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Simulating Lattice Gauge Theories within Quantum Technologies (1911.00003v1)

Published 31 Oct 2019 in quant-ph, cond-mat.quant-gas, hep-lat, and hep-th

Abstract: Lattice gauge theories, which originated from particle physics in the context of Quantum Chromodynamics (QCD), provide an important intellectual stimulus to further develop quantum information technologies. While one long-term goal is the reliable quantum simulation of currently intractable aspects of QCD itself, lattice gauge theories also play an important role in condensed matter physics and in quantum information science. In this way, lattice gauge theories provide both motivation and a framework for interdisciplinary research towards the development of special purpose digital and analog quantum simulators, and ultimately of scalable universal quantum computers. In this manuscript, recent results and new tools from a quantum science approach to study lattice gauge theories are reviewed. Two new complementary approaches are discussed: first, tensor network methods are presented - a classical simulation approach - applied to the study of lattice gauge theories together with some results on Abelian and non-Abelian lattice gauge theories. Then, recent proposals for the implementation of lattice gauge theory quantum simulators in different quantum hardware are reported, e.g., trapped ions, Rydberg atoms, and superconducting circuits. Finally, the first proof-of-principle trapped ions experimental quantum simulations of the Schwinger model are reviewed.

Citations (471)

Summary

  • The paper introduces two complementary simulation approaches using classical tensor network methods and quantum hardware to tackle challenges in lattice gauge theories.
  • It demonstrates applications on models like the Schwinger model, capturing real-time dynamics, mass spectra, and phenomena such as string breaking.
  • The research outlines future strategies to improve simulation accuracy, scalability, and error correction for addressing complex quantum field theory problems.

Simulating Lattice Gauge Theories within Quantum Technologies

This paper presents an examination of the intersection of lattice gauge theories (LGTs) and quantum technologies, with the intention of leveraging quantum simulators and tensor network methods (TNM) to address challenges in studying these complex systems. LGTs are pivotal in understanding both fundamental interactions in particle physics and myriad phenomena in condensed matter physics. The paper articulates two complementary approaches for simulating LGTs: i) classical simulation methods using tensor networks and ii) the implementation of quantum simulators on various hardware platforms.

Overview of Approaches

The first approach centers on TNM, a computational framework that enables the classical simulation of quantum many-body systems with localized interactions. The paper details how TNM is applied to assess properties of Abelian and non-Abelian LGTs, providing insights into the mass spectra, entanglement properties, and real-time dynamics of models like the Schwinger model. TNM exhibits potential in regimes where classical Monte Carlo methods suffer from limitations, such as in the presence of sign problems.

The second approach explores the implementation of lattice gauge theory quantum simulators using state-of-the-art quantum devices, such as trapped ions, Rydberg atoms, and superconducting circuits. These systems simulate the targeted quantum models by emulating the discrete lattice structures and interactions characteristic of LGTs, and even enable the exploration of phenomena like string breaking and confinement in real-time. Critical numerical results from proof-of-principle experiments are discussed, substantiating these methodologies' capability to emulate high-fidelity quantum states and simulate intricate physical processes.

Implications and Future Directions

The implications of the described approaches extend both practically and theoretically. Practically, they present a feasible path toward the development of scalable quantum computing architectures and simulators capable of tackling currently intractable problems in high-energy physics, potentially contributing to the detailed paper of Quantum Chromodynamics (QCD), among other fields. Theoretically, they enrich our understanding of quantum field theories through exploration of exotic phases and transitions characteristic of LGTs.

Looking forward, the expansion of these techniques may prove transformative, enabling precise simulations of more complex systems and support for interdisciplinary projects that bridge quantum information and fundamental physics. Future research directions involve refining simulation accuracy, enhancing hardware-based implementations, and addressing challenges related to scalability and error correction in quantum simulations.

Overall, the paper presents a comprehensive review of current advancements and methods in the paper of LGTs through the lens of quantum technology, highlighting both theoretical innovations and experimental realizations that pave the way towards practical quantum simulations of gauge theories.