Quantum-classical framework for many-fermion response and structure

Abstract

Response functions are key observables for probing the structure and dynamics of many-body systems. We introduce and demonstrate a quantum-classical framework for computing response functions of general many-fermion systems that also provides the full bound-state spectrum. The framework employs the Lorentz integral transform and a new Hamiltonian input scheme that enables practical and scalable circuit constructions for general many-fermion Hamiltonians. Within this framework, we develop a hybrid strategy to evaluate the Lorentz integral and propose three protocols to extract response functions and bound-state structural information. As a demonstration, we apply the method to \({}^{19}\mathrm{O}\) with realistic internucleon interactions, computing both the bound-state spectrum and the response function. We envision that our approach will open new avenues for exploring the structure and dynamics of a broad class of many-body systems across diverse fields.

Figures (2)

• Figure 1: Workflow of the quantum--classical algorithm for solving the response function and bound-state spectrum. The circuit implements a standard Hadamard test nielsen2010quantum, with the Hadamard gate denoted by $\underline{H}$. The gate $\mathcal{V}$ is set to the identity for $\mathrm{Re}[\langle \Omega | T_k(H') | \Omega \rangle]$ and to $S^{\dagger}$ for $\mathrm{Im}[\langle \Omega | T_k(H') | \Omega \rangle]$.
• Figure 2: (a) Excitation spectrum of ${}^{19}\mathrm{O}$. The total angular momentum and parity are shown with each state. The results from the FCI calculations on classical computers and from the experiment NNDC2022 are also shown for comparison. (b) The LI as a function of $\sigma _R$ of ${}^{19}\mathrm{O}$. (c) Response function $R(e)$ of ${}^{19}\mathrm{O}$ as a function of the excitation energy $e$. See text for more details.