210 research outputs found
Wavelets and Wavelet Packets on Quantum Computers
We show how periodized wavelet packet transforms and periodized wavelet
transforms can be implemented on a quantum computer. Surprisingly, we find that
the implementation of wavelet packet transforms is less costly than the
implementation of wavelet transforms on a quantum computer.Comment: 11 pages, 10 postscript figure, to appear in Proc. of Wavelet
Applications in Signal and Image Processing VI
On the Monomiality of Nice Error Bases
Unitary error bases generalize the Pauli matrices to higher dimensional
systems. Two basic constructions of unitary error bases are known: An algebraic
construction by Knill, which yields nice error bases, and a combinatorial
construction by Werner, which yields shift-and-multiply bases. An open problem
posed by Schlingemann and Werner (see
http://www.imaph.tu-bs.de/qi/problems/6.html) relates these two constructions
and asks whether each nice error basis is equivalent to a shift-and-multiply
basis. We solve this problem and show that the answer is negative. However, we
also show that it is always possible to find a fairly sparse representation of
a nice error basis.Comment: 6 page
Hybrid Codes
A hybrid code can simultaneously encode classical and quantum information
into quantum digits such that the information is protected against errors when
transmitted through a quantum channel. It is shown that a hybrid code has the
remarkable feature that it can detect more errors than a comparable quantum
code that is able to encode the classical and quantum information. Weight
enumerators are introduced for hybrid codes that allow to characterize the
minimum distance of hybrid codes. Surprisingly, the weight enumerators for
hybrid codes do not obey the usual MacWilliams identity.Comment: 5 page
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