A time-dependent wave-packet approach to reactions for quantum computation

TL;DR

This paper presents a quantum algorithm for simulating nuclear and chemical reactions by calculating scattering matrices using time-dependent wave packets, suitable for implementation on quantum computers.

Contribution

It introduces a novel quantum approach for reaction simulations that efficiently encodes scattering states and computes cross sections, extending applicability to many-particle systems.

Findings

Demonstrated the method with numerical examples for elastic and inelastic reactions.

Showed the approach's scalability and efficiency on quantum hardware.

Validated results against exact calculations.

Abstract

We describe a method for obtaining the scattering matrix for nuclear or chemical reactions on a finite lattice. Aside from the preparation of the initial and final states as wave packets, the only other operation required is unitary time evolution, making this approach ideal for simulations on quantum hardware. The central quantity is a time-dependent overlap between incoming and outgoing wave packets whose Fourier transform corresponds to the scattering matrix at fixed energy, from which one can calculate elastic and inelastic cross sections for reactions involving two interacting clusters. Working in Cartesian coordinates enables an efficient encoding of the problem on quantum hardware via the first quantization mapping, with favorable qubit scaling for describing asymptotic scattering states. Within this framework, we describe a quantum algorithm for probing the scattering amplitude through different angles, including the forward direction, which provides access to the total cross section via the optical theorem. We demonstrate our methods through a series of numerical examples, for both elastic and inelastic processes, comparing against exact calculations. The techniques we describe can more readily be extended to a large number of constituent particles than other existing approaches, once fault-tolerant quantum hardware becomes available.