Gauge-invariant quantum circuits for U (1) and Yang-Mills lattice gauge theories

@article{Mazzola2021GaugeinvariantQC,
  title={Gauge-invariant quantum circuits for 
U
(1) and Yang-Mills lattice gauge theories},
  author={Giulia Mazzola and Simon V. Mathis and Guglielmo Mazzola and Ivano Tavernelli},
  journal={Physical Review Research},
  year={2021}
}
Quantum computation represents an emerging framework to solve lattice gauge theories (LGT) with arbitrary gauge groups, a general and long-standing problem in computational physics. While quantum computers may encode LGT using only polynomially increasing resources, a major openissue concerns the violation of gauge-invariance during the dynamics and the search for groundstates. Here, we propose a new class of parametrized quantum circuits that can represent states belonging only to the physical… 

Figures from this paper

Dynamical quantum phase transitions in a noisy lattice gauge theory
Lattice gauge theories (LGTs) form an intriguing class of theories highly relevant to both high-energy particle physics and low-energy condensed matter physics with the rapid development of
Tunable Confinement-Deconfinement Transition in an Ultracold Atom Quantum Simulator
The one-dimensional lattice Schwinger model has recently been realized by using bosons in optical lattices. This model contains both confinement and deconfinement phases, whose phase diagram is
Orders of magnitude reduction in the computational overhead for quantum many-body problems on quantum computers via an exact transcorrelated method
Igor O. Sokolov, ∗ Werner Dobrautz, 3, † Hongjun Luo, ‡ Ali Alavi, 4, § and Ivano Tavernelli ¶ IBM Quantum, IBM Research Zurich, Switzerland Max Planck Institute for Solid State Research,
Matrix-Model Simulations Using Quantum Computing, Deep Learning, and Lattice Monte Carlo
1 Physics Department, University of Michigan, Ann Arbor, Michigan 48109, USA 2 Theoretical Quantum Physics Laboratory, Cluster for Pioneering Research, RIKEN, Wako, Saitama 351-0198, Japan 3
Strategies for the Determination of the Running Coupling of $(2+1)$-dimensional QED with Quantum Computing
TLDR
This paper provides the setup for the quantum computation and shows results for the mass gap and the plaquette expectation value, and discusses some ideas that can be applied to the computation of the running coupling.

References

SHOWING 1-10 OF 82 REFERENCES
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.
Toward scalable simulations of lattice gauge theories on quantum computers
The simulation of real-time dynamics in lattice gauge theories is particularly hard for classical computing due to the exponential scaling of the required resources. On the other hand, quantum
Gauss’s law, duality, and the Hamiltonian formulation of U(1) lattice gauge theory
Quantum computers have the potential to explore the vast Hilbert space of entangled states that play an important role in the behavior of strongly interacting matter. This opportunity motivates
A scalable realization of local U(1) gauge invariance in cold atomic mixtures
TLDR
A scalable analog quantum simulator of a U(1) gauge theory in one spatial dimension is proposed using interspecies spin-changing collisions in an atomic mixture to achieve gauge-invariant interactions between matter and gauge fields with spin- and species-independent trapping potentials.
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. Future
Observation of gauge invariance in a 71-site Bose-Hubbard quantum simulator.
TLDR
The quantum simulation of an extended U(1) lattice gauge theory is reported, and the degree to which Gauss's law is violated is measured by extracting probabilities of locally gauge-invariant states from correlated atom occupations, providing a way to explore gauge symmetry in the interplay of fundamental particles using controllable large-scale quantum simulators.
Self-verifying variational quantum simulation of lattice models
TLDR
Experiments are presented that demonstrate self-verifying, hybrid, variational quantum simulation of lattice models in condensed matter and high-energy physics, enabling the study of a wide variety of previously intractable target models.
Gauge-Symmetry Protection Using Single-Body Terms
Quantum-simulator hardware promises new insights into problems from particle and nuclear physics. A major challenge is to reproduce gauge invariance, as violations of this quintessential property of
Quantum simulations of gauge theories with ultracold atoms: Local gauge invariance from angular-momentum conservation
Quantum simulations of High Energy Physics, and especially of gauge theories, is an emerging and exciting direction in quantum simulations. However, simulations of such theories, compared to
...
...