111 research outputs found
Experimental observation of impossible-to-beat quantum advantage on a hybrid photonic system
Quantum resources outperform classical ones for certain communication and
computational tasks. Remarkably, in some cases, the quantum advantage cannot be
improved using hypothetical postquantum resources. A class of tasks with this
property can be singled out using graph theory. Here we report the experimental
observation of an impossible-to-beat quantum advantage on a four-dimensional
quantum system defined by the polarization and orbital angular momentum of a
single photon. The results show pristine evidence of the quantum advantage and
are compatible with the maximum advantage allowed using postquantum resources.Comment: REVTeX4, 5 pages, 2 figure
Quantum Convolutional BCH Codes
Quantum convolutional codes can be used to protect a sequence of qubits of
arbitrary length against decoherence. We introduce two new families of quantum
convolutional codes. Our construction is based on an algebraic method which
allows to construct classical convolutional codes from block codes, in
particular BCH codes. These codes have the property that they contain their
Euclidean, respectively Hermitian, dual codes. Hence, they can be used to
define quantum convolutional codes by the stabilizer code construction. We
compute BCH-like bounds on the free distances which can be controlled as in the
case of block codes, and establish that the codes have non-catastrophic
encoders.Comment: 4 pages, minor changes, accepted for publication at the 10th Canadian
Workshop on Information Theory (CWIT'07
Engineering Functional Quantum Algorithms
Suppose that a quantum circuit with K elementary gates is known for a unitary
matrix U, and assume that U^m is a scalar matrix for some positive integer m.
We show that a function of U can be realized on a quantum computer with at most
O(mK+m^2log m) elementary gates. The functions of U are realized by a generic
quantum circuit, which has a particularly simple structure. Among other
results, we obtain efficient circuits for the fractional Fourier transform.Comment: 4 pages, 2 figure
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