QUANTUM COMPUTING - Bio-Inspired and Nanoscale Integrated Computing - page 79

the cavities to establish the distributed entanglement. Various basic difficulties
were overcome. They are explained below.
How can one do state transfer distribution? Bennett et al. [166, 167] and
Brassard [168] developed a technique known as teleportation to transmit
arbitrary input states with perfect fidelity. It does this by separating the
input state into classical and quantum components. The input can then be
reconstructed from these components with perfect fidelity.
How can one cope with communication errors and attenuation in a quantum
network? Wootters, Zurek [169] proved that a single quantum cannot be
cloned. (Note: Buzek, Hillery [170] recently claimed a universal optimal
cloning of qubits and quantum registers in a distributed quantum network,
but this seems inconsistent with the no-cloning theorem.) That no-cloning
theorem implies that once a signal becomes attenuated in an optical fiber
communication channel, then it cannot (generally) be amplified. It would
at first appear that communication and quantum network links may be
limited to distances of the order of the attenuation length in the fiber.
However, the range of quantum communication could be extended using
quantum repeaters that do quantum error correction, restoring the quan-
tum signal without reading the quantum information. Ekert, Huelga et al.
[171] extend the techniques of distributed quantum computation to noisy
channels, and showed that for quantum memories and quantum commu-
nication, a state can be transmitted over arbitrary distances with bounded
error, provided a minimum gate accuracy can be achieved—a constant
factor of this error.
3.8. OTHER ALGORITHMIC APPLICATIONS OF QC
The early literature in QC provided some examples of QC algorithms for problems
constructed for the reasonable purpose of showing that QC can solve some
problems more efficiently than conventional sequential computing models. Later,
quantum algorithms were developed for variety of useful applications. See the
texts on quantum algorithms: [27-34, 40].
Quantum Fourier Transforms. Drutsch, Jozsa [49] gave an O(n) time
quantum algorithm for creating a uniform superposition of all possible
values of n bits, which is a quantum Fourier transform over the finite field of
size 2. Simon [172] used this quantum Fourier transform to give an efficient
time quantum algorithm for determining whether a function over a finite
domain is invariant under some XOR-mask. This provided one of the first
examples of a quantum algorithm which efficiently solves an interesting
problem that is costly for classical computation. Brassard, Hoyer [173]
gave improvements to Simon's algorithm. There have been a number of