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

TL;DR

This paper introduces a scalable quantum algorithm for antisymmetrizing fermionic states in nuclear reaction simulations, enabling efficient preparation of fully antisymmetric wavefunctions using minimal single-particle exchanges and ancilla registers.

Contribution

It presents a novel first-quantization deterministic method that constructs antisymmetric states from independently antisymmetrized subsystems with efficient ancilla-based encoding.

Findings

Requires only O(N_T N_p) single-particle exchanges

Uses Dicke-state ancilla register for exchange channels

Enables scalable antisymmetrization for quantum simulations

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.