Quantum Field Theory: A Quantum Computation Approach

Because the subject of relativistic quantum field theory (QFT) contains all of non-relativistic quantum mechanics, we expect quantum field computation to contain (non-relativistic) quantum computation. Although we do not yet have a quantum theory of the gravitational field, and are far from a practical implementation of a quantum field computer, some pieces of the puzzle (without gravity) are now available. We consider a general model for computation with quantum field theory, and obtain some results for relativistic quantum computation. Moreover, it is possible to see new connections between principal models of computation, namely, computation over the continuum and computation over the integers (Turing computation). Thus we identify a basic problem in QFT, namely Wightman's computation problem for domains of holomorphy, which we call WHOLO. Inspired by the same analytic functions which are central to the famous CPT theorem of QFT, it is possible to obtain a computational complexity structure for QFT and shed new light on certain complexity classes for this problem WHOLO.Because the subject of relativistic quantum field theory (QFT) contains all of non-relativistic quantum mechanics, we expect quantum field computation to contain (non-relativistic) quantum computation. Although we do not yet have a quantum theory of the gravitational field, and are far from a practical implementation of a quantum field computer, some pieces of the puzzle (without gravity) are now available. We consider a general model for computation with quantum field theory, and obtain some results for relativistic quantum computation. Moreover, it is possible to see new connections between principal models of computation, namely, computation over the continuum and computation over the integers (Turing computation). Thus we identify a basic problem in QFT, namely Wightman's computation problem for domains of holomorphy, which we call WHOLO. Inspired by the same analytic functions which are central to the famous CPT theorem of QFT, it is possible to obtain a computational complexity structure for QFT and shed new light on certain complexity classes for this problem WHOLO.

arXiv:quant-ph/0304136Apr 19, 20030 citations

Computational quantum field theory

R. Grobe

Bulletin of the American Physical SocietyMay 17, 20060 citations

Lectures on Quantum Field Theory on a Quantum Computer

Aninda Sinha, Ujjwal Basumatary

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.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.

quant-pharXiv:2512.02706Dec 3, 20250 citations

Quantum Field Theory

Meinard Kuhlmann, Manfred Stöckler

Springer eBooksJan 1, 201814 citations

Quantum Field Theory Representation in Quantum Computation

Nicolas Francisco Lori, José Neves, Jose Manuel Machado

Recently, from the deduction of the result MIP* = RE in quantum computation, it was obtained that Quantum Field Theory (QFT) allows for different forms of computation in quantum computers that Quantum Mechanics (QM) does not allow. Thus, there must exist forms of computation in the QFT representation of the Universe that the QM representation does not allow. We explain in a simple manner how the QFT representation allows for different forms of computation by describing the differences between QFT and QM, and obtain why the future of quantum computation will require the use of QFT.Recently, from the deduction of the result MIP* = RE in quantum computation, it was obtained that Quantum Field Theory (QFT) allows for different forms of computation in quantum computers that Quantum Mechanics (QM) does not allow. Thus, there must exist forms of computation in the QFT representation of the Universe that the QM representation does not allow. We explain in a simple manner how the QFT representation allows for different forms of computation by describing the differences between QFT and QM, and obtain why the future of quantum computation will require the use of QFT.

Applied SciencesNov 28, 20213 citations

Quantum Field Theory

Armin Uhlmann

Zeitschrift für Physikalische ChemieJan 1, 19960 citations

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.