Robustness Analysis for Quantum Systems Controlled by Continuous-Time Pulses

Abstract

Differential sensitivity techniques originally developed to study the robustness of energy landscape controllers are generalized to the important case of closed quantum systems subject to continuously varying controls. Vanishing sensitivity to parameter variation is shown to coincide with perfect fidelity, as was the case for time-invariant controls. Upper bounds on the magnitude of the differential sensitivity to any parameter variation are derived based simply on knowledge of the system Hamiltonian and the maximum size of the control inputs.

Figures (2)

• Figure 1: Plot comparing $|\partial_\mu \mathsf{F}_S |$ for $\mu=\set{0,1,2}$ with $\beta$ from Theorem \ref{['theorem: upper_bound_on_sensitivity']}. Though computed only from the nominal system and control data, the bound has an accuracy to within slightly more than one order of magnitude. The controllers are ordered by increasing fidelity so that the controller with index 1 yields the smallest fidelity and that with index 8 yields the greatest.
• Figure 2: Plot of $\beta$ as given in Theorem \ref{['theorem: upper_bound_on_sensitivity']} for the gate synthesis case with $|\partial_\mu \mathsf{F}_S |$ for $\mu=\set{0,1,2}$. The bound $\beta$ predicts the largest sensitivity to collective uncertainty in any of the Hamiltonian matrices to within an order of magnitude. The controllers are ordered by increasing fidelity so that the controller with index 1 yields the smallest fidelity and that with index 15 yields the greatest.

Theorems & Definitions (6)

• Theorem 1
• Corollary 1
• Proposition 1
• proof
• Theorem 2
• proof