Vol.6 No.2
March 1, 2006
Research Articles:
Quantum accuracy
threshold for concatenated distance3 code
(pp097165)
P. Aliferis, D. Gottesman, and J. Preskill
We prove a new version of the quantum threshold theorem
that applies to concatenation of a quantum code that corrects only one
error, and we use this theorem to derive a rigorous lower bound on the
quantum accuracy threshold $\varepsilon_0$. Our proof also applies to
concatenation of higherdistance codes, and to noise models that allow
faults to be correlated in space and in time. The proof uses new
criteria for assessing the accuracy of faulttolerant circuits, which
are particularly conducive to the inductive analysis of recursive
simulations. Our lower bound on the threshold, $\varepsilon_0 \ge
2.73\times 10^{5}$ for an adversarial independent stochastic noise
model, is derived from a computerassisted combinatorial analysis; it is
the best lower bound that has been rigorously proven so far.
Quantum
entanglement measure based on wedge product
(pp166172)
H. Heydari
We construct an entanglement measure that coincides with
the generalized concurrence for a general pure bipartite state based on
wedge product. Moreover, we construct an entanglement measure for pure
multiqubit states, which are entanglement monotones. Furthermore, we
generalize our result on a general pure multipartite state.
The computational power of the
W and GHZ states
(pp173183)
E. D'Hondt and P.
Panangaden
It is well understood that the use of quantum
entanglement significantly enhances the computational power of systems.
Much of the attention has focused on Bell states and their multipartite
generalizations. However, in the multipartite case it is known that
there are several inequivalent classes of states, such as those
represented by the Wstate and the GHZstate. Our main contribution is a
demonstration of the special computational power of these states in the
context of paradigmatic problems from classical distributed computing.
Concretely, we show that the Wstate is the only pure state that
can be used to exactly solve the problem of leader election in anonymous
quantum networks. Similarly we show that the GHZstate is the only one
that can be used to solve the problem of distributed consensus when no
classical postprocessing is considered. These results generalize to a
family of W and GHZlike states. At the heart of the proofs of these
impossibility results lie symmetry arguments.
A quantum circuit for Shor's factoring algorithm using 2n+2 qubits
(pp184192)
Y. Takahashi and N.
Kunihiro
We construct a quantum circuit for Shor's factoring
algorithm that uses 2n+2 qubits, where n is the length of the number to
be factored. The depth and size of the circuit are O(n^3) and O(n^3\log
n), respectively. The number of qubits used in the circuit is less than
that in any other quantum circuit ever constructed for Shor's factoring
algorithm. Moreover, the size of the circuit is about half the size of
Beauregard's quantum circuit for Shor's factoring algorithm, which uses
2n+3 qubits.
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