Precision of electromagnetic control of a quantum system

TL;DR

This paper develops a diagrammatic formalism to analyze the quantum noise in electromagnetic control of a two-level quantum system, providing insights into decoherence and relaxation relevant for fault-tolerant quantum computing.

Contribution

It introduces a new diagrammatic approach to evaluate quantum noise in TLS under optical control, extending from Markovian to non-Markovian regimes without stochastic assumptions.

Findings

Quantitative evaluation of quantum noise for small times

Extension of the model to non-Markovian dynamics

Identification of coherent Rabi oscillations and relaxation processes

Abstract

Coherent control of a spin is limited by both the decoherence due to coupling with the environment and noise coming from the quantized control. The quantum noise study of this system is particularly important in fault tolerant quantum computation where a very high fidelity is demanded. Here, we present a time evolution study of a two level system (TLS) interacting with a laser pulse and the electromagnetic vacuum based on the multimode Jaynes-Cummings model. We develop a diagrammatic formalism in which one can easily identify the coherent Rabi oscillation of the TLS and its relaxation from corresponding diagrams. In the small time limit ($t\ll T_1$), where the noise level is small but still an issue to fault tolerant quantum computing, this method gives a quantitative evaluation of the quantum noise of the TLS under an optical control with an arbitrary pulse shape. Furthermore, this approach can be naturally extended from the Markovian to the non-Markovian regime, resulting in dynamics different from that obtained in the optical Bloch analysis. All these calculations are done without any stochastic assumption.