Exact and Approximate Unitary 2-Designs: Constructions and Applications

Details Exact and Approximate Unitary 2-Designs: Constructions and Applications Exact and Approximate Unitary 2-Designs: Constructions and Applications

2006-06-20

arxiv.org/abs/quant-ph/0606161v1

Physics

Quantum Physics

5 pages

Scientific paper

We consider an extension of the concept of spherical t-designs to the unitary group in order to develop a unified framework for analyzing the resource requirements of randomized quantum algorithms. We show that certain protocols based on twirling require a unitary 2-design. We describe an efficient construction for an exact unitary 2-design based on the Clifford group, and then develop a method for generating an epsilon-approximate unitary 2-design that requires only O(n log(1/epsilon)) gates, where n is the number of qubits and epsilon is an appropriate measure of precision. These results lead to a protocol with exponential resource savings over existing experimental methods for estimating the characteristic fidelities of physical quantum processes.

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