3,113 research outputs found
Equivalences of Zt×Z22-cocyclic Hadamard matrices
One of the most promising structural approaches to resolving the
Hadamard Conjecture uses the family of cocyclic matrices over Zt × Z2
2.
Two types of equivalence relations for classifying cocyclic matrices over
Zt × Z2
2 have been found. Any cocyclic matrix equivalent by either of
these relations to a Hadamard matrix will also be Hadamard.
One type, based on algebraic relations between cocycles over any fi-
nite group, has been known for some time. Recently, and independently,
a second type, based on four geometric relations between diagrammatic
visualisations of cocyclic matrices over Zt × Z2
2, has been found. Here
we translate the algebraic equivalences to diagrammatic equivalences and
show one of the diagrammatic equivalences cannot be obtained this way.
This additional equivalence is shown to be the geometric translation of
matrix transposition
Trades in complex Hadamard matrices
A trade in a complex Hadamard matrix is a set of entries which can be changed
to obtain a different complex Hadamard matrix. We show that in a real Hadamard
matrix of order all trades contain at least entries. We call a trade
rectangular if it consists of a submatrix that can be multiplied by some scalar
to obtain another complex Hadamard matrix. We give a
characterisation of rectangular trades in complex Hadamard matrices of order
and show that they all contain at least entries. We conjecture that all
trades in complex Hadamard matrices contain at least entries.Comment: 9 pages, no figure
Single and double qubit gates by manipulating degeneracy
A novel mechanism is proposed for single and double qubit state manipulations
in quantum computation with four-fold degenerate energy levels. The principle
is based on starting with a four fold degeneracy, lifting it stepwise
adiabatically by a set of control parameters and performing the quantum gate
operations on non-degenerate states. A particular realization of the proposed
mechanism is suggested by using inductively coupled rf-squid loops in the
macroscopic quantum tunnelling regime where the energy eigen levels are
directly connected with the measurable flux states. The one qubit and two qubit
controlled operations are demonstrated explicitly. The appearance of the flux
states also allows precise read-in and read-out operations by the measurement
of flux.Comment: 6 pages + 5 figures (separately included
A High performance and low cost hardware arcitecture for H.264 transform and quantization algorithms
In this paper, we present a high performance and low cost hardware architecture for real-time implementation of forward transform and quantization and inverse transform and quantization algorithms used in H.264 / MPEG4 Part 10 video coding standard. The hard-ware architecture is based on a reconfigurable datapath with only one multiplier. This hardware is designed to be used as part of a complete low power H.264 video coding system for portable appli-cations. The proposed architecture is implemented in Verilog HDL. The Verilog RTL code is verified to work at 81 MHz in a Xilinx Virtex II FPGA and it is verified to work at 210 MHz in a 0.18´ ASIC implementation. The FPGA and ASIC implementations can code 27 and 70 VGA frames (640x480) per second respectively
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