Lower Bounds on Quantum Query Complexity

Shor's and Grover's famous quantum algorithms for factoring and searching show that quantum computers can solve certain computational problems significantly faster than any classical computer. We discuss here what quantum computers_cannot_ do, and specifically how to prove limits on their computational power. We cover the main known techniques for proving lower bounds, and exemplify and compare the methods.Comment: survey, 23 page

The Heisenberg Representation of Quantum Computers

Since Shor's discovery of an algorithm to factor numbers on a quantum computer in polynomial time, quantum computation has become a subject of immense interest. Unfortunately, one of the key features of quantum computers - the difficulty of describing them on classical computers - also makes it difficult to describe and understand precisely what can be done with them. A formalism describing the evolution of operators rather than states has proven extremely fruitful in understanding an important class of quantum operations. States used in error correction and certain communication protocols can be described by their stabilizer, a group of tensor products of Pauli matrices. Even this simple group structure is sufficient to allow a rich range of quantum effects, although it falls short of the full power of quantum computation.Comment: 20 pages, LaTeX. Expanded version of a plenary speech at the 1998 International Conference on Group Theoretic Methods in Physic

Seven myths about young children and technology

Parents and educators tend to have many questions about young children's play with computers and other technologies at home. They can find it difficult to know what is best for children because these toys and products were not around when they were young. Some will tell you that children have an affinity for technology that will be valuable in their future lives. Others think that children should not be playing with technology when they could be playing outside or reading a book