Quantum Verification of Matrix Products
量子物理
2007-05-23 v2
摘要
We present a quantum algorithm that verifies a product of two n*n matrices over any field with bounded error in worst-case time n^{5/3} and expected time n^{5/3} / min(w,sqrt(n))^{1/3}, where w is the number of wrong entries. This improves the previous best algorithm that runs in time n^{7/4}. We also present a quantum matrix multiplication algorithm that is efficient when the result has few nonzero entries.
引用
@article{arxiv.quant-ph/0409035,
title = {Quantum Verification of Matrix Products},
author = {Harry Buhrman and Robert Spalek},
journal= {arXiv preprint arXiv:quant-ph/0409035},
year = {2007}
}
备注
15 pages, submitted; v2: rewritten, clarified, and fixed some proofs