Analytic Filter-Function Derivatives for Quantum Optimal Control

Physical Review Applied, vol. 17

Abstract

Autocorrelated 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 autocorrelated 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 2 orders of magnitude faster for our test cases. We also provide a modular computational implementation compatible with quantum optimal control packages.

Authors 5

1. Isabel Nha Minh Le Aachen JARA-FIT Institute for Quantum Information

   Forschungszentrum Jülich · Jülich Aachen Research Alliance · RWTH Aachen University

   Affiliation as printed

   JARA-FIT Institute for Quantum Information, Forschungszentrum Jülich GmbH and RWTH Aachen University, 52074 Aachen, Germany

2. Julian D. Teske Aachen JARA-FIT Institute for Quantum Information

   Forschungszentrum Jülich · Jülich Aachen Research Alliance · RWTH Aachen University

   Affiliation as printed

   JARA-FIT Institute for Quantum Information, Forschungszentrum Jülich GmbH and RWTH Aachen University, 52074 Aachen, Germany

3. Tobias Hangleiter Aachen JARA-FIT Institute for Quantum Information

   Forschungszentrum Jülich · Jülich Aachen Research Alliance · RWTH Aachen University

   Affiliation as printed

   JARA-FIT Institute for Quantum Information, Forschungszentrum Jülich GmbH and RWTH Aachen University, 52074 Aachen, Germany

4. Pascal Cerfontaine Aachen JARA-FIT Institute for Quantum Information

   Forschungszentrum Jülich · Jülich Aachen Research Alliance · RWTH Aachen University

   Affiliation as printed

   JARA-FIT Institute for Quantum Information, Forschungszentrum Jülich GmbH and RWTH Aachen University, 52074 Aachen, Germany

5. Hendrik Bluhm Aachen JARA-FIT Institute for Quantum Information

   Forschungszentrum Jülich · Jülich Aachen Research Alliance · RWTH Aachen University

   Affiliation as printed

   JARA-FIT Institute for Quantum Information, Forschungszentrum Jülich GmbH and RWTH Aachen University, 52074 Aachen, Germany