A quantum coupler and the harmonic oscillator interacting with a reservoir: Defining the relative phase gate

Abstract

In order to be able to study dissipation, the interaction between a single system and their environment was introduced in quantum mechanics. Master and quantum Langeving equations was derived. Moreover, decoherence has been studied using this approach. One of the most commonly used model in this research field is a single harmonic oscillator interacting with a reservoir. In this work we analytically solve this model, in the resonance case, using the evolution operator method. Then, we use this result to study a quantum coupler, which is a particular case where there are a finite number of harmonic oscillators interacting with the single one. After that, we focuses in the analisis of the conditional quantum dynamics of the quantum coupler (using the computational basis of two qubits) by choosing a proper interaction time. This conditional dynamics provides a realization of a new quantum phase gate, which we call the relative phase gate. To the best of our knowledge, this phase gate has not been previously defined or proposed.