Scalable improvement of the generalized Toffoli gate realization using trapped-ion-based qutrits

TL;DR

This paper demonstrates a scalable method for implementing multi-qubit Toffoli gates using trapped-ion qutrits, improving efficiency and accuracy in quantum algorithms like Grover's search.

Contribution

It introduces a qutrit-based approach for scalable Toffoli gates that reduces resource requirements and enhances algorithm fidelity in trapped-ion quantum systems.

Findings

Successfully implemented up to 10-qubit Toffoli gates.

Compared standard qubit decomposition with qutrit approach, showing resource savings.

Enhanced Grover's search accuracy by monitoring leakage during gate operation.

Abstract

An efficient implementation of the Toffoli gate is of conceptual importance for running various quantum algorithms, including Grover's search and Shor's integer factorization. However, direct implementation of the Toffoli gate either entails a prohibitive increase in the number of two-qubit gates or requires ancilla qubits, whereas both of these resources are limited in the current generation of noisy intermediate-scale quantum devices. Here, we experimentally demonstrate a scalable $N$-qubit Toffoli gate improvement using $^{171}$Yb$^{+}$ trapped-ion-based optical-metastable-ground encoded qutrits for the cases of up to $N$=10. With the use of the Molmer-Sorensen gate as a basic entangling operation, we compare the standard qubit decomposition with the qutrit approach, where upper levels are used as ancillas.The presented decomposition requires only global control of the ancilla levels, which simplifies experimental implementation of the proposed approach. Using the example of a three-qubit Grover's search, we also demonstrate an increase in the algorithm's accuracy by monitoring the leakage from the qubit subspace during a qutrit-based Toffoli gate implementation.