To understand why quantum computers can be faster than classical computers, we need to use probability theory to describe what exactly happens in quantum computation. In probability theory, one of the most important theorems is the Central Limit Theorem, which states that the iterated convolution of a density function tends to a Gaussian distribution. We introduced a notion of quantum convolution in quantum systems, and prove the Quantum Central Limit Theorem, based on our quantum convolution. This is a joint work with Kaifeng Bu and Arthur Jaffe.
