WADT'22 - 26th International Workshop on Algebraic Development Techniques 2022
Aveiro, 28 - 30 June 2022
Plenary Talk: Number-theoretic methods in quantum computing
Abstract: An important problem in quantum computing is the so-called
approximate synthesis problem: to find a circuit, preferably as short
as possible, that approximates a given unitary operator up to a given
epsilon. Until 2012, the standard solution to this problem was the
Solovay-Kitaev algorithm, which is based on geometric ideas. This
algorithm produces circuits of size O(log^c(1/epsilon)), where c is
approximately 3.97.
In 2012, a new class of approximate synthesis algorithms was
discovered that are based on ideas from algebraic number theory. These
algorithms achieve circuit size O(log(1/epsilon)). In certain
important cases, such as the commonly used Clifford+T gate set, one
can even find algorithms that are optimal in an absolute sense: the
algorithm finds the shortest circuit whatsoever for the given problem
instance. I will review some 400-year-old number theory and explain
how it can be used to solve the approximate synthesis problem. This is
joint work with Neil J. Ross.
Peter Selinger (Dalhousie University)
Peter Selinger is a Professor of Mathematics and Computer Science at Dalhousie University. He received his PhD from the University of Pennsylvania in 1997. His main research interest is the semantics of programming languages, and specifically the theory of programming languages for quantum computing, which he helped pioneer. More recently, he also became interested in the application of number-theoretic methods to unitary approximation problems. He is an editor of the journal Logical Methods in Computer Science and a founder of the workshop series Quantum Physics and Logic. He has served on numerous program committees, and has given plenary lectures at international conferences including MFPS, TLCA, CTCS, FLOPS, POPL, WoLLIC, and TYPES.