Analytic Filter Function Derivatives for Quantum Optimal Control

TL;DR

This paper introduces analytically derived filter function gradients for quantum optimal control, enabling faster and more efficient design of control pulses in the presence of auto-correlated noise.

Contribution

It presents the first analytical expressions for filter function derivatives, improving the efficiency of quantum gate optimization under noise.

Findings

Gradient-based optimization is about 100 times faster than gradient-free methods.

The analytical gradients enable more efficient quantum control pulse design.

The implementation is modular and compatible with existing quantum control software.

Abstract

Auto-correlated noise appears in many solid state qubit systems and hence needs to be taken into account when developing gate operations for quantum information processing. However, explicitly simulating this kind of noise is often less efficient than approximate methods. Here, we focus on the filter function formalism, which allows the computation of gate fidelities in the presence of auto-correlated classical noise. Hence, this formalism can be combined with optimal control algorithms to design control pulses, which optimally implement quantum gates. To enable the use of gradient-based algorithms with fast convergence, we present analytically derived filter function gradients with respect to control pulse amplitudes, and analyze the computational complexity of our results. When comparing pulse optimization using our derivatives to a gradient-free approach, we find that the gradient-based method is roughly two orders of magnitude faster for our test cases. We also provide a modular computational implementation compatible with quantum optimal control packages.