|Affiliation:||IQC, Perimeter Institute for Theoretical Physics, University of Waterloo|
To capture the power of quantum algorithms in practice requires translating high-level instructions into low-level machine instructions. An important part of this sequence of transformations is the synthesis and optimization of high-level operations in terms of fault-tolerant quantum gates. A number of interesting mathematical problems emerge, including matroid partitioning, decoding Reed-Muller codes, and problems in algorithmic number theory.
I will overview the current state of global efforts to build a large-scale fault-tolerant quantum computer, and of quantum compiling, and give some examples of the mathematical tools being developed and applied for the compiling of quantum algorithms.