Optimal universal programming of unitary gates

Understand

A universal quantum processor is a device that takes as input a (quantum) program, containing an encoding of an arbitrary unitary gate, and a (quantum) data register, on which the encoded gate is applied.

• While no perfect universal quantum processor can exist, approximate processors have been proposed in the past two decades.
• A fundamental open question is how the size of the smallest quantum program scales with the approximation error.
• 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.