The discrete adiabatic quantum linear system solver has lower constant factors than the randomized adiabatic solver
arxiv(2023)
摘要
The solution of linear systems of equations is the basis of many other
quantum algorithms, and recent results provided an algorithm with optimal
scaling in both the condition number κ and the allowable error
ϵ [PRX Quantum 3, 0403003 (2022)]. That work was based on the
discrete adiabatic theorem, and worked out an explicit constant factor for an
upper bound on the complexity. Here we show via numerical testing on random
matrices that the constant factor is in practice about 1,500 times smaller than
the upper bound found numerically in the previous results. That means that this
approach is far more efficient than might naively be expected from the upper
bound. In particular, it is over an order of magnitude more efficient than
using a randomised approach from [arXiv:2305.11352] that claimed to be more
efficient.
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