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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.arXiv:quant-ph/0409035v2 fatcat:wg56esv63vho3m6qayj37jztgu