Michael A. Nielsen

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M. A. Nielsen* Department of Physics, MC 12-33, California Institute of Technology, Pasadena, California 91125 (Received 2 December 1998) Suppose Alice and Bob jointly possess a pure state, jc . Using local operations on their respective systems and classical communication it may be possible for Alice and Bob to transform jc into another joint state jf .(More)
This pedagogical review presents the proof of the Solovay-Kitaev theorem in the form of an efficient classical algorithm for compiling an arbitrary single-qubit gate into a sequence of gates from a fixed and finite set. The algorithm can be used, for example, to compile Shor’s algorithm, which uses rotations of π/2, into an efficient fault-tolerant form(More)
A remarkable feature of quantum entanglement is that an entangled state of two parties, Alice ( A) and Bob ( B), may be more disordered locally than globally. That is, S(A)>S(A,B), where S(*) is the von Neumann entropy. It is known that satisfaction of this inequality implies that a state is nonseparable. In this paper we prove the stronger result that for(More)
This article is a short introduction to and review of the cluster-state model of quantum computation, in which coherent quantum information processing is accomplished via a sequence of single-qubit measurements applied to a fixed quantum state known as a cluster state. We also discuss a few novel properties of the model, including a proof that the cluster(More)
Locomotor activity recorded in an automated open-field apparatus was increased substantially by unilateral injections of carbachol, a cholinergic agonist, into the dentate gyrus of the hippocampus. Hyperactivity elicited in this way was reduced significantly when glutamate antagonists were injected into the ipsilateral nucleus accumbens. Injecting(More)
Majorization is a powerful, easy-to-use and exible tool which arises frequently in quantum mechanics as a consequence of fundamental connections between unitarity and the majorization relation. Entanglement theory does not escape from its in uence. Thus the interconversion of bipartite pure states by means of local manipulations turns out to be ruled to a(More)
In this Letter we numerically investigate the fault-tolerant threshold for optical cluster-state quantum computing. We allow both photon loss noise and depolarizing noise (as a general proxy for all local noise), and obtain a threshold region of allowed pairs of values for the two types of noise. Roughly speaking, our results show that scalable optical(More)