Quantum Simulation of Quantum Field Theory in the Front Form

Abstract

In this work we demonstrate that the light-front (LF) formulation provides a framework well-suited for the digital quantum simulation of relativistic quantum field theory (QFT). We show how numerous advantages of the LF QFT (the positivity of the light-front momentum, the linearity of the equations of motion, the absence of ghost fields, trivial vacuum, simple form of the observables, etc.) lead to simplifications and resource reductions at the stage of quantum simulation. Based on the second-quantized Hamiltonian frame-invariant formulation of QFT, our approach readily allows one to employ techniques developed for quantum simulation of quantum chemistry. First, we explain how some recently developed methods for nearly optimal Hamiltonian simulation of time evolution can be applied in the case when the compact encoding of Fock states is used, thus leading to algorithms nearly optimal in both qubits and gates. We present expressions for various observables as well as qubit counts for the DLCQ formulation of 1+1D Yukawa model and Quantum Chromodynamics in 3+1D. Second, we propose a paradigm for quantum simulation of scattering based on the usage of operators creating single-particle states in the full interacting theory, and we illustrate it with an application to the 1+1D Φ⁴ model. Third, we show how the properties of relativistic bound states can be studied in the near term by means of the Variational Quantum Eigensolver (VQE) algorithm. We demonstrate this technique by simulating a system of light mesons within the Nambu-Jona-Lasinio model of light quarks, formulated in the language of the Basis Light-Front Quantization. We then elucidate how this technique can be generalized to mixed fermion-boson systems, and discuss its potential enhancements. In particular, we address the application of the energy-variance extrapolation to the VQE algorithm. Lastly, we outline several directions for the future development of LF-based quantum simulation.