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:: Fri 3/20, 1:30 in 6C-442

Richard Cleve (IQC, University of Waterloo)
Near-linear constructions of exact unitary 2-designs

We present exact unitary 2-designs on n qubits that can be implemented with (n) elementary gates from the Clifford group. This is essentially a quadratic improvement over all previous constructions that are exact or approximate (for sufficiently strong approximations). This is joint work with Debbie Leung, Li Liu, and Chunhao Wang.


:: Fri 5/1, 2:00 in 6C-442

William Wooters (Williams College)
Cycling through mutually unbiased bases

Two orthogonal bases for a Hilbert space are called mutually unbiased if each vector in one basis is an equal-magnitude superposition of all the vectors in the other basis. The maximum number of mutually unbiased bases in a space of dimension d is d+1; so a set of d+1 such bases is called complete. Complete sets of mutually unbiased bases play significant roles in quantum cryptography and quantum tomography. For certain values of d, it is possible to find a single unitary transformation that, by repeated application, generates a complete set of mutually unbiased bases starting with the standard basis. This talk reviews our current understanding of such cycling unitaries and related transformations, and shows how their effects can be pictured in a discrete phase space.


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