An explicit family of unitaries with exponentially minimal length Pauli geodesics

Details An explicit family of unitaries with exponentially minimal length Pauli geodesics An explicit family of unitaries with exponentially minimal length Pauli geodesics

2007-01-28

arxiv.org/abs/quant-ph/0701202v1

Physics

Quantum Physics

4 pages, accepted as poster presentation in QIP07

Scientific paper

Recently, Nielsen et al have proposed a geometric approach to quantum computation. They've shown that the size of the minimum quantum circuits implementing a unitary U, up to polynomial factors, equals to the length of minimal geodesic from identity I through U. They've investigated a large class of solutions to the geodesic equation, called Pauli geodesics. They've raised a natural question whether we can explicitly construct a family of unitaries U that have exponentially long minimal length Pauli geodesics? We give a positive answer to this question.

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