Characteristics, Implementation and Applications of Special Perfect Entangler Circuits

TL;DR

This paper explores special perfect entangler circuits, their characteristics, implementation via cross-resonance interaction, and their applications in generating universal and multi-qubit entangled states, with experimental validation and fidelity analysis.

Contribution

It introduces a method to construct and implement special perfect entangler circuits, analyzes their entangling power, and demonstrates their use in generating complex multi-qubit entangled states.

Findings

Implementation of a special perfect entangler circuit with high fidelity.

Demonstration of universal two-qubit circuits using special perfect entanglers.

Generation of three-qubit perfect W state with improved fidelity.

Abstract

We discuss the characteristics of special perfect entanglers and construct single parameter two-qubit circuits which are locally equivalent to special perfect entanglers. We present the results obtained from the implementation of one of the circuits using cross-resonance interaction and discuss their applications. First, we show that the ability of two-qubit gates to create entangled states can be described using the chords present in the argand diagram of squared eigenvalues of nonlocal part of two-qubit gates. We show that the entangling power of a two-qubit gate is proportional to the mean squared length of the chords. We deduce the entangling characteristics of special perfect entanglers from the argand diagram associated with them. We implement a special perfect entangler circuit using echoed cross-resonance gate and pulse-level programming for nine different circuit parameters. For a particular input state, we perform quantum state tomography and calculate state fidelity and concurrence of the obtained output density matrices. We also measure the average gate fidelity for B gate circuit. We construct two universal two-qubit quantum circuits using the special perfect entangler circuits. These universal circuits can be used to generate all two-qubit gates. We 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. Perfect W state generated using pulse-level programming shows better fidelity than the state generated using echoed cross-resonance gate.