Gauge Field

1+1 (QED) Lattice field

Quantum localization bounds Trotter errors in digital quantum simulation appendix

The lattice Schwinger model of 1+1D quantum electrodynamics (QED) can be described by the Hamiltonian (with spin system) \(H_{sm}=H_{\pm}+H_Z\) where

\[ H_{\pm} = \sum_{l=1}^{n-1} H_{\pm}^l, \; H_{\pm}^l = \frac{w}{2} [X_l X_{l+1}+ Y_l Y_{l+1}] \]

and

\[ H_Z = \frac{m}{2} \sum_{l=1}^n (-1)^l Z_l + J \sum_{l=1}^n L_l^2, \; L_n = \frac{1}{2} [Z_l + (-1)^l] \]

Here, \(m\) is the rest mass of the fermionic particles and anti-particles, and \(w\) describes their kinetic energy. The term proportional to \(J\) is the energy of the U(1) gauge fields.

Real-time dynamics of lattice gauge theories with a few-qubit quantum computer

The vacuum decay continuously produces entanglement, as particles and antiparticles are constantly generated and propagate away from each other, thus correlating distant parts of the system. Entanglement plays a crucial role in the characterization of dynamical processes in quantum many-body systems, and its analysis permits us to quantify the quantum character of the generated correlations.

QCD

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