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Reducing Sequencing Complexity In Dynamical Quantum Error Suppression By Walsh Modulation, David Hayes, Kaveh Khodjasteh, Lorenza Viola, Michael J. Biercuk
Reducing Sequencing Complexity In Dynamical Quantum Error Suppression By Walsh Modulation, David Hayes, Kaveh Khodjasteh, Lorenza Viola, Michael J. Biercuk
Dartmouth Scholarship
We study dynamical error suppression from the perspective of reducing sequencing complexity, with an eye toward facilitating the development of efficient semiautonomous quantum-coherent systems. To this end, we focus on digital sequences where all interpulse time periods are integer multiples of a minimum clock period and compatibility with digital classical control circuitry is intrinsic. We use so-called Walsh functions as a unifying mathematical framework; the Walsh functions are an orthonormal set of basis functions which may be associated directly with the control propagator for a digital modulation scheme. Using this insight, we characterize the suite of resulting Walsh dynamical decoupling …
Mutually Unbiased Bases And Trinary Operator Sets For N Qutrits, Jay Lawrence
Mutually Unbiased Bases And Trinary Operator Sets For N Qutrits, Jay Lawrence
Dartmouth Scholarship
A complete orthonormal basis of N-qutrit unitary operators drawn from the Pauli Group consists of the identity and 9^N-1 traceless operators. The traceless ones partition into 3^N+1 maximally commuting subsets (MCS's) of 3^N-1 operators each, whose joint eigenbases are mutually unbiased. We prove that Pauli factor groups of order 3^N are isomorphic to all MCS's, and show how this result applies in specific cases. For two qutrits, the 80 traceless operators partition into 10 MCS's. We prove that 4 of the corresponding basis sets must be separable, while 6 must be totally entangled (and Bell-like). For three qutrits, 728 operators …