Table 1 Sixteen single-qubit basis operations.Pθ=e−iθ2P denotes the gate of rotation along the *P* axis by an angle of θ, where *P* = *X*, *Y*, *Z*. *M*_{P} denotes the operation of measuring the eigenvalue of the Pauli operator *P* whose outcomes are ±1. MI+P2 and *M*_{P} are the same operation, but outcomes are noted differently, and MI+P2 denotes the operation of measuring the eigenvalue of the operator I+P2 whose outcomes are 0 and 1. *R*_{∣ψ〉} denotes the operation of resetting the qubit state to ∣ψ〉. For composed operations, operations are implemented from left to right in sequence. These basis operations are linearly independent and complete; therefore, all single-qubit operations can be decomposed as linear combinations of basis operations. Non-unital operations, i.e., reset gates, are necessary in the basis set to efficiently decompose the non-unital part of an operation. The basis set minimizing the variance of the computation result is preferred.