Giulio Chiribella (University of Hong Kong): Optimal programming of quantum gates

Team-Net Quantum Computing Colloquium

A universal quantum processor is a device that can approximately implement any desired quantum gate on a given system. The specification of the desired gate is provided by a program, which in most implementations of quantum computing consists of classical data. From the foundational point of view, however, it is interesting to explore the more general scenario where the program is itself a quantum system. In the past two decades, a major open question has been to determine how the size of the smallest quantum program scales with the required accuracy in the implementation of the desired gate. Here we answer the question, by proving a bound on the size of the program and designing a concrete protocol that attains the bound in the asymptotic limit. Our result is based the representation theory of the special unitary group. It provides improved bounds on the estimation of unitary gates, and on the implementation of quantum protocols subject to conservation laws.

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