Mapping a Multiple-control Toffoli Gate Cascade to an Elementary Quantum Gate Circuit.

Xueyun Cheng, Zhijin Guan, Weiping Ding

Laxmidhar Biswal, Chandan Bandyopadhyay, Robert Wille +2 more

Multiple Control Toffoli (MCT) gates are the main constituent of reversible circuits. For quantum circuits, MCT gates are realized using quantum gate libraries such as NCV or NCVW which are composed of universal quantum gates like NOT, CNOT, V/V+, and W/W+. In order to improve the design of quantum circuits, the mapping of MCT gates to a cascade of these quantum gates has to be improved as well. In this work, we propose reconfigured structures of quantum gates realizing MCT gates. To this end, we rely on the established mapping structure, but append redundant gates which can be used afterwards for simplifications. Eventually, the proposed design is mapped to an NCVW quantum circuit. We have successfully tested our mapping technique. The obtained results have experimentally been compared to related work.

Philipp Niemann, Chandan Bandyopadhyay, Rolf Drechsler

Quantum computation received a steadily growing attention in recent years, especially supported by the emergence of publicly available quantum computers like the popular IBM QX series. In order to execute a reversible or quantum circuit on those devices, a mapping is required that replaces each reversible or quantum gate by an equivalent cascade of elementary, i.e. directly executable, gates-a task which tends to induce a significant mapping overhead. Several approaches have been proposed for this task which either rely on the swapping of physically adjacent qubits or the use of precomputed templates, so-called remote CNOT gates. In this paper, we show that combining both, swapping and remote gates, at the reversible circuit level has the prospect of significantly reducing the mapping overhead. We propose a methodology to compute the optimal combination of swaps and templates for Multiple-Controlled Toffoli gates. By using a formulation as a single-source shortest-path problem, a complete database of optimal combinations can be computed efficiently. Experimental results indicate that the mapping overhead can be significantly reduced.

Xiao‐Qiang Shao, Hong‐Fu Wang, Li Chen +2 more

Hyeong-Jin Kim

Zahra Sasanian, D. Michael Miller

Multiple-control Toffoli (MCT) gates are widely used in the synthesis of reversible circuits. These gates are not usually directly implemented and need to be mapped to circuits of more elementary components such as quantum gates. In this work, the realization of MCT gates with mixed controls is explored for the NCV quantum library containing NOT, CNOT, V and V+gates. The results show that the proposed approach significantly improves the best known NCV costs for MCT gates.