Optimal universal programming of 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.
Cite
@article{arxiv.2007.10363,
title = {Optimal universal programming of unitary gates},
author = {Yuxiang Yang and Renato Renner and Giulio Chiribella},
journal= {arXiv preprint arXiv:2007.10363},
year = {2021}
}
Comments
4 pages, 2 figures + Appendix; the upper bound's scaling with respect to d is improved compared to the published version (the main result remains unchanged)