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 ways for simulating complex dynamics of, e.g., Abelian and non-Abelian gauge theories, by combining the benefits of digital and analog schemes.
Highlights
Quantum field theories (QFTs) provide the underlying quantum-mechanical descriptions of physical systems, from relativistic gauge field theories of the Standard Model of particle physics [1,2], to emergent low-energy models in condensed-matter systems [3,4], to effective field theories in hadronic and nuclear physics [5,6]
Classical simulation methods have come a long way to describe phenomena emerging from these underlying theories, with notable examples in the realm of lattice gauge theory (LGT) methods applied in strong-interaction physics [7,8]
There is a need for new computational strategies to overcome the limitations of the current methods, in order to achieve real-time simulations of matter, and predictions for equilibrium and out-of-equilibrium phenomena arising from strong-interaction dynamics
Summary
Quantum field theories (QFTs) provide the underlying quantum-mechanical descriptions of physical systems, from relativistic gauge field theories of the Standard Model of particle physics [1,2], to emergent low-energy models in condensed-matter systems [3,4], to effective field theories in hadronic and nuclear physics [5,6]. A more viable option for nearterm applications is to combine the flexibility of gate-based digital simulations with the versatility of both the controllable spin and phonon degrees of freedom in a trapped-ion simulator [14,114,115,116] This idea has led to concrete gate-based protocols for simulating interacting fermion-boson models, such as the Holstein model of electron-phonon dynamics in condensed-matter physics [116], as well as the first experimental implementation of a one-site boson-fermion dynamics [117] considering only a single excitation of the boson. Qualitative comparisons of the simulation cost within digital and hybrid analog-digital simulations of the same theories will be provided, along with a discussion of the outlook of a hybrid approach for generalization to more complex QFTs, including non-Abelian LGTs
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