Demystifying Quantum Gate Fidelity for Electronics Engineers

The implementation of quantum gates by means of microwave cryo-RFICs controlling qubits is a promising path toward scalable quantum processors. Quantum gate fidelity quantifies how well an actual quantum gate produces a quantum state close to the desired ideal one. Regrettably, the literature usually reports on quantum gate fidelity in a highly theoretical way, making it hard for RFIC designers to understand. This paper explains quantum gate fidelity by moving from Shannon's concept of fidelity and proposing a detailed mathematical proof of a valuable integral formulation of quantum gate fidelity. Shannon's information theory and the simple mathematics adopted for the proof are both expected to be in the background of electronics engineers. By using Shannon's fidelity, this paper rationalizes the integral formulation of quantum gate fidelity. Because of the simple mathematics adopted, this paper also demystifies to electronics engineers how this integral formulation can be reduced to a more practical algebraic product matrix. This paper makes evident the practical utility of this matrix formulation by applying it to the specific examples of one- and two-qubit quantum gates. Moreover, this paper also compares mixed states, entanglement fidelity, and the error rate's upper bound.