Analytic Filter Function Derivatives for Quantum Optimal Control

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.

Revised arguments in section 7, results unchanged. 13 pages, 7 figures. Open-source software available at https://github.com/qutech/filter_functions

References in corpus (8)

• The Magnus expansion and some of its applications
• Dynamical decoupling and noise spectroscopy with a superconducting flux qubit
• Experimental noise filtering by quantum control
• Low-frequency spin qubit detuning noise in highly purified ${}^{28}$Si/SiGe
• Robust quantum gates for stochastic time-varying noise
• Noise-compensating pulses for electrostatically controlled silicon spin qubits
• Filter Functions for Quantum Processes under Correlated Noise
• Role of the filter functions in noise spectroscopy

Cited by in corpus (11)

• qopt: An experiment-oriented Qubit Simulation and Quantum Optimal Control Package
• Compensating for non-linear distortions in controlled quantum systems
• Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe
• Quantum simulation of time-dependent Hamiltonians via commutator-free quasi-Magnus operators
• Completely Positive Map for Noisy Driven Quantum Systems Derived by Keldysh Expansion
• Bringing Quantum Systems under Control: A Tutorial Invitation to Quantum Computing and Its Relation to Bilinear Control Systems
• Expedited Noise Spectroscopy of Transmon Qubits
• An automated geometric space curve approach for designing dynamically corrected gates
• Enhanced Quantum Signal Control and Sensing Under Multicolored Noise via Generalized Filter Function Framework
• Filter Function Formalism and Software Package to Compute Quantum Processes of Gate Sequences for Classical Non-Markovian Noise
• Evolutionary reduction of the laser noise impact on quantum gates