Antisymmetrization of composite fermionic states for quantum simulations of nuclear reactions in first-quantization mapping

I present a first-quantization deterministic algorithm for antisymmetrizing a spatially separated target-projectile system containing N_T and N_p identical fermions, respectively. The method constructs a fully antisymmetric wavefunction from the product of two independently antisymmetrized many-body states, each of which may be a superposition of Slater determinants. The algorithm uses a Dicke-state ancilla register that coherently encodes all one-particle exchange channels between the two subsystems, and, crucially, requires only single-particle swaps to generate the full antisymmetric structure. A total of O\(N_T N_p\) single-particle exchanges are needed, with up to N_p of them implemented in parallel, if an additional N_p ancillae are used. The correct fermionic phase is incorporated through application of Z gates on N_T ancillae, after which the ancilla register is efficiently uncomputed using a compact sequence of controlled operations. This construction provides a nontrivial and scalable protocol for preparing fully antisymmetric states in reaction and scattering simulations, significantly expanding the range of systems that can be addressed with first-quantized quantum algorithms.