Toward superpolynomial quantum speedup of equivariant quantum algorithms with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>SU</mml:mi> <mml:mo>(</mml:mo> <mml:mi>d</mml:mi>
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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+.