Methods, apparatuses, and systems include: based on a parameter of a quantum gate, generating representations of m1 random unitary quantum gates; determining a representation of a first quantum-gate sequence equivalent to an identity operator; determining a representation of a second quantum-gate sequence equivalent to the identity operator; sending, to a quantum computing device, hardware instructions corresponding to the representation of the first quantum-gate sequence the second quantum-gate sequence; receiving a first number of measurements of a qubit after applying the first quantum-gate sequence to the qubit for the first number of times by the quantum computing device and a second number of measurements of the qubit after applying the second quantum-gate sequence to the qubit for the second number of times by the quantum computing device; and determining a fidelity value of the quantum gate based on a first probability and a second probability.