Abstract
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 sector of the total Hilbert space. This class of circuits is compact yet flexible enough to be used as a variational ansatz to study ground state properties, as well as representing states originating from a real-time dynamics. Concerning the first application, the structure of the wavefunction ansatz guarantees the preservation of physical constraints such as the Gauss law along the entire optimization process, enabling reliable variational calculations. As for the second application, this class of quantum circuits can be used in combination with timedependent variational quantum algorithms, thus drastically reducing the resource requirements to access dynamical properties.
Highlights
Gauge theories lie at the heart of the standard model of particle physics and represent the most successful description of elementary particles and their fundamental interactions [1,2]
These theories represent a generalization of quantum electrodynamics (QED) which elucidates the behavior of charged particles and photons, and quantum chromodynamics (QCD) which describes the strong interactions between quarks, the elementary constituents of protons and neutrons
We specialize to the U (1) case of the Yang-Mills model (1), and study the phenomenon of string breaking in (1+1)- and (2+1)-dimensional lattice QED which is reminiscent of confinement in QCD
Summary
Gauge theories lie at the heart of the standard model of particle physics and represent the most successful description of elementary particles and their fundamental interactions [1,2]. These theories represent a generalization of quantum electrodynamics (QED) which elucidates the behavior of charged particles and photons, and quantum chromodynamics (QCD) which describes the strong interactions between quarks, the elementary constituents of protons and neutrons. QCD can be studied perturbatively in the limit of high energy while in the low-energy regime, the strong interactions grow so large that a perturbative analysis is not possible anymore.
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