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Recent investigations show that conservation laws limit the accuracy of gateoperations in quantum computing. The inevitable error under the angularmomentum conservation law has been evaluated so far for the CNOT, Hadamard, andNOT gates for spin 1/2 qubits, while the SWAP gate has no constraint. Here, weextend the above results to general single-qubit gates. We obtain an upperbound of the gate fidelity of arbitrary single-qubit gates implemented underarbitrary conservation laws, determined by the geometry of the conservation lawand the gate operation on the Bloch sphere as well as the size of the ancilla.

Gate fidelity of arbitrary single-qubit gates constrained by conservation laws