



01347nas a2200145   4500008004100000245012000041210006900161260001500230520084500245100002401090700001301114700001801127700001901145856003701164       2023                        eng d00aThe discrete adiabatic quantum linear system solver has lower constant factors than the randomized adiabatic solver0 adiscrete adiabatic quantum linear system solver has lower consta  c12/12/20233 a<p>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 \textbf{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.</p>1 aCosta, Pedro, C. S.1 aAn, Dong1 aBabbush, Ryan1 aBerry, Dominic  uhttps://arxiv.org/abs/2312.07690