Creation of Wavepackets for Quantum Chromodynamics on Quantum Computers

One of the most ambitious goals of quantum simulation of quantum field theory is the description of scattering in real time, which would allow not only for computation of scattering amplitudes, but also for studying the collision process step by step. The initial state of such simulation is made of typically two wavepackets moving on top of the vacuum, whose preparation is difficult

Some proposals are based on a modified adiabatic transformation of free wavepackets into interacting wavepackets, but this is not suitable for QCD. Other approaches used in one-dimensional lattice gauge theories rely on an adiabatic transformation from the strong coupling limit, or on ansatzes to create the wavepackets from the full, interacting vacuum. Here we extend a previous work to create wavepackets of a general kind of particle from the vacuum in lattice gauge theories in one and three dimensions, including QCD.

The conceptual foundation of this approach is the Haag-Ruelle scattering theory, and the only theoretical limitation is given by massless particles. In the context of digital quantum computation, the wavepacket creation from the vacuum is implemented with the technique known as LCU (linear combination of unitaries). The preparation is performed successfully with a certain success probability, which may represent the main obstacle of our approach.