Characteristics, implementation, and applications of special perfect entanglers

In this paper, we discuss the characteristics of special perfect entanglers from a new perspective, present the results obtained from the implementation of special perfect entangler circuits using cross-resonance interaction, and discuss their applications. First, we show that the entangling power of a two-qubit gate is proportional to the mean squared length of the chords present in the argand diagram of squared eigenvalues of the nonlocal part of the gate, and derive the entangling characteristics of special perfect entanglers from the argand diagram associated with them. Next, we discuss the implementation of a single-parameter special perfect entangler circuit in an IBM quantum processor. We implement the circuit for nine different parameters using two methods. In the first method, we use two echoed cross-resonance gates for implementation, and in the second method, we use pulse-level programming to define the pulse sequence of part of the circuits. For a particular input state, we perform quantum state tomography, calculate state fidelity and concurrence of the output density matrices, and compare the results obtained in both methods of implementation. We also measure the average gate fidelity for the B gate circuit. We construct a universal two-qubit quantum circuit using the special perfect entangler circuit. This universal circuit can be used to generate all two-qubit gates in IBM quantum processors. We also show that \((n-1)\) B gate circuits can be used to generate n-qubit GHZ and perfect W states. We generate three-qubit perfect W state in IBM quantum processor. Perfect W state generated using pulse-level programming shows better fidelity than the state generated using four echoed cross-resonance gates.