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

Journal of computing sciences in colleges

Scalable computational methods in quantum field theory

Jason Slaunwhite

Published May 1, 2004• 0 citations
OpenAlex

Abstract

Matrix eigenvalue problems arise in several areas of science and engineering. Particle physicists, in particular, are interested in solving eigenvalue problems that describe relativistic subatomic interactions. Quantum field theory provides a formal mathematical approach for specifying the eigenvalue problems, but it also introduces some complications. A particularly problematic complication is accounting for an infinite number of particles. It is not necessary to deal practically with infinities: the system maybe truncated to a discrete number. In the case of strong coupling, however, it is inaccurate to truncate at small particle numbers. Scalable computational methods are vital to the exploration of quantum field theory since they facilitate inclusion of increasing numbers of particles.

Related papers

Quantum Algorithms for Quantum Field Theories

Stephen P. Jordan, Keith S. M. Lee, John P. Preskill

Quantum Leap? Quantum computers are expected to be able to solve some of the most difficult problems in mathematics and physics. It is not known, however, whether quantum field theories (QFTs) can be simulated efficiently with a quantum computer. QFTs are used in particle and condensed matter physics and have an infinite number of degrees of freedom; discretization is necessary to simulate them digitally. Jordan et al. (p. 1130 ; see the Perspective by Hauke et al. ) present an algorithm for the efficient simulation of a particular kind of QFT (with quartic interactions) and estimate the error caused by discretization. Even for the most difficult case of strong interactions, the run time of the algorithm was polynomial (rather than exponential) in parameters such as the number of particles, their energy, and the prescribed precision, making it much more efficient than the best classical algorithms.

arXiv:1111.3633•Science•May 31, 2012•519 citations

A nonperturbative coupled-cluster method for quantum field theories

John R. Hiller

The nonperturbative Hamiltonian eigenvalue problem for bound states of a quantum field theory is formulated in terms of Dirac's light-front coordinates and then approximated by the exponential operator technique of the many-body coupled-cluster method. This approximation eliminates any need for the usual approximation of Fock-space truncation. Instead, the exponentiated operator is truncated, and the terms retained are determined by a set of nonlinear integral equations. These equations are solved simultaneously with an effective eigenvalue problem in the valence sector, where the number of constituents is small. Matrix elements can be calculated, with extensions of techniques from many-body coupled-cluster theory, to obtain form factors and other observables.

arXiv:1208.6503•AIP conference proceedings•Jan 1, 2013•0 citations

A Theory of Quantum Subspace Diagonalization

Ethan N. Epperly, Lin Lin, Yuji Nakatsukasa

Quantum subspace diagonalization methods are an exciting new class of algorithms for solving large-scale eigenvalue problems using quantum computers. Unfortunately, these methods require the solution of an ill-conditioned generalized eigenvalue problem, with a matrix pencil corrupted by a nonnegligible amount of noise that is far above the machine precision. Despite pessimistic predictions from classical worst-case perturbation theories, these methods can perform reliably well if the generalized eigenvalue problem is solved using a standard truncation strategy. By leveraging and advancing classical results in matrix perturbation theory, we provide a theoretical analysis of this surprising phenomenon, proving that under certain natural conditions, a quantum subspace diagonalization algorithm can accurately compute the smallest eigenvalue of a large Hermitian matrix. We give numerical experiments demonstrating the effectiveness of the theory and providing practical guidance for the choice of truncation level. Our new results can also be of independent interest to solving eigenvalue problems outside the context of quantum computation.

arXiv:2110.07492•SIAM Journal on Matrix Analysis and Applications•Aug 1, 2022•67 citations

Nonperturbative Methods in Quantum Field Theory

Ivan Kukuljan

<!--HTML-->Hamiltonian truncation methods represent a powerful toolbox for a set of problems that are otherwise very challenging in strongly coupled quantum field theory: nonequilibrium physics and real time evolution. In many such cases analytical approaches are limited as well as numerical tools like lattice gauge theory and tensor networks. I will talk about recent developments in this field with emphasis to entanglement properties of QFT, connection to ultra cold atomic simulators and exploring new fundamental phenomena.

•Jan 1, 2022•0 citations

Title: Modular Quantum Field Theory for Quantum Simulation of Complex Phenomena

Jincheng Zhang

This paper presents a novel framework for constructing modular quantum field theories (QFTs) designed to facilitate efficient simulation of complex quantum phenomena. Traditional QFTs often struggle with scalability and complex dynamics, hindering their application to real-world problems. This work proposes a method of representing QFTs as a collection of interconnected modules, each representing a fundamental physical process. The resulting system offers significant advantages in terms of simulation, analysis, and adaptability, paving the way for breakthroughs in areas such as condensed matter physics, materials science, and quantum computing. We explore the design principles and mathematical foundations of this approach, demonstrating its potential to overcome limitations inherent in existing QFT techniques. This paper provides a comprehensive overview of the proposed framework and its implications for future research.

•Sep 4, 2026•0 citations

FEATURES OF THE COMPUTATIONAL TECHNIQUES IN THE QUANTUM FIELD THEORY

A. L. Bugrimov, Nikolai Vital’evich Zverev

The computational techniques in the quantum field theory are compared with the ordinary numerical methods in the system analysis, information management and processing.In the course of comparison, coinciding and partially coinciding computational principles and techniques in these sciences have been found.In addition, a number of features of the computational methods related only to the quantum field theory are observed.These features are noted to reflect the basic principles of the quantum field theory and the physics of elementary particles.

Bulletin of the Moscow State Regional University (Physics and mathematics)•Jan 1, 2016•0 citations
Matrix eigenvalue problems arise in several areas of science and engineering. Particle physicists, in particular, are interested in solving eigenvalue problems that describe relativistic subatomic interactions. Quantum field theory provides a formal mathematical approach for specifying the eigenvalue problems, but it also introduces some complications. A particularly problematic complication is accounting for an infinite number of particles. It is not necessary to deal practically with infinities: the system maybe truncated to a discrete number. In the case of strong coupling, however, it is inaccurate to truncate at small particle numbers. Scalable computational methods are vital to the exploration of quantum field theory since they facilitate inclusion of increasing numbers of particles.
Quantum Leap? Quantum computers are expected to be able to solve some of the most difficult problems in mathematics and physics. It is not known, however, whether quantum field theories (QFTs) can be simulated efficiently with a quantum computer. QFTs are used in particle and condensed matter physics and have an infinite number of degrees of freedom; discretization is necessary to simulate them digitally. Jordan et al. (p. 1130 ; see the Perspective by Hauke et al. ) present an algorithm for the efficient simulation of a particular kind of QFT (with quartic interactions) and estimate the error caused by discretization. Even for the most difficult case of strong interactions, the run time of the algorithm was polynomial (rather than exponential) in parameters such as the number of particles, their energy, and the prescribed precision, making it much more efficient than the best classical algorithms.
The nonperturbative Hamiltonian eigenvalue problem for bound states of a quantum field theory is formulated in terms of Dirac's light-front coordinates and then approximated by the exponential operator technique of the many-body coupled-cluster method. This approximation eliminates any need for the usual approximation of Fock-space truncation. Instead, the exponentiated operator is truncated, and the terms retained are determined by a set of nonlinear integral equations. These equations are solved simultaneously with an effective eigenvalue problem in the valence sector, where the number of constituents is small. Matrix elements can be calculated, with extensions of techniques from many-body coupled-cluster theory, to obtain form factors and other observables.
Quantum subspace diagonalization methods are an exciting new class of algorithms for solving large-scale eigenvalue problems using quantum computers. Unfortunately, these methods require the solution of an ill-conditioned generalized eigenvalue problem, with a matrix pencil corrupted by a nonnegligible amount of noise that is far above the machine precision. Despite pessimistic predictions from classical worst-case perturbation theories, these methods can perform reliably well if the generalized eigenvalue problem is solved using a standard truncation strategy. By leveraging and advancing classical results in matrix perturbation theory, we provide a theoretical analysis of this surprising phenomenon, proving that under certain natural conditions, a quantum subspace diagonalization algorithm can accurately compute the smallest eigenvalue of a large Hermitian matrix. We give numerical experiments demonstrating the effectiveness of the theory and providing practical guidance for the choice of truncation level. Our new results can also be of independent interest to solving eigenvalue problems outside the context of quantum computation.
<!--HTML-->Hamiltonian truncation methods represent a powerful toolbox for a set of problems that are otherwise very challenging in strongly coupled quantum field theory: nonequilibrium physics and real time evolution. In many such cases analytical approaches are limited as well as numerical tools like lattice gauge theory and tensor networks. I will talk about recent developments in this field with emphasis to entanglement properties of QFT, connection to ultra cold atomic simulators and exploring new fundamental phenomena.
This paper presents a novel framework for constructing modular quantum field theories (QFTs) designed to facilitate efficient simulation of complex quantum phenomena. Traditional QFTs often struggle with scalability and complex dynamics, hindering their application to real-world problems. This work proposes a method of representing QFTs as a collection of interconnected modules, each representing a fundamental physical process. The resulting system offers significant advantages in terms of simulation, analysis, and adaptability, paving the way for breakthroughs in areas such as condensed matter physics, materials science, and quantum computing. We explore the design principles and mathematical foundations of this approach, demonstrating its potential to overcome limitations inherent in existing QFT techniques. This paper provides a comprehensive overview of the proposed framework and its implications for future research.
The computational techniques in the quantum field theory are compared with the ordinary numerical methods in the system analysis, information management and processing.In the course of comparison, coinciding and partially coinciding computational principles and techniques in these sciences have been found.In addition, a number of features of the computational methods related only to the quantum field theory are observed.These features are noted to reflect the basic principles of the quantum field theory and the physics of elementary particles.