Efficient classical simulation of the approximate quantum Fourier transform

We present a method for classically simulating quantum circuits based on the tensor contraction model of Markov and Shi (quant-ph/0511069). Using this method we are able to classically simulate the approximate quantum Fourier transform in polynomial time. Moreover, our approach allows us to formulate a condition for the composability of simulable quantum circuits. We use this condition to show that any circuit composed of a constant number of approximate quantum Fourier transform circuits and log-depth circuits with limited interaction range can also be efficiently simulated.Comment: 5 pages, 3 figure

Classical simulation of limited-width cluster-state quantum computation

We present a classical protocol, using the matrix product state representation, to simulate cluster-state quantum computation at a cost polynomial in the number of qubits in the cluster and exponential in d -- the width of the cluster. We use this result to show that any log-depth quantum computation in the gate array model, with gates linking only nearby qubits, can be simulated efficiently on a classical computer.Comment: 4 pages, 1 figur

Methods for Reliable Teleportation

Recent experimental results and proposals towards implementation of quantum teleportation are discussed. It is proved that reliable (theoretically, 100% probability of success) teleportation cannot be achieved using the methods applied in recent experiments, i.e., without quantum systems interacting one with the other. Teleportation proposal involving atoms and electro-magnetic cavities are reviewed and the most feasible methods are described. In particular, the language of nonlocal measurements has been applied which has also been used for presenting a method for teleportation of quantum states of systems with continuous variables.Comment: 11 pages, 5eps figure

Classical simulability and the significance of modular exponentiation in Shor's algorithm

We show that a classical algorithm efficiently simulating the modular exponentiation circuit, for certain product state input and with measurements in a general product state basis at the output, can efficiently simulate Shor's factoring algorithm. This is done by using the notion of the semi-classical Fourier transform due to Griffith and Niu, and further discussed in the context of Shor's algorithm by Browne.Comment: 4 pages, 2 figure