Simulating lattice gauge theories on a quantum computer (熱場の量子論とその応用)

@inproceedings{Byrnes2006SimulatingLG,
  title={Simulating lattice gauge theories on a quantum computer (熱場の量子論とその応用)},
  author={Tim Byrnes and Yoshihisa Yamamoto},
  year={2006}
}
We examine the problem of simulating lattice gauge theories on a universal quantum computer. The basic strategy of our approach is to transcribe lattice gauge theories in the Hamiltonian formulation into a Hamiltonian involving only Pauli spin operators such that the simulation can be performed on a quantum computer using only one- and two-qubit manipulations. We examine three models, the U(1), SU(2), and SU(3) lattice gauge theories, which are transcribed into a spin Hamiltonian up to a cutoff… Expand

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References

SHOWING 1-10 OF 50 REFERENCES
Quantum link models: A discrete approach to gauge theories☆
We construct lattice gauge theories in which the elements of the link matrices are represented by non-commuting operators acting in a Hilbert space. These quantum link models are related to ordinaryExpand
An introduction to lattice gauge theory and spin systems
This article is an interdisciplinary review of lattice gauge theory and spin systems. It discusses the fundamentals, both physics and formalism, of these related subjects. Spin systems are models ofExpand
Quantum algorithms for fermionic simulations
We investigate the simulation of fermionic systems on a quantum computer. We show in detail how quantum computers avoid the dynamical sign problem present in classical simulations of these systems,Expand
Algebraic approach to interacting quantum systems
We present an algebraic framework for interacting extended quantum systems to study complex phenomena characterized by the coexistence and competition of different states of matter. We start byExpand
Guided random walks for solving Hamiltonian lattice gauge theories
Abstract Motivated by developments for many-particle quantum systems, a Monte Carlo method for solving Hamiltonian lattice gauge theories without fermions is presented in which a stochastic randomExpand
Simulating physical phenomena by quantum networks
Physical systems, characterized by an ensemble of interacting constituents, can be represented and studied by different algebras of operators (observables). For example, a fully polarized electronicExpand
Atomic quantum simulator for lattice gauge theories and ring exchange models.
TLDR
A setup where this coupling term may allow for the realization and observation of exotic quantum phases, including a deconfined insulator described by the Coulomb phase of a three-dimensional U(1) lattice gauge theory is discussed. Expand
Hamiltonian Formulation of Wilson's Lattice Gauge Theories
Wilson's lattice gauge model is presented as a canonical Hamiltonian theory. The structure of the model is reduced to the interactions of an infinite collection of coupled rigid rotators. TheExpand
Application of the Green's-function Monte Carlo method to the compact Abelian lattice gauge theory
We have applied the Green's-function Monte Carlo (GFMC) method to the Hamiltonian formulation of the compact U(1) lattice gauge theory in three and two (space) dimensions on small lattices, 3 x 3 x 3Expand
The density-matrix renormalization group
The density-matrix renormalization group (DMRG) is a numerical algorithm for the efficient truncation of the Hilbert space of low-dimensional strongly correlated quantum systems based on a ratherExpand
...
1
2
3
4
5
...