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Quantum Verification of Matrix Products

Harry Buhrman·Robert Spalek
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Abstract

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.

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Harry Buhrman, Robert Spalek. 2005-07-06. Quantum Verification of Matrix Products. https://arxiv.org/abs/quant-ph/0409035

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