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
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.
Key words: decoherence suppression / error correction / open-loop control / dynamic error suppression / quantum control / quantum logic / qubit / Walsh function / functional analysis
© Ball and Biercuk; licensee Springer., 2015