Effective Hamiltonian Theory and Its Applications in Quantum Information

TL;DR

This paper introduces a compact formula for deriving effective Hamiltonians that describe the averaged dynamics of detuned and stochastic quantum systems, with applications demonstrated in quantum processes and logic gates.

Contribution

It provides a novel formalism for calculating effective Hamiltonians applicable to both deterministic and stochastic quantum systems.

Findings

Derived a compact formula for effective Hamiltonians

Applied the formalism to Raman processes and Bloch-Siegert shifts

Demonstrated usefulness in quantum logic gate analysis

Abstract

This paper presents a useful compact formula for deriving an effective Hamiltonian describing the time-averaged dynamics of detuned quantum systems. The formalism also works for ensemble-averaged dynamics of stochastic systems. To illustrate the technique we give examples involving Raman processes, Bloch-Siegert shifts and Quantum Logic Gates.