Comment on "On the uncomputability of the spectral gap"

TL;DR

This paper clarifies misunderstandings regarding the comparison of results on the spectral gap's uncomputability, emphasizing distinctions between recent and earlier findings in quantum computation and spectral gap theory.

Contribution

It provides a clarification of claims made in a previous comparison, highlighting differences between recent and earlier results on the spectral gap's uncomputability.

Findings

Clarifies the distinction between recent and earlier results.

Addresses misconceptions in previous claims.

Emphasizes the importance of precise comparisons in spectral gap research.

Abstract

The aim of this short note is to clarify some of the claims made in the comparison made in [S. Lloyd, On the uncomputability of the spectral gap, arXiv:1602.05924] between our recent result [T.S. Cubitt, D. Perez-Garcia, M.M. Wolf, Undecidability of the spectral gap, Nature 528, 207-211 (2015), arXiv:1502.04573] and his 1994 paper [S. Lloyd, Necessary and sufficient conditions for quantum computation, J. Mod. Opt. 41(12), 2503-2520 (1994)].