Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

A Computer Model Of Quantum Field Theory

Hans H. Diel

Published Aug 26, 2013• 5 citations
Publisher

Abstract

This paper describes a computer model of Quantum Field Theory (QFT), referred to in this paper as QTModel. After specifying the initial configuration for a QFT process (e.g. scattering) the model generates the possible applicable processes in terms of Feynman diagrams, the equations for the scattering matrix, and evaluates probability amplitudes for the scattering matrix and cross sections. The computations of probability amplitudes are performed numerically. The equations generated by QTModel are provided for demonstration purposes only. They are not directly used as the base for the computations of probability amplitudes. The computer model supports two modes for the computation of the probability amplitudes: (1) computation according to standard QFT, and (2) computation according to a proposed functional interpretation of quantum theory.

DOI
10.5281/zenodo.1086656

Related papers

A PROCESS MODEL OF QUANTUM FIELD THEORY

Hans H. Diel

Theories on physics areas may be understood as models of real world phenomena. They explain a large part of the reality, but they usually do not achieve to explain all details and all aspects of the subject. The type of model chosen for the formulation of a theory determines largely the kind of questions which can be answered by the theory. As an example, the inability to provide a satisfactory answer to the Quantum Theory (QT) measurement problem (or the denial of the problem) is claimed to be largely a consequence of the fact that the present standard model of QT does not support the terms and concepts required for a proper formulation of the problem. This paper describes a process model for QT with emphasis on Quantum Field Theory (QFT). A process model describes how things work. Usually this implies the chronological order in which things happen. With quantum theory there are many questions which cannot be answered by the present theory or its model. It is claimed that a process model of QT is (a) not yet available, and (b) a prerequisite for solutions to certain open problems of QT, such as the measurement problem. The model is based on QFT with the perturbation (Feynman) approach. Key features of the proposed process model are (1) discrete representation of the QT observables (momentum, position, spin) and of the paths resulting from an interaction (2) particle/wave fluctuations taking the role of virtual particles (3) transition from probabilities to facts which is not tied to measurements (4) path collections in support of entanglement. In contrast to the standard theory of QT/QFT, process models are hard to describe in terms of the purely axiomatic mathematics and hard to evaluate by only derivations of mathematical formulas. In order to enable an evaluation of the proposed process model, including showing compatibility with the predictions of standard QFT, a computer program has been implemented which supports both, standard QFT and the proposed process model.

•Jan 1, 2012•0 citations

A Functional Interpretation Of Quantum Theory

Hans H. Diel

In this paper a functional interpretation of quantum theory (QT) with emphasis on quantum field theory (QFT) is proposed. Besides the usual statements on relations between a functions initial state and final state, a functional interpretation also contains a description of the dynamic evolution of the function. That is, it describes how things function. The proposed functional interpretation of QT/QFT has been developed in the context of the author-s work towards a computer model of QT with the goal of supporting the largest possible scope of QT concepts. In the course of this work, the author encountered a number of problems inherent in the translation of quantum physics into a computer program. He came to the conclusion that the goal of supporting the major QT concepts can only be satisfied, if the present model of QT is supplemented by a "functional interpretation" of QT/QFT. The paper describes a proposal for that

World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering•Feb 21, 2013•5 citations

Quantum Mechanics and Quantum Field Theory: Algebraic and Geometric Approaches

Igor Frolov, Albert S. Schwarz

This is a non-standard exposition of the main notions of quantum mechanics and quantum field theory, including recent results. It is based on the algebraic approach in which the starting point is a star-algebra and on the geometric approach in which the starting point is a convex set of states. Standard formulas for quantum probabilities are derived from decoherence. This derivation allows us to go beyond quantum theory in the geometric approach. Particles are defined as elementary excitations of the ground state (and quasiparticles as elementary excitations of any translation invariant state). The conventional scattering matrix does not work for quasiparticles (or even for particles if the theory does not have particle interpretation). The analysis of scattering in these cases is based on the notion of an inclusive scattering matrix, which is closely related to inclusive cross-sections. It is proven that the conventional scattering matrix can be expressed in terms of Green functions (LSZ formula) and the inclusive scattering matrix can be expressed in terms of generalized Green functions that appear in the Keldysh formalism of non-equilibrium statistical physics. The derivation of the expression of the evolution operator and other physical quantities in terms of functional integrals is based on the notion of the symbol of an operator; these arguments can be applied in the geometric approach as well. In particular, this result can be used to provide a simple derivation of the diagram technique for generalized Green functions. The notion of an inclusive scattering matrix makes sense in the geometric approach, although it seems that a definition of the conventional scattering matrix cannot be provided in this situation. The geometric approach is used to show that quantum mechanics and its generalizations can be considered as classical theories where our devices are able to measure only a part of the observables.

arXiv:2301.03804•Universe•Jul 17, 2023•2 citations

Quantum simulation of scattering amplitudes and interferences in perturbative QCD

Herschel A. Chawdhry, Mathieu Pellen, Simon Williams

A flagship application of quantum computers is the simulation of other quantum systems, including quantum field theories. In this article, we show how quantum computers can be employed to naturally calculate Feynman diagrams and their interferences in Quantum Chromodynamics (QCD). We simulate the colour parts of the interactions directly on the quantum computer, while the kinematic parts are for now pre-computed classically. For processes where some of the external particles are identical, we find the first hints of a potential quantum advantage. We validate our techniques using simulated quantum computers. Furthermore, for toy examples we also demonstrate our algorithms on a 56-qubit trapped-ion quantum computer. The work constitutes a further key step towards a full quantum simulation of generic perturbative QCD processes.

arXiv:2507.07194•Jul 9, 2025•0 citations

Quantum simulation of scattering amplitudes and interferences in perturbative QCD

Herschel A. Chawdhry, Mathieu Pellen, Simon Williams

Abstract A flagship application of quantum computers is the simulation of other quantum systems, including quantum field theories. In this article, we show how quantum computers can be employed to naturally calculate Feynman diagrams and their interferences in Quantum Chromodynamics (QCD). We simulate the colour parts of the interactions directly on the quantum computer, while the kinematic parts are for now pre-computed classically. For processes where some of the external particles are identical, we find the first hints of a potential quantum advantage. We validate our techniques using simulated quantum computers. Furthermore, for toy examples we also demonstrate our algorithms on a 56-qubit trapped-ion quantum computer. The work constitutes a further key step towards a full quantum simulation of generic perturbative QCD processes.

The European Physical Journal C•Aug 11, 2026•0 citations

Physics as quantum information processing: Quantum fields as quantum automata

Giacomo Mauro D’Ariano

Can we reduce Quantum Field Theory (QFT) to a quantum computation? Can physics be simulated by a quantum computer? Do we believe that a quantum field is ultimately made of a numerable set of quantum systems that are unitarily interacting? A positive answer to these questions corresponds to substituting QFT with a theory of quantum cellular automata (QCA), and the present work is examining this hypothesis. These investigations are part of a large research program on a quantum-digitalization of physics, with Quantum Theory as a special theory of information, and Physics as emergent from the same quantum-information processing. A QCA-based QFT has tremendous potential advantages compared to QFT, being quantum ab-initio and free from the problems plaguing QFT due to the continuum hypothesis. Here I will show how dynamics emerges from the quantum processing, how the QCA can reproduce the Dirac-field phenomenology at large scales, and the kind of departures from QFT that that should be expected at a Planckscale discreteness. I will introduce the notions of linear field quantum automaton and local-matrix quantum automaton, in terms of which I will provide the solution to the Feynman's problem about the possibility of simulating a Fermi field with a quantum computer.

AIP conference proceedings•Jan 1, 2012•10 citations
This paper describes a computer model of Quantum Field Theory (QFT), referred to in this paper as QTModel. After specifying the initial configuration for a QFT process (e.g. scattering) the model generates the possible applicable processes in terms of Feynman diagrams, the equations for the scattering matrix, and evaluates probability amplitudes for the scattering matrix and cross sections. The computations of probability amplitudes are performed numerically. The equations generated by QTModel are provided for demonstration purposes only. They are not directly used as the base for the computations of probability amplitudes. The computer model supports two modes for the computation of the probability amplitudes: (1) computation according to standard QFT, and (2) computation according to a proposed functional interpretation of quantum theory.
Theories on physics areas may be understood as models of real world phenomena. They explain a large part of the reality, but they usually do not achieve to explain all details and all aspects of the subject. The type of model chosen for the formulation of a theory determines largely the kind of questions which can be answered by the theory. As an example, the inability to provide a satisfactory answer to the Quantum Theory (QT) measurement problem (or the denial of the problem) is claimed to be largely a consequence of the fact that the present standard model of QT does not support the terms and concepts required for a proper formulation of the problem. This paper describes a process model for QT with emphasis on Quantum Field Theory (QFT). A process model describes how things work. Usually this implies the chronological order in which things happen. With quantum theory there are many questions which cannot be answered by the present theory or its model. It is claimed that a process model of QT is (a) not yet available, and (b) a prerequisite for solutions to certain open problems of QT, such as the measurement problem. The model is based on QFT with the perturbation (Feynman) approach. Key features of the proposed process model are (1) discrete representation of the QT observables (momentum, position, spin) and of the paths resulting from an interaction (2) particle/wave fluctuations taking the role of virtual particles (3) transition from probabilities to facts which is not tied to measurements (4) path collections in support of entanglement. In contrast to the standard theory of QT/QFT, process models are hard to describe in terms of the purely axiomatic mathematics and hard to evaluate by only derivations of mathematical formulas. In order to enable an evaluation of the proposed process model, including showing compatibility with the predictions of standard QFT, a computer program has been implemented which supports both, standard QFT and the proposed process model.
In this paper a functional interpretation of quantum theory (QT) with emphasis on quantum field theory (QFT) is proposed. Besides the usual statements on relations between a functions initial state and final state, a functional interpretation also contains a description of the dynamic evolution of the function. That is, it describes how things function. The proposed functional interpretation of QT/QFT has been developed in the context of the author-s work towards a computer model of QT with the goal of supporting the largest possible scope of QT concepts. In the course of this work, the author encountered a number of problems inherent in the translation of quantum physics into a computer program. He came to the conclusion that the goal of supporting the major QT concepts can only be satisfied, if the present model of QT is supplemented by a "functional interpretation" of QT/QFT. The paper describes a proposal for that
This is a non-standard exposition of the main notions of quantum mechanics and quantum field theory, including recent results. It is based on the algebraic approach in which the starting point is a star-algebra and on the geometric approach in which the starting point is a convex set of states. Standard formulas for quantum probabilities are derived from decoherence. This derivation allows us to go beyond quantum theory in the geometric approach. Particles are defined as elementary excitations of the ground state (and quasiparticles as elementary excitations of any translation invariant state). The conventional scattering matrix does not work for quasiparticles (or even for particles if the theory does not have particle interpretation). The analysis of scattering in these cases is based on the notion of an inclusive scattering matrix, which is closely related to inclusive cross-sections. It is proven that the conventional scattering matrix can be expressed in terms of Green functions (LSZ formula) and the inclusive scattering matrix can be expressed in terms of generalized Green functions that appear in the Keldysh formalism of non-equilibrium statistical physics. The derivation of the expression of the evolution operator and other physical quantities in terms of functional integrals is based on the notion of the symbol of an operator; these arguments can be applied in the geometric approach as well. In particular, this result can be used to provide a simple derivation of the diagram technique for generalized Green functions. The notion of an inclusive scattering matrix makes sense in the geometric approach, although it seems that a definition of the conventional scattering matrix cannot be provided in this situation. The geometric approach is used to show that quantum mechanics and its generalizations can be considered as classical theories where our devices are able to measure only a part of the observables.
A flagship application of quantum computers is the simulation of other quantum systems, including quantum field theories. In this article, we show how quantum computers can be employed to naturally calculate Feynman diagrams and their interferences in Quantum Chromodynamics (QCD). We simulate the colour parts of the interactions directly on the quantum computer, while the kinematic parts are for now pre-computed classically. For processes where some of the external particles are identical, we find the first hints of a potential quantum advantage. We validate our techniques using simulated quantum computers. Furthermore, for toy examples we also demonstrate our algorithms on a 56-qubit trapped-ion quantum computer. The work constitutes a further key step towards a full quantum simulation of generic perturbative QCD processes.
Abstract A flagship application of quantum computers is the simulation of other quantum systems, including quantum field theories. In this article, we show how quantum computers can be employed to naturally calculate Feynman diagrams and their interferences in Quantum Chromodynamics (QCD). We simulate the colour parts of the interactions directly on the quantum computer, while the kinematic parts are for now pre-computed classically. For processes where some of the external particles are identical, we find the first hints of a potential quantum advantage. We validate our techniques using simulated quantum computers. Furthermore, for toy examples we also demonstrate our algorithms on a 56-qubit trapped-ion quantum computer. The work constitutes a further key step towards a full quantum simulation of generic perturbative QCD processes.
Can we reduce Quantum Field Theory (QFT) to a quantum computation? Can physics be simulated by a quantum computer? Do we believe that a quantum field is ultimately made of a numerable set of quantum systems that are unitarily interacting? A positive answer to these questions corresponds to substituting QFT with a theory of quantum cellular automata (QCA), and the present work is examining this hypothesis. These investigations are part of a large research program on a quantum-digitalization of physics, with Quantum Theory as a special theory of information, and Physics as emergent from the same quantum-information processing. A QCA-based QFT has tremendous potential advantages compared to QFT, being quantum ab-initio and free from the problems plaguing QFT due to the continuum hypothesis. Here I will show how dynamics emerges from the quantum processing, how the QCA can reproduce the Dirac-field phenomenology at large scales, and the kind of departures from QFT that that should be expected at a Planckscale discreteness. I will introduce the notions of linear field quantum automaton and local-matrix quantum automaton, in terms of which I will provide the solution to the Feynman's problem about the possibility of simulating a Fermi field with a quantum computer.