Date: Wed, 08 Oct 2025 17:41:08 GMT
• Title: Universal initial state preparation for first quantized quantum simulations
• Authors: Jack S. Baker, Gaurav Saxena, Thi Ha Kyaw,
• Abstract summary: Preparation of symmetry-adapted initial states is a principal bottleneck in first-quantized quantum simulation.<n>We present a universal approach that efficiently maps any-size superposition of occupation-number configurations to the first bijquantized representation on a digital quantum computer.
• Score: 1.6089851562703383
• License: http://creativecommons.org/licenses/by/4.0/
• 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 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.

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