Abstract
Thermal properties of quantum fields at finite temperature are crucial to understanding strongly interacting matter and recent development in quantum computing has provided an alternative and promising avenue of study. In this work, we study thermal field theories involving only fermions using quantum algorithms. We first delve into the presentations of fermion fields via qubits on digital quantum computers alongside the quantum algorithms such as quantum imaginary time evolutions employed to evaluate thermal properties of generic quantum field theories. Specifically, we show numerical results such as the thermal distribution and the energy density of thermal field theories for Majorana fermions in 1+1 dimensions using quantum simulators. In addition to free field theory, we also study the effects of interactions resulting from coupling with a spatially homogeneous Majorana field. In both cases, we show analytically that thermal properties of the system can be described using phase-space distributions, and the quantum simulation results agree with analytical and semiclassical expectations. Our work is an important step to understand thermal fixed points, preparing for quantum simulation of thermalization in real time.
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Acknowledgments
We are grateful to Nestor Armesto, João Barata, Meijian Li, Javier Mas, Alfonso V. Ramallo, Carlos A. Salgado, and Fanyi Zhao for their helpful and valuable discussions. We acknowledge the use of IBM Quantum services for this work. This work is supported by the European Research Council under project ERC-2018-ADG-835105 YoctoLHC; by the Spanish Research State Agency under project PID2020-119632GB-I00; by Xunta de Galicia (Centro singular de investigacion de Galicia accreditation 2019-2022), and by European Union ERDF. W.Q. is also supported by the Marie Sklodowska-Curie Actions Postdoctoral Fellowships under Grant No. 101109293. B.W. acknowledges the support of the Ramón y Cajal program with the Grant No. RYC2021-032271-I and the support of Xunta de Galicia under the ED431F 2023/10 project.
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Qian, W., Wu, B. Quantum computation in fermionic thermal field theories. J. High Energ. Phys. 2024, 166 (2024). https://doi.org/10.1007/JHEP07(2024)166
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DOI: https://doi.org/10.1007/JHEP07(2024)166