Optimal universal programming of unitary gates

TL;DR

This paper establishes a fundamental bound on the size of quantum programs needed for approximate universal quantum processors, linking programming, learning, and estimation of unitary gates.

Contribution

It proves a bound on program size related to approximation error and designs a protocol that achieves this bound asymptotically, connecting quantum programming with metrology.

Findings

Derived a bound on quantum program size for approximate universality.

Designed a protocol that attains the bound asymptotically.

Established equivalence between programming, learning, and estimating unitary gates.

Abstract

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. Our result is based on a connection between optimal programming and the Heisenberg limit of quantum metrology, and establishes an asymptotic equivalence between the tasks of programming, learning, and estimating unitary gates.