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Bulletin of the American Physical Society

Filter functions for robust quantum control

Tobias Hangleiter, Julian D. Teske, Isabel Nha Minh Le, Pascal Cerfontaine, Hendrik Bluhm

Published Mar 17, 2021• 0 citations
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Engineering-inspired filter functions are a powerful heuristic for the development of noise-robust quantum logic operations. We expand on existing single-qubit approaches and present a generalized, computationally efficient framework to calculate filter functions for operations performed on D-dimensional manifolds such as pairs of interacting qubits (including spectator levels), and qudits. We describe two applications of the generalized filter functions to superconducting qubits: 1. The design of robust controls for parametric gates. 2. Using entangled states as a probe for noise characterization.
The performance of quantum processors in the noisy intermediate-scale quantum (NISQ) era is severely constrained by environmental noise and other uncertainties. While the recently proposed quantum control robustness landscape (QCRL) offers a powerful framework for generating robust control pulses for parametric gate families, its application has been practically restricted to quasi-static noise. To address the spectrally complex, time-varying noise prevalent in reality, we propose filter function-enhanced QCRL (FF-QCRL), which integrates filter function formalism into the QCRL framework. The resulting FF-QCRL algorithm minimizes a generalized robustness metric that faithfully encodes the impact of stochastic processes, enabling robust pulse-family generation for parametric gates under realistic time-varying noise. Numerical validation in a representative single-qubit setting confirms the effectiveness of the proposed method.