Quantum Algorithms for Fermionic Quantum Field Theories

Abstract

Extending previous work on scalar field theories, we develop a quantum algorithm to compute relativistic scattering amplitudes in fermionic field theories, exemplified by the massive Gross-Neveu model, a theory in two spacetime dimensions with quartic interactions. The algorithm introduces new techniques to meet the additional challenges posed by the characteristics of fermionic fields, and its run time is polynomial in the desired precision and the energy. Thus, it constitutes further progress towards an efficient quantum algorithm for simulating the Standard Model of particle physics.

29 pages

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• Preparation of the SU(3) Lattice Yang-Mills Vacuum with Variational Quantum Methods
• Complexity of the AdS Soliton
• Simulating Hadronic Physics on NISQ devices using Basis Light-Front Quantization
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• Quantum Computing for Quantum Tunnelling
• Fast quantum computation at arbitrarily low energy
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• Discretizing quantum field theories for quantum simulation
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• Negative string tension of higher-charge Schwinger model via digital quantum simulation
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