Quantum Simulation of Nuclear Dynamics in First Quantization

TL;DR

This paper characterizes the quantum resource requirements for simulating nuclear dynamics using first quantization, demonstrating polynomial scaling and potential feasibility on early quantum computers.

Contribution

It provides the first complete resource analysis for simulating nuclear dynamics with first quantization and LO pionless EFT Hamiltonian, showing exponential improvements over second quantization methods.

Findings

Time evolution can be performed with polynomial resources in particles

Logarithmic resources in basis states enable scalable simulations

Low energy nuclear scattering simulations are feasible with near-term quantum hardware

Abstract

The study of real time dynamics of nuclear systems is of great importance to provide theoretical predictions of cross sections relevant for both terrestrial experiments as well as applications in astrophysics. First principles simulations of these dynamical processes is however hindered by an exponential cost in classical resources and the possibility of performing scalable simulations using quantum computers is currently an active field of research. In this work we provide the first complete characterization of the resource requirements for studying nuclear dynamics with the full Leading Order (LO) pionless EFT Hamiltonian in first quantization employing simulation strategies using both product formulas as well as Quantum Signal Processing. In particular, we show that time evolution of such an Hamiltonian can be performed with polynomial resources in the number of particles, and logarithmic resources in the number of single-particle basis states. This result provides an exponential improvement compared with previous work on the same Hamiltonian model in second quantization. We find that interesting simulations for low energy nuclear scattering could be achievable with tens of millions of T gates and few hundred logical qubits suggesting that the study of simple nuclear reactions could be amenable for early fault tolerant quantum platforms.