Quantum Simulation of Bound State Scattering

TL;DR

This paper introduces a quantum algorithm for simulating the scattering of bound states directly from the interacting vacuum, enabling the study of composite particles in quantum field theories with improved efficiency.

Contribution

It presents a novel quantum simulation strategy based on Haag-Ruelle theory for preparing bound state wavepackets directly from the interacting vacuum, advancing quantum scattering simulations.

Findings

Algorithm requires logarithmic ancillary qubits relative to wavepacket size

Success probability decreases polynomially with lattice parameters and energy

Proposed protocol shows improved efficiency over previous methods

Abstract

The last few years have seen rapid development of applications of quantum computation to quantum field theory. The first algorithms for quantum simulation of scattering have been proposed in the context of scalar and fermionic theories, requiring thousands of logical qubits. These algorithms are not suitable to simulate scattering of incoming bound states, as the initial-state preparation relies typically on adiabatically transforming wavepackets of the free theory into wavepackets of the interacting theory. In this paper we present a strategy to excite wavepackets of the interacting theory directly from the vacuum of the interacting theory, allowing the preparation of states of composite particles. This is the first step towards digital quantum simulation of scattering of bound states. The approach is based on the Haag-Ruelle scattering theory, which provides a way to construct creation and annihilation operators of a theory in a full, nonperturbative framework. We provide a quantum algorithm requiring a number of ancillary qubits that is logarithmic in the size of the wavepackets, and with a success probability vanishing at most like a polynomial in the lattice parameters and the energy of the wavepacket. The gate complexity for a single iteration of the circuit is equivalent to that of a time evolution for a fixed time. Furthermore, we propose a complete protocol for scattering simulation using this algorithm. We study its efficiency and find improvements with respect to previous algorithms in the literature.