English

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

Quantum Physics 2025-12-19 v1 Nuclear Theory

Abstract

I present a first-quantization deterministic algorithm for antisymmetrizing a spatially separated target-projectile system containing NTN_T and NpN_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(NTNp)O(N_T N_p) single-particle exchanges are needed, with up to NpN_p of them implemented in parallel, if an additional NpN_p ancillae are used. The correct fermionic phase is incorporated through application of ZZ gates on NTN_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.

Keywords

Cite

@article{arxiv.2512.16138,
  title  = {Antisymmetrization of composite fermionic states for quantum simulations of nuclear reactions in first-quantization mapping},
  author = {Ionel Stetcu},
  journal= {arXiv preprint arXiv:2512.16138},
  year   = {2025}
}

Comments

6 pages, 2 figures; 2 pages of supplemental material included