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- Christopher M. Dawson, Michael A. Nielsen
- Quantum Information & Computation
- 2006

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 k , into an efficient fault-tolerant form… (More)

- M. A. Nielsen
- 1999

Suppose Alice and Bob jointly possess a pure state, jc͘. Using local operations on their respective systems and classical communication it may be possible for Alice and Bob to transform jc͘ into another joint state jf͘. This Letter gives necessary and sufficient conditions for this process of entanglement transformation to be possible. These conditions… (More)

- Howard Barnum, Emanuel Knill, Michael A. Nielsen
- IEEE Trans. Information Theory
- 2000

— We show the equivalence of two different notions of quantum channel capacity: that which uses the en-tanglement fidelity as its criterion for success in transmission , and that which uses the minimum fidelity of pure states in a subspace of the input Hilbert space as its criterion. As a corollary, any source with entropy less than the capacity may be… (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)

This Letter presents a simple formula for the average fidelity between a unitary quantum gate and a general quantum operation on a qudit, generalizing the formula for qubits found by Bowdrey et al. [Phys. Lett. A 294 (2002) 258]. This formula may be useful for experimental determination of average gate fidelity. We also give a simplified proof of a formula… (More)

- Michael A. Nielsen
- Quantum Information & Computation
- 2006

- Nicolas C Menicucci, Peter van Loock, Mile Gu, Christian Weedbrook, Timothy C Ralph, Michael A Nielsen
- Physical review letters
- 2006

We describe a generalization of the cluster-state model of quantum computation to continuous-variable systems, along with a proposal for an optical implementation using squeezed-light sources, linear optics, and homodyne detection. For universal quantum computation, a nonlinear element is required. This can be satisfied by adding to the toolbox any… (More)

- Michael A Nielsen, Mark R Dowling, Mile Gu, Andrew C Doherty
- Science
- 2006

Quantum computers hold great promise for solving interesting computational problems, but it remains a challenge to find efficient quantum circuits that can perform these complicated tasks. Here we show that finding optimal quantum circuits is essentially equivalent to finding the shortest path between two points in a certain curved geometry. By recasting… (More)

- Michael A. Nielsen, Dénes Petz
- Quantum Information & Computation
- 2005

- Benjamin C. Travaglione, Michael A. Nielsen, Howard M. Wiseman, Andris Ambainis
- Quantum Information & Computation
- 2002

We introduce a model of computation based on read only memory (ROM), which allows us to compare the space-efficiency of reversible, error-free classical computation with reversible, error-free quantum computation. We show that a ROM-based quantum computer with one writable qubit is universal, whilst two writable bits are required for a universal classical… (More)