A General Transfer-Function Approach to Noise Filtering in Open-Loop Quantum Control

Abstract

We present a general transfer-function approach to noise filtering in open-loop Hamiltonian engineering protocols for open quantum systems. We show how to identify a computationally tractable set of fundamental filter functions, out of which arbitrary transfer filter functions may be assembled up to arbitrary high order in principle. Besides avoiding the infinite recursive hierarchy of filter functions that arises in general control scenarios, this fundamental filter-functions set suffices to characterize the error suppression capabilities of the control protocol in both the time and frequency domain. We prove that the resulting notion of filtering order reveals conceptually distinct, albeit complementary, features of the controlled dynamics as compared to the order of error cancellation, traditionally defined in the Magnus sense. Examples and implications are discussed.

Paper plus supplementary material. 10 pages, 1 figure. Unnumbered equation between 2 and 3 corrected. Results are unchanged

References in corpus (8)

• The Magnus expansion and some of its applications
• Dynamical decoupling and noise spectroscopy with a superconducting flux qubit
• Fault-Tolerant Quantum Dynamical Decoupling
• How to Enhance Dephasing Time in Superconducting Qubits
• Dynamically Error-Corrected Gates for Universal Quantum Computation
• Quantum Feedback Networks: Hamiltonian Formulation
• Experimental noise filtering by quantum control
• Anomalous behavior of control pulses in presence of noise with singular autocorrelation

Cited by in corpus (2)

• Experimental noise filtering by quantum control
• Walsh-synthesized noise-filtering quantum logic