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We propose and demonstrate scheme for direct experimental testing of quantumcommutation relations for Pauli operators. The implemented device is anadvanced quantum processor that involves two programmable quantum gates.Depending on a state of two-qubit program register, we can test eithercommutation or anti-commutation relations. Very good agreement between theoryand experiment is observed, indicating high-quality performance of theimplemented quantum processor and reliable verification of commutationrelations for Pauli operators.

Direct experimental verification of quantum commutation relations for Pauli operators