Richard Cleve

Harnessing quantum information

Quantum mechanical systems have strange properties. They can exist in several states simultaneously, similar to the way a shuffled deck of cards can appear to be “spread out” over all its possible orderings. Except that, unlike with cards, they cannot be described by standard probability theory: some of their “probabilities” are negative. “There’s a mathematical framework for this,” notes Richard Cleve, “and allowing the quantum probabilities to be negative means interference effects can occur; a particle may have multiple paths that cancel each other out, resulting in the particle being observed in a strange place.”

This “quantum randomness” may look like an exotic kind of noise that should be suppressed. In fact, Richard points out, quantum systems can perform remarkable feats in information processing, such as factorizing integers exponentially faster than our conventional algorithms. “Rather than trying to defeat nature, we gain by exploring its logical consequences.”

One of Professor Cleve’s current projects involves modelling quantum algorithms as continuous time processes. Even quantum computing scientists have tended to think about computations in terms of a series of discrete gates. “Some remarkable new algorithms have been discovered in a continuous-time paradigm,” says Richard, “and then, using various approaches, we can convert them into discrete algorithms.”

What does this mean for quantum computing? New and potentially useful applications of the theory. Richard’s interest is also driven by a more personal motivation: “I just love contemplating the counter-intuitive nature of the subject. Even when I understand the underlying mathematics, I often find what happens in quantum systems to be mind-boggling at the intuitive level.”

University of Waterloo Mathematics, Annual Report 2006