Toward Super-polynomial Quantum Speedup of Equivariant Quantum Algorithms with SU(d) Symmetry

2022/07/15 by Zheng, Han, Li, Zimu, Strelchuk, Sergii +2 · 1 citation
#Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #FOS: Physical sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2207.07250

Abstract

We introduce a framework of the equivariant convolutional quantum algorithms which is tailored for a number of machine-learning tasks on physical systems with arbitrary SU(d) symmetries. It allows us to enhance a natural model of quantum computation -- permutational quantum computing (PQC) -- and define a more powerful model: PQC+. While PQC was shown to be efficiently classically simulatable, we exhibit a problem which can be efficiently solved on PQC+ machine, whereas no classical polynomial time algorithm is known; thus providing evidence against PQC+ being classically simulatable. We further discuss practical quantum machine learning algorithms which can be carried out in the paradigm of PQC+.

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