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If two separated observers are supplied with entanglement, in the form of n pairs of particles in identical partly-entangled pure states, one member of each pair being given to each observer; they can, by local actions of each observer, concentrate this entangle-ment into a smaller number of maximally-entangled pairs of particles, for example… (More)

- Howard N. Barnum, Shang Song, +15 authors Luis Davidovich
- 1998

iii To m y family iv Acknowledgments I h a ve been extraordinarily fortunate to have Carlton Caves as advisor for my graduate work. I have learned much a b o u t p h ysics, life, and life as a physicist from him, and I am deeply grateful for his advice and friendship. His steady vision of the role of theory in physics, his perseverance in pursuing this… (More)

Quantum computers are computational devices that use the dynamics of atomic-scale objects to store and manipulate information. Only a few, small-scale quantum computers have been built to date, but quantum computers can in principle outperform all possible classical computers in significant ways. Quantum computation is therefore a subject of considerable… (More)

This paper documents the discovery of a new, better-than-classical quantum algorithm for the depth-two AND/OR tree problem. We describe the genetic programming system that was constructed specifically for this work, the quantum computer simulator that is used to evaluate the fitness of evolving quantum algorithms, and the newly discovered algorithm.

Genetic programming can be used to automatically discover algorithms for quantum computers that are more efficient than any classical computer algorithms for the same problems. In this paper we exhibit the first evolved better-than-classical quantum algorithm, for Deutsch's " early promise " problem. We also demonstrate a technique for evolving scalable… (More)

We give the first quantum circuit for computing f (0) OR f (1) more reliably than is classically possible with a single evaluation of the function. OR therefore joins XOR (i.e. parity, f (0) ⊕ f (1)) to give the full set of logical connectives (up to relabelling of inputs and outputs) for which there is quantum speedup.

We explore tradeoffs between classical communication and entanglement-generating powers of unitary 2-qubit gates. The exploration is aided by a computational search technique called genetic programming. We explore tradeoffs between classical communication and entanglement-generating powers of unitary 2-qubit gates. The exploration is aided by a… (More)

- Lawrence C. Andrews, Herbert J. Bernstein
- Journal of applied crystallography
- 2014

Niggli reduction can be viewed as a series of operations in a six-dimensional space derived from the metric tensor. An implicit embedding of the space of Niggli-reduced cells in a higher-dimensional space to facilitate calculation of distances between cells is described. This distance metric is used to create a program, BGAOL, for Bravais lattice… (More)

- Herbert J. Bernstein
- Inf. Process. Lett.
- 1986

- Herbert J. Bernstein, Max Goldstein
- Computing
- 1986