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Exact and approximate unitary 2-designs and their application to fidelity estimation
We develop the concept of a unitary $t$-design as a means of expressing operationally useful subsets of the stochastic properties of the uniform (Haar) measure on the unitary group $U({2}^{n})$ on
Exact and Approximate Unitary 2-Designs: Constructions and Applications
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.
Efficient Simulation of Random Quantum States and Operators
We investigate the generation of quantum states and unitary operations that are ``random'' in certain respects. We show how to use such states to estimate the average fidelity, an important measure