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- Asymptotically Optimal Topological Quantum Compiling

In a topological

quantum computer, universality is achieved by braiding and quantum information

is natively protected from small local errors. We address the problem of

compiling single-qubit quantum operations into braid representations for

non-abelian quasiparticles described by the Fibonacci anyon model. We develop a

probabilistically polynomial algorithm that outputs a braid pattern to

approximate a given single-qubit unitary to a desired precision. We also

classify the single-qubit unitaries that can be implemented exactly by a

Fibonacci anyon braid pattern and present an efficient algorithm to produce

their braid patterns. Our techniques produce braid patterns that meet the

uniform asymptotic lower bound on the compiled circuit depth and thus are

depth-optimal asymptotically. Our compiled circuits are significantly shorter

than those output by prior state-of-the-art methods, resulting in improvements

in depth by factors ranging from 20 to 1000 for precisions ranging between 10^{−10}

and 10^{−30}.

Event Type:

Seminar

Collection/Series:

Scientific Area(s):

Speaker(s):

Event Date:

Wednesday, October 30, 2013 - 16:00 to 17:30

Location:

Time Room

©2012 Perimeter Institute for Theoretical Physics