  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.
