Stesso: A reconfigurable decomposition of $n$-bit Toffoli gates using symmetrical logical structures and adjustable support qubits

TL;DR

Stesso introduces a reconfigurable decomposition method for $(n+1)$-bit Toffoli gates using support qubits, optimizing quantum costs and enabling flexible circuit design for symmetrical quantum computer layouts.

Contribution

The paper presents a novel, reconfigurable decomposition approach for Toffoli gates that reduces quantum costs and supports various circuit polarities using support qubits.

Findings

Lower quantum costs compared to conventional methods

Supports various circuit polarities and configurations

Effective for symmetrical quantum computer layouts

Abstract

An $(n+1)$-bit Toffoli gate is mainly utilized to construct other quantum gates and operators, such as Fredkin gates, arithmetical adders, and logical comparators, where $n \geq 2$. Several researchers introduced different methods to decompose $(n+1)$-bit Toffoli gates in a quantum circuit into a set of standard 3-bit Toffoli gates or a set of elementary quantum gates, such as single-qubit and two-qubit gates. However, these methods are not effectively reconfigurable for linearly connected symmetrical structures (layouts) of contemporary quantum computers, usually utilizing more ancilla qubits. This paper introduces a new structural design method to effectively decompose $(n+1)$-bit Toffoli gates by utilizing configurable ancilla qubits, which we named the ``support qubits". Collectively, we call our decomposition method for symmetrical structures using support qubits the ``step-decreasing structures shaped operators (Stesso)". The main advantage of Stesso is to configurable construct different decomposed operators of various polarities and intermediate sub-circuits, such as Positive Polarity-Stesso, Mixed Polarity-Stesso, and Generalized-Stesso. With Stesso, it has been experimentally proven that $(n+1)$-bit Toffoli gates always have lower quantum costs than using conventional composition methods.