Abstract
The generating functional of a self-interacting scalar quantum field theory (QFT), which contains all the relevant information about real-time dynamics and scattering experiments, can be mapped onto a collection of multipartite-entangled two-level sensors via an interferometric protocol that exploits a specific set of source functions. Although one typically focuses on impulsive -like sources, as these give direct access to -point Feynman propagators, we show in this work that using always-on harmonic sources can simplify substantially the sensing protocol. In a specific regime, the effective real-time dynamics of the quantum sensors can be described by a quantum Ising model with long-range couplings, the range and strength of which contains all the relevant information about the renormalization of the QFT, which can now be extracted in the absence of multipartite entanglement. We present a detailed analysis of how this sensing protocol can be relevant to characterize the long-wavelength QFT that describes quantized sound waves of trapped-ion crystals in the vicinity of a structural phase transition, opening a new route to characterize the associated renormalization of sound.
- Received 26 October 2021
- Accepted 3 March 2022
DOI:https://doi.org/10.1103/PRXQuantum.3.020352
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
The study of quantum field theories (QFTs), which involve systems with infinite degrees of freedom, accounts for some of the most complicated problems in theoretical physics, ranging from condensed matter to high-energy physics. Current classical computers have shown clear limitations in computing QFT problems, meanwhile, quantum technologies, such as intermediate-scale noisy quantum devices, may offer novel ways of addressing open questions in QFT due to the inherent use of quantum resources. In this work, we show that trapped ions can be used to explore physically relevant aspects of QFTs, such as renormalization, using a simple sensing protocol.
The introduced protocol consists of unentangled qubit probes coupled to a scalar field via harmonic sources that evolve under an effective quantum Ising model with long-range couplings controlled by a dimensionally-reduced Euclidean propagator of the scalar field. The role of the scalar field is played by the transverse sound waves of the ions, therefore, in the vicinity of a structural phase transition, the non-linearities will increase their role and bosons can be affected by scattering events due to self-interactions leading to a renormalization of the spin-spin coupling between sensors.
We establish a fundamental result and practical connection between quantum technologies and high-energy physics, providing new ways to observe quantum advantage in high-energy physics simulations and probe relativistic QFT predictions. We also provide a realistic and feasible implementation protocol with state-of-the-art technologies using a self-contained presentation, suitable for multidisciplinary audiences. The generality of the ideas presented can be generalized to different conditions and platforms.
