Variational Quantum Algorithm based circuit that implements the Toffoli gate with multi inputs

TL;DR

This paper develops variational quantum algorithms to implement multi-input Toffoli gates using only single-qubit gates and CNOTs, optimizing circuit design with cost functions based on Hilbert-Schmidt inner product and observable expectation.

Contribution

It introduces two novel variational quantum algorithms for multi-input Toffoli gates, utilizing specific cost functions and ansatz architectures for efficient implementation.

Findings

Successful development of VQAs for multi-input Toffoli gates

Use of Hilbert-Schmidt inner product as a cost function

Implementation with PennyLane and specific ansatz circuits

Abstract

The prime objective of this study is to seek a circuit diagram for a multi-inputs Toffoli gate including only single qubit gates and CNOTs. In this regard, we have developed two variational quantum algorithms that can be used to implement a multi-inputs Toffoli gate. The cost functions of these two VQAs are derived by using the Hilbert Schmidt inner product and the expected value of an observable that can capture the difference between the inputs and outputs of a Toffoli gate. We employ two ansatz circuit architectures and use the PennyLane package to execute the optimization.