Walsh-synthesized noise-filtering quantum logic

TL;DR

This paper introduces Walsh-synthesized control protocols for robust single-qubit quantum gates that effectively suppress noise, leveraging filter-transfer functions and digital-compatible pulse sequences, with practical considerations for experimental constraints.

Contribution

It presents a novel Walsh-synthesis framework for designing noise-filtering quantum gates, including analytic design rules and optimized modulation protocols for non-Markovian noise.

Findings

Developed Walsh-modulated noise filters for dephasing and amplitude damping.

Demonstrated compatibility with digital logic and clocking.

Analyzed effects of experimental constraints like bandwidth limitations.

Abstract

We study a novel class of open-loop control protocols constructed to perform arbitrary nontrivial single-qubit logic operations robust against time-dependent non-Markovian noise. Amplitude and phase modulation protocols are crafted leveraging insights from functional synthesis and the basis set of Walsh functions. We employ the experimentally validated generalized filter-transfer function formalism in order to find optimized control protocols for target operations in SU(2) by defining a cost function for the filter-transfer function to be minimized through the applied modulation. Our work details the various techniques by which we define and then optimize the filter-synthesis process in the Walsh basis, including the definition of specific analytic design rules which serve to efficiently constrain the available synthesis space. This approach yields modulated-gate constructions consisting of chains of discrete pulse-segments of arbitrary form, whose modulation envelopes possess intrinsic compatibility with digital logic and clocking. We derive novel families of Walsh-modulated noise filters designed to suppress dephasing and coherent amplitude-damping noise, and describe how well-known sequences derived in NMR also fall within the Walsh-synthesis framework. Finally, our work considers the effects of realistic experimental constraints such as limited modulation bandwidth on achievable filter performance.