Vol.6 No.2 March 1, 2006
Research Articles:
Quantum accuracy threshold for concatenated distance-3 code (pp097-165)
         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 higher-distance 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 fault-tolerant 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 computer-assisted combinatorial analysis; it is the best lower bound that has been rigorously proven so far.

Quantum entanglement measure based on wedge product (pp166-172)
         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 multi-qubit 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 (pp173-183)
         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 W-state and the GHZ-state. 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 W-state 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 GHZ-state is the only one that can be used to solve the problem of distributed consensus when no classical post-processing is considered. These results generalize to a family of W- and GHZ-like 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 (pp184-192)
         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.