Generalized Toffoli gate decomposition using ququints: Towards realizing Grover's algorithm with qudits

TL;DR

This paper introduces an efficient method for decomposing generalized Toffoli gates using five-level qudits (ququints), enabling scalable quantum computation and demonstrating advantages in implementing Grover's algorithm with qudits.

Contribution

It presents a novel decomposition of the generalized Toffoli gate on ququints with linear depth and no ancillary qubits, facilitating scalable quantum algorithms with qudits.

Findings

O(N) asymptotic depth for N-qubit Toffoli gate decomposition

Efficient implementation of Grover's algorithm using qudits

Potential applicability across various quantum hardware platforms

Abstract

Qubits, which are quantum counterparts of classical bits, are used as basic information units for quantum information processing, whereas underlying physical information carriers, e.g. (artificial) atoms or ions, admit encoding of more complex multilevel states -- qudits. Recently, significant attention is paid to the idea of using qudit encoding as a way for further scaling quantum processors. In this work, we present an efficient decomposition of the generalized Toffoli gate on the five-level quantum systems, so-called ququints, that uses ququints' space as the space of two qubits with a joint ancillary state. The basic two-qubit operation that we use is a version of controlled-phase gate. The proposed $N$-qubit Toffoli gate decomposition has $O(N)$ asymptotic depth using no ancillary qubits. We then apply our results for Grover's algorithm, where we indicate on the sizable advantage of the using qudit-based approach with the proposed decomposition. We expect that our results are applicable for quantum processors based on various physical platforms.