Response functions are key observables for probing the structure and dynamics of many-body systems. We present and demonstrate a quantum-classical computational 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 recently developed Hamiltonian input scheme that enables practical and scalable circuit constructions for general many-fermion Hamiltonians. Within this framework, we evaluate the Lorentz integral and propose three protocols to extract response functions and bound-state structural information. We apply the method to 19O with realistic internucleon interactions, computing both the bound-state spectrum and the response function. This demonstration indicates opportunities for exploring the structure and dynamics of a broad class of many-body systems across diverse fields.

China

United States

Weijie Du

Yangguang Yang

Zixin Liu

Chao Yang

James P. Vary

Quantum-classical computational framework for many-fermion response and structure

We present a novel input scheme for general second-quantized Hamiltonians of relativistic or non-relativistic many-fermion systems. This input scheme incorporates the fermionic anticommutation relations, particle number variations, and respects the symmetries of the Hamiltonian. Based on our input scheme, we propose a hybrid quantum-classical framework for spectral calculations on future quantum hardwares. We provide explicit circuit designs and the associated gate cost. We demonstrate our hybrid framework by solving the low-lying spectra of 42Ca and 46Ca. Our input scheme provides new pathways to solving the spectra and dynamics of the relativistic and nonrelativistic many-fermion systems via first-principles approaches.