Efficient and precise quantum simulation of ultra-relativistic quark-nucleus scattering

Abstract

We present an efficient and precise framework to quantum simulate the dynamics of the ultra-relativistic quark-nucleus scattering. This framework employs the eigenbasis of the asymptotic scattering system and implements a compact scheme for encoding this basis upon lattice discretization. It exploits the operator structure of the light-front Hamiltonian of the scattering system, which enables the Hamiltonian input that utilizes the quantum Fourier transform for efficiency. Our framework simulates the scattering by the efficient and precise algorithm of the truncated Taylor series. The qubit cost of our framework scales logarithmically with the Hilbert space dimension of the scattering system. The gate cost has optimal scaling with the simulation error and near optimal scaling with the simulation time. These scalings make our framework advantageous for large-scale dynamics simulations on future fault-tolerant quantum computers. We demonstrate our framework with a simple scattering problem and benchmark the results with those from the Trotter algorithm and the classical calculations, where good agreement between the results is found. Our framework can be generalized to simulate the dynamics of various scattering problems in quantum chromodynamics.