σ Models on Quantum Computers.

@article{Alexandru2019MO,
  title={$\sigma$ Models on Quantum Computers.},
  author={Andrei Alexandru and Paulo Bedaque and Henry Lamm and Scott Lawrence},
  journal={Physical review letters},
  year={2019},
  volume={123 9},
  pages={
          090501
        }
}
We formulate a discretization of σ models suitable for simulation by quantum computers. Space is substituted with a lattice, as usually done in lattice field theory, while the target space (a sphere) is replaced by the "fuzzy sphere", a construction well known from noncommutative geometry. Contrary to more naive discretizations of the sphere, in this construction the exact O(3) symmetry is maintained, which suggests that the discretized model is in the same universality class as the continuum… Expand
Gluon field digitization for quantum computers
Simulations of gauge theories on quantum computers require the digitization of continuous field variables. Digitization schemes that uses the minimum amount of qubits are desirable. We present aExpand
State preparation and measurement in a quantum simulation of the O(3) sigma model
Recently, Singh and Chandrasekharan [Phys. Rev. D 100, 054505 (2019)] showed that fixed points of the nonlinear O(3) sigma model can be reproduced near a quantum phase transition of a spin model withExpand
Quantum algorithms for disordered physics
We show how a quantum computer may efficiently simulate a disordered Hamiltonian, by incorporating a pseudo-random number generator directly into the time evolution circuit. This technique is appliedExpand
Negative string tension of higher-charge Schwinger model via digital quantum simulation
We study some properties of generalized global symmetry for the charge-q Schwinger model in the Hamiltonian formalism, which is the (1 + 1)-dimensional quantum electrodynamics with a charge-q DiracExpand
Digital Quantum Simulation of the Schwinger Model with Topological Term via Adiabatic State Preparation
We perform a digital quantum simulation of a gauge theory with a topological term in Minkowski spacetime, which is practically inaccessible by standard lattice Monte Carlo simulations. We focus onExpand
Qubit regularization of the O(3) sigma model
We construct a qubit regularization of the $O(3)$ non-linear sigma model in two and three spatial dimensions using a quantum Hamiltonian with two qubits per lattice site. Using a worldlineExpand
Digital quantum simulation for screening and confinement in gauge theory with a topological term
We perform digital quantum simulation to study screening and confinement in a gauge theory with a topological term, focusing on ($1+1$)-dimensional quantum electrodynamics (Schwinger model) with aExpand
Deeply inelastic scattering structure functions on a hybrid quantum computer
We outline a strategy to compute deeply inelastic scattering structure functions using a hybrid quantum computer. Our approach takes advantage of the representation of the fermion determinant in theExpand
Emergence of Gauss' law in a Z2 lattice gauge theory in 1 + 1 dimensions
Abstract We explore a Z 2 Hamiltonian lattice gauge theory in one spatial dimension with a coupling h, without imposing any Gauss' law constraint. We show that in our model h = 0 is a free deconfinedExpand
Quantum computation of thermal averages in the presence of a sign problem
We illustrate the application of Quantum Computing techniques to the investigation of the thermodynamical properties of a simple system, made up of three quantum spins with frustrated pairExpand
...
1
2
3
...

References

SHOWING 1-10 OF 74 REFERENCES
Quantum Simulation of the Universal Features of the Polyakov Loop.
TLDR
The Abelian Higgs model in 1+1 dimensions is shown to be a prime candidate for an experimental quantum simulation of a lattice gauge theory, and a discrete tensor reformulation is used to smoothly connect the space-time isotropic version used in most numerical lattice simulations to the continuous-time limit corresponding to the Hamiltonian formulation. Expand
Lattice simulations of real-time quantum fields
We investigate lattice simulations of scalar and non-Abelian gauge fields in Minkowski space-time. For SU(2) gauge-theory expectation values of link variables in 3+1 dimensions are constructed by aExpand
Quantum simulation of lattice gauge theories using Wilson fermions
Quantum simulators have the exciting prospect of giving access to real-time dynamics of lattice gauge theories, in particular in regimes that are difficult to compute on classical computers. FutureExpand
Oracles for Gauss's law on digital quantum computers
Formulating a lattice gauge theory using only physical degrees of freedom generically leads to non-local interactions. A local Hamiltonian is desirable for quantum simulation, and this is possible byExpand
Digitizing gauge fields: Lattice Monte Carlo results for future quantum computers
In the near-future noisy intermediate-scale quantum (NISQ) era of quantum computing technology, applications of quantum computing will be limited to calculations of very modest scales in terms of theExpand
Real-time dynamics of lattice gauge theories with a few-qubit quantum computer
TLDR
This work reports the experimental demonstration of a digital quantum simulation of a lattice gauge theory, by realizing (1 + 1)-dimensional quantum electrodynamics (the Schwinger model) on a few-qubit trapped-ion quantum computer and explores the Schwinger mechanism of particle–antiparticle generation by monitoring the mass production and the vacuum persistence amplitude. Expand
Quantum-classical computation of Schwinger model dynamics using quantum computers
We present a quantum-classical algorithm to study the dynamics of the two-spatial-site Schwinger model on IBM's quantum computers. Using rotational symmetries, total charge, and parity, the number ofExpand
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
QCD as a quantum link model
QCD is constructed as a lattice gauge theory in which the elements of the link matrices are represented by non-commuting operators acting in a Hilbert space. The resulting quantum link model for QCDExpand
Gauge-invariant implementation of the Abelian-Higgs model on optical lattices
© 2015 American Physical Society. We present a gauge-invariant effective action for the Abelian-Higgs model (scalar electrodynamics) with a chemical potential μ on a (1+1)-dimensional lattice. ThisExpand
...
1
2
3
4
5
...