EPJ Quantum Technol. (2015) 2: 11
https://doi.org/10.1140/epjqt/s40507-015-0022-4

Research

Walsh-synthesized noise filters for quantum logic

¹ ARC Centre for Engineered Quantum Systems, School of Physics, The University of Sydney, Sydney, NSW, 2006, Australia
² National Measurement Institute, West Lindfield, Sydney, NSW, 2070, Australia

^* e-mail: michael.biercuk@sydney.edu.au

Received: 13 December 2014
Accepted: 19 March 2015
Published online: 14 May 2015

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.