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Towards optimization of quantum circuits

100%
Sedlák M., Plesch M.
Open Physics
|
2008
|
vol. 6
|
issue 1
128-134
EN
Any unitary operation in quantum information processing can be implemented via a sequence of simpler steps - quantum gates. However, actual implementation of a quantum gate is always imperfect and takes a finite time. Therefore, searching for a short sequence of gates - efficient quantum circuit for a given operation, is an important task. We contribute to this issue by proposing optimization of the well-known universal procedure proposed by Barenco et al. [Phys. Rev. A 52, 3457 (1995)]. We also created a computer program which realizes both Barenco’s decomposition and the proposed optimization. Furthermore, our optimization can be applied to any quantum circuit containing generalized Toffoli gates, including basic quantum gate circuits.
2
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System Size Dependence of Entanglement in Quantum One-Dimensional Models

76%
Jakubczyk D., Jakubczyk P.
Acta Physica Polonica A
|
2017
|
vol. 132
|
issue 1
158-160
EN
We show that entanglement in one-dimensional spin and electron systems, with one excitation, depends only on the system size and has very simple form in both multipartite and bipartite case. Regarding the multipartite case, we present very simple expressions for global entanglement and N-concurrence, and show that they are mutually related. In the bipartite case, we give expressions for I-concurrence and negativity, and show that they are also dependent on each other.
3
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Magnetic Pentagonal Ring - Galois Extensions and Crystallography

64%
Labuz M., Lulek T.
Acta Physica Polonica A
|
2017
|
vol. 132
|
issue 1
97-99
EN
The Galois symmetry of exact Bethe Ansatz eigenstates for magnetic pentagonal ring is shown to bear a close analogy to some crystallographic constructions. Automorphisms of number field extensions associated with these eigenstates prove to be related to choices of the Bravais cells in the finite crystal lattice ℤ₂×ℤ₂, responsible for extension of the cyclotomic field by the Bethe parameters.
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