A Practical Explanation of Backward Sign Propagation in Quantum Computing

Abstract

In this paper, we perform a practical explanation of backward sign propagation in quantum computing. In our work, a 2-qubit quantum state is applied on the CNOT gate. The first qubit acts as a target qubit and the second qubit behaves as a control qubit. In this 2-qubit system, a phase error occurs on the target qubit. Our work is in the form of mathematical calculations, i.e. the calculation of the state, the density operator, the trace, and the Bloch vector of our quantum system. We also design its quantum circuit. The circuit is executed on IBM Qiskit and IBM Q Experience. As a result, we show the backward sign propagation occurs in separable and pure quantum state with the Hadamard basis state of the target qubit for any state of the control qubit.