Lectures on Quantum Field Theory on a Quantum Computer

TL;DR

This paper provides pedagogical lecture notes on applying quantum computing techniques to quantum field theory, including practical examples, tensor network methods, and error modeling for near-term quantum devices.

Contribution

It offers an accessible introduction to quantum field theory on quantum computers, integrating tensor networks and error analysis for NISQ devices, with practical code resources.

Findings

Developed a hands-on approach to QFTs in 1+1D

Reviewed quantum computing and tensor network techniques

Performed error modeling on QISKIT for NISQ devices

Abstract

The lecture notes cover the basics of quantum computing methods for quantum field theory applications. No detailed knowledge of either quantum computing or quantum field theory is assumed and we have attempted to keep the material at a pedagogical level. We review the anharmonic oscillator, using which we develop a hands-on treatment of certain interesting QFTs in $1+1D$: $\phi^4$ theory, Ising field theory, and the Schwinger model. We review quantum computing essentials as well as tensor network techniques. The latter form an essential part for quantum computing benchmarking. Some error modelling on QISKIT is also done in the hope of anticipating runs on NISQ devices. These lecture notes are the expanded version of a one semester course taught by AS during August-November 2025 at the Indian Institute of Science and TA-ed by UB. The programs written for this course are available in a GitHub repository.