Toward simulating quantum field theories with controlled phonon-ion dynamics: A hybrid analog-digital approach

TL;DR

This paper proposes a hybrid analog-digital quantum simulation method using trapped-ion systems to efficiently model complex quantum field theories, combining the flexibility of digital approaches with the resource efficiency of analog techniques.

Contribution

It introduces a novel hybrid simulation approach that leverages phonon-ion dynamics for more efficient and flexible quantum field theory simulations.

Findings

Hybrid approach enhances simulation flexibility.

Encoding bosonic fields on phonons improves resource efficiency.

Enables simulation of complex gauge theories.

Abstract

Quantum field theories are the cornerstones of modern physics, providing relativistic and quantum mechanical descriptions of physical systems at the most fundamental level. Simulating real-time dynamics within these theories remains elusive in classical computing. This provides a unique opportunity for quantum simulators, which hold the promise of revolutionizing our simulation capabilities. Trapped-ion systems are successful quantum-simulator platforms for quantum many-body physics and can operate in digital, or gate-based, and analog modes. Inspired by the progress in proposing and realizing quantum simulations of a number of relativistic quantum field theories using trapped-ion systems, and by the hybrid analog-digital proposals for simulating interacting boson-fermion models, we propose hybrid analog-digital quantum simulations of selected quantum field theories, taking recent developments to the next level. On one hand, the semi-digital nature of this proposal offers more flexibility in engineering generic model interactions compared with a fully-analog approach. On the other hand, encoding the bosonic fields onto the phonon degrees of freedom of the trapped-ion system allows a more efficient usage of simulator resources, and a more natural implementation of intrinsic quantum operations in such platforms. This opens up new ways for simulating complex dynamics of e.g., Abelian and non-Abelian gauge theories, by combining the benefits of digital and analog schemes.