Quantum Electrodynamics of qubits

TL;DR

This paper develops a quantum electrodynamics framework for qubits, using relativistic QED tools like Feynman diagrams to analyze their interaction with electromagnetic fields, providing detailed calculations of polarizability and susceptibility.

Contribution

It introduces a QED-based formalism for two-level systems (qubits), extending relativistic techniques to simplify and clarify their electromagnetic interactions.

Findings

Calculated polarizability and susceptibility up to fourth order perturbation.

Resolved sign and damping ambiguities in phenomenological models.

Extended methods to multi-level systems like atoms with degenerate states.

Abstract

Systematic description of a spin one-half system endowed with magnetic moment or any other two-level system (qubit) interacting with the quantized electromagnetic field is developed. This description exploits a close analogy between a two-level system and the Dirac electron that comes to light when the two-level system is described within the formalism of second quantization in terms of fermionic creation and annihilation operators. The analogy enables one to introduce all the powerful tools of relativistic QED (albeit in a greatly simplified form). The Feynman diagrams and the propagators turn out to be very useful. In particular, the QED concept of the vacuum polarization finds its close counterpart in the photon scattering off a two level-system leading via the linear response theory to the general formulas for the atomic polarizability and the dynamic single spin susceptibility. To illustrate the usefulness of these methods, we calculate the polarizability and susceptibility up to the fourth order of perturbation theory. These {\em ab initio} calculations resolve some ambiguities concerning the sign prescription and the optical damping that arise in the phenomenological treatment. We also show that the methods used to study two-level systems (qubits) can be extended to many-level systems (qudits). As an example, we describe the interaction with the quantized electromagnetic field of an atom with four relevant states: one S state and three degenerate P states.