# 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

#### Supplemental Presentations

#### 82 Citations

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#### References

SHOWING 1-10 OF 50 REFERENCES

Quantum link models: A discrete approach to gauge theories☆

- Physics
- 1997

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 ordinary… Expand

An introduction to lattice gauge theory and spin systems

- Physics
- 1979

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 of… Expand

Quantum algorithms for fermionic simulations

- Physics
- 2001

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

- Physics
- 2004

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 by… Expand

Guided random walks for solving Hamiltonian lattice gauge theories

- Physics
- 1984

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 random… Expand

Simulating physical phenomena by quantum networks

- Physics
- 2002

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 electronic… Expand

Atomic quantum simulator for lattice gauge theories and ring exchange models.

- Physics, Medicine
- Physical review letters
- 2005

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

- Physics
- 1975

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. The… Expand

Application of the Green's-function Monte Carlo method to the compact Abelian lattice gauge theory

- Physics
- 1983

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 3… Expand

The density-matrix renormalization group

- Physics
- 2005

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 rather… Expand