164,206 research outputs found
Use of non-adiabatic geometric phase for quantum computing by nuclear magnetic resonance
Geometric phases have stimulated researchers for its potential applications
in many areas of science. One of them is fault-tolerant quantum computation. A
preliminary requisite of quantum computation is the implementation of
controlled logic gates by controlled dynamics of qubits. In controlled
dynamics, one qubit undergoes coherent evolution and acquires appropriate
phase, depending on the state of other qubits. If the evolution is geometric,
then the phase acquired depend only on the geometry of the path executed, and
is robust against certain types of errors. This phenomenon leads to an
inherently fault-tolerant quantum computation.
Here we suggest a technique of using non-adiabatic geometric phase for
quantum computation, using selective excitation. In a two-qubit system, we
selectively evolve a suitable subsystem where the control qubit is in state
|1>, through a closed circuit. By this evolution, the target qubit gains a
phase controlled by the state of the control qubit. Using these geometric phase
gates we demonstrate implementation of Deutsch-Jozsa algorithm and Grover's
search algorithm in a two-qubit system
Topological Computation without Braiding
We show that universal quantum computation can be performed within the ground
state of a topologically ordered quantum system, which is a naturally protected
quantum memory. In particular, we show how this can be achieved using brane-net
condensates in 3-colexes. The universal set of gates is implemented without
selective addressing of physical qubits and, being fully topologically
protected, it does not rely on quasiparticle excitations or their braiding.Comment: revtex4, 4 pages, 4 figure
Stable and Reliable Computation of Eigenvectors of Large Profile Matrices
Independent eigenvector computation for a given set of eigenvalues of typical engineering
eigenvalue problems still is a big challenge for established subspace solution methods. The
inverse vector iteration as the standard solution method often is not capable of reliably computing
the eigenvectors of a cluster of bad separated eigenvalues.
The following contribution presents a stable and reliable solution method for independent
and selective eigenvector computation of large symmetric profile matrices. The method
is an extension of the well-known and well-understood QR-method for full matrices thus
having all its good numerical properties. The effects of finite arithmetic precision of
computer representations of eigenvalue/eigenvector solution methods are analysed and it is
shown that the numerical behavior of the new method is superior to subspace solution methods
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