



@article {3426,
	title = {The discrete adiabatic quantum linear system solver has lower constant factors than the randomized adiabatic solver},
	year = {2023},
	month = {12/12/2023},
	abstract = {<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>},
	url = {https://arxiv.org/abs/2312.07690},
	author = {Pedro C. S. Costa and Dong An and Ryan Babbush and Dominic Berry}
}
@article {2926,
	title = {Optimal scaling quantum linear systems solver via discrete adiabatic theorem},
	year = {2021},
	month = {11/15/2021},
	abstract = {<p>Recently, several approaches to solving linear systems on a quantum computer have been formulated in terms of the quantum adiabatic theorem for a continuously varying Hamiltonian. Such approaches enabled near-linear scaling in the condition number κ of the linear system, without requiring a complicated variable-time amplitude amplification procedure. However, the most efficient of those procedures is still asymptotically sub-optimal by a factor of log(κ). Here, we prove a rigorous form of the adiabatic theorem that bounds the error in terms of the spectral gap for intrinsically discrete time evolutions. We use this discrete adiabatic theorem to develop a quantum algorithm for solving linear systems that is asymptotically optimal, in the sense that the complexity is strictly linear in κ, matching a known lower bound on the complexity. Our O(κlog(1/ε)) complexity is also optimal in terms of the combined scaling in κ and the precision ε. Compared to existing suboptimal methods, our algorithm is simpler and easier to implement. Moreover, we determine the constant factors in the algorithm, which would be suitable for determining the complexity in terms of gate counts for specific applications.\&nbsp;</p>},
	url = {https://arxiv.org/abs/2111.08152},
	author = {Pedro C. S. Costa and Dong An and Yuval R. Sanders and Yuan Su and Ryan Babbush and Dominic W. Berry}
}
