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

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+.

Presented in TQC 2022

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Cited by in corpus (3)

• SnCQA: A hardware-efficient equivariant quantum convolutional circuit architecture
• Precise Image Generation on Current Noisy Quantum Computing Devices
• Permutation-equivariant quantum convolutional neural networks