Look-ahead Schemes for Nearest Neighbor Optimization of 1D and 2D Quantum Circuits

Ensuring nearest neighbor compliance of quantum circuits by inserting SWAP gates has heavily been considered in the past. Here, quantum gates are considered which work on non-adjacent qubits. SWAP gates are applied in order to "move" these qubits onto adjacent positions. However, a decision how exactly the SWAPs are "moved" has mainly been made without considering the effect a "movement" of qubits may have on the remaining circuit. In this work, we propose a methodology for nearest neighbor optimization which addresses this problem by means of a look-ahead scheme. To this end, two representative implementations are presented and discussed in detail. Experimental evaluations show that, in the best case, reductions in the number of SWAP gates of 56% (compared to the state-of-the-art methods) can be achieved following the proposed methodology.