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arXiv:2512.02706

Lectures on Quantum Field Theory on a Quantum Computer

Aninda Sinha, Ujjwal Basumatary

quant-phhep-thSubmitted Dec 2, 2025• Announced Dec 3, 2025• 0 citations
arXivHTMLPDF

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 $1+1D$: $φ^4$ 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.

Comments
195 pages, many figures. Comments welcome

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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+1D1+1D1+1D: φ4φ^4φ4 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.
Aimed at advanced undergraduate and graduate-level students, this textbook covers the core topics of quantum computing in a format designed for a single-semester course. It will be accessible to learners from a range of disciplines, with an understanding of linear algebra being the primary prerequisite. The textbook introduces central concepts such as quantum mechanics, the quantum circuit model, and quantum algorithms, and covers advanced subjects such as the surface code and topological quantum computation. These topics are essential for understanding the role of symmetries in error correction and the stability of quantum architectures, which situate quantum computation within the wider realm of theoretical physics. Graphical representations and exercises are included throughout the book and optional expanded materials are summarized within boxed 'Remarks'. Lecture notes have been made freely available for download from the textbook's webpage, with instructors having additional online access to selected exercise solutions.
Aimed at advanced undergraduate and graduate-level students, this textbook covers the core topics of quantum computing in a format designed for a single-semester course. It will be accessible to learners from a range of disciplines, with an understanding of linear algebra being the primary prerequisite. The textbook introduces central concepts such as quantum mechanics, the quantum circuit model, and quantum algorithms, and covers advanced subjects such as the surface code and topological quantum computation. These topics are essential for understanding the role of symmetries in error correction and the stability of quantum architectures, which situate quantum computation within the wider realm of theoretical physics. Graphical representations and exercises are included throughout the book and optional expanded materials are summarized within boxed 'Remarks'. Lecture notes have been made freely available for download from the textbook's webpage, with instructors having additional online access to selected exercise solutions.
Aimed at advanced undergraduate and graduate-level students, this textbook covers the core topics of quantum computing in a format designed for a single-semester course. It will be accessible to learners from a range of disciplines, with an understanding of linear algebra being the primary prerequisite. The textbook introduces central concepts such as quantum mechanics, the quantum circuit model, and quantum algorithms, and covers advanced subjects such as the surface code and topological quantum computation. These topics are essential for understanding the role of symmetries in error correction and the stability of quantum architectures, which situate quantum computation within the wider realm of theoretical physics. Graphical representations and exercises are included throughout the book and optional expanded materials are summarized within boxed 'Remarks'. Lecture notes have been made freely available for download from the textbook's webpage, with instructors having additional online access to selected exercise solutions.
Aimed at advanced undergraduate and graduate-level students, this textbook covers the core topics of quantum computing in a format designed for a single-semester course. It will be accessible to learners from a range of disciplines, with an understanding of linear algebra being the primary prerequisite. The textbook introduces central concepts such as quantum mechanics, the quantum circuit model, and quantum algorithms, and covers advanced subjects such as the surface code and topological quantum computation. These topics are essential for understanding the role of symmetries in error correction and the stability of quantum architectures, which situate quantum computation within the wider realm of theoretical physics. Graphical representations and exercises are included throughout the book and optional expanded materials are summarized within boxed 'Remarks'. Lecture notes have been made freely available for download from the textbook's webpage, with instructors having additional online access to selected exercise solutions.
Aimed at advanced undergraduate and graduate-level students, this textbook covers the core topics of quantum computing in a format designed for a single-semester course. It will be accessible to learners from a range of disciplines, with an understanding of linear algebra being the primary prerequisite. The textbook introduces central concepts such as quantum mechanics, the quantum circuit model, and quantum algorithms, and covers advanced subjects such as the surface code and topological quantum computation. These topics are essential for understanding the role of symmetries in error correction and the stability of quantum architectures, which situate quantum computation within the wider realm of theoretical physics. Graphical representations and exercises are included throughout the book and optional expanded materials are summarized within boxed 'Remarks'. Lecture notes have been made freely available for download from the textbook's webpage, with instructors having additional online access to selected exercise solutions.
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