Optimizing Qubit Routing with Bridge Gates: Extending Quantum Circuit Efficiency Across Arbitrary Distances

Qubit routing is a critical challenge in quantum computing,
essential for implementing quantum circuits on hardware with limited
connectivity. This paper introduces a novel perspective on qubit routing by exploring the use of bridge gates, which enable the execution of
controlled NOT (CNOT) operations over non-adjacent qubits without re-routing the qubits. The study highlights the advantages of bridge gates
compared to SWAP gates, particularly their ability to preserve qubit
assignments and potentially optimize subsequent routing steps.
We propose an extension to the concept of bridge gates by generalizing
them for arbitrary distances and provide constructions demonstrating
their feasibility. By analysing their performance, we show that larger-distance bridge gates can significantly reduce the number of CNOT gates
in certain circuits. Furthermore, a new qubit routing problem is defined,
incorporating both SWAP and bridge gates, and we discuss how this
impacts the complexity of the problem.