Linear Circuit Synthesis using Weighted Steiner Trees

Abstract

CNOT circuits are a common building block of general quantum circuits. The problem of synthesizing and optimizing such circuits has received a lot of attention in the quantum computing literature. This problem is especially challenging for quantum devices with restricted connectivity, where two-qubit gates can only be placed between adjacent qubits. The state-of-the-art algorithms for optimizing the number of CNOT gates are heuristic algorithms that are based on Gaussian elimination and that use Steiner trees to connect between different subsets of qubits. In this article we suggest to consider weighted Steiner trees, and we present a simple low-cost heuristics to compute weights. The experimental evaluation shows that the suggested heuristic is always beneficial and reduces the number of the CNOT gates by up to 10%.