Comment on "Storage properties of a quantum perceptron"

TL;DR

This paper critiques the derivation of critical capacity in a quantum perceptron model, offering a more rigorous approach and evaluating an alternative problem relevant to the original quantum perceptron proposal.

Contribution

It identifies issues in the original derivation, proposes a more principled method, and assesses an alternative problem for the quantum perceptron.

Findings

Original derivation has issues upon close inspection

Proposed a more rigorous derivation method

Evaluated an alternative constraint satisfaction problem

Abstract

The recent paper "Storage properties of a quantum perceptron" [Phys. Rev. E 110, 024127] considers a quadratic constraint satisfaction problem, motivated by a quantum version of the perceptron. In particular, it derives its critical capacity, the density of constraints at which there is a satisfiability transition. The same problem was considered before in another context (classification of geometrically structured inputs, see [Phys. Rev. Lett. 125, 120601; Phys. Rev. E 102, 032119; J. Stat. Mech. (2021) 113301]), but the results on the critical capacity drastically differ. In this note, I substantiate the claim that the derivation performed in the quantum scenario has issues when inspected closely, I report a more principled way to perform it and I evaluate the critical capacity of an alternative constraint satisfaction problem that I consider more relevant for the quantum perceptron rule proposed by the article in question.