We present a stochastic quantum computing algorithm that can prepare any eigenvector of Hamiltonian within selected energy interval $[E\ensuremath{-}\ensuremath{\epsilon},E+\ensuremath{\epsilon}]$. In order to reduce the spectral weight all other eigenvectors by suppression factor $\ensuremath{\delta}$, required computational effort scales as $O[|\mathrm{log}\ensuremath{\delta}|/(p\ensuremath{\...

*Département d’informatique et de recherche opérationnelle, Université de Montréal, C.P. 6128, succursale centre-ville, Montréal, QC H3C 3J7 Canada; ‡IBM Almaden Research Center, 650 Harry Road, San Jose, CA 95120; §Massachusetts Institute of Technology, Department of Mechanical Engineering, MIT 3-160, Cambridge, MA 02139; and ¶National Institute of Standards and Technology, Time and Frequency ...

The main features of quantum computing are described in the framework of spin resonance methods. Stress is put on the fact that quantum computing is in itself nothing but a re-interpretation (fruitful indeed) of well-known concepts. The role of the two basic operations, one-spin rotation and controlledNOT gates, is analyzed, and some exercises are proposed.

Changing the model underlying information and computation from a classical mechanical to a quantum mechanical one yields faster algorithms, novel cryptographic mechanisms, and alternative methods of communication. Quantum algorithms can perform a select set of tasks vastly more efficiently than any classical algorithm, but for many tasks it has been proven that quantum algorithms provide no adv...

One of the main potential applications of uncertainty in computations is quantum computing. In this paper, we show that the success of quantum computing can be explained by the fact that quantum states are, in effect, tensors. Keywords— Quantum computing, physics, tensors

Preface Quantum computing is nothing like you have seen before. It has many possibilities and even more new hurdles. It is a concept that defies the things you took for granted and it fuels the imagination. Yet quantum computing is nothing new. It is simply how nature works: it is nature. It is nature working in the most bedazzling way you have ever seen.

3. Complete the proof of the decomposition theorem in quantum communication complexity. More specifically, Alice and Bob communicate in the Hilbert space HA⊗C ⊗HB: they begin with the (unentangled) state |0, 0, 0〉, and apply in turn unitary operators U1(X), U2(Y ), . . . , U2t−1(X), U2t(Y ) such that U2i−1(X) depends only on Alice’s private input X and acts in the spaceHA⊗C, and likewise for Bo...