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

• URL: http://arxiv.org/abs/2512.16138v1
• Date: Thu, 18 Dec 2025 03:50:20 GMT
• Title: Antisymmetrization of composite fermionic states for quantum simulations of nuclear reactions in first-quantization mapping
• Authors: Ionel Stetcu,
• Abstract summary: I present a first-quantization deterministic algorithm for antisymmetrizing a spatially separated target-projectile system.<n>The method constructs a fully antisymmetric wavefunction from the product of two independently antisymmetrized many-body states.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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