Researchers have established a mathematical framework to optimize qubit routing on restricted quantum hardware, significantly reducing the number of required CNOT gates. The proof provides bounds for synthesizing n-qubit phase polynomials with g terms, ranging from O(gn/max(log g, 1)) to O(gn) gates. This breakthrough is crucial when targeting hardware with limitations on CNOT gate applications, as not all CNOTs are permissible. By developing a method to route qubits using SWAP-based techniques, the need for excessive gate overhead is alleviated, allowing for more efficient quantum computation. The findings have significant implications for quantum computing, as they enable the execution of complex quantum operations on restricted hardware with reduced overhead1. This matters to quantum computing practitioners because it enables them to perform complex quantum operations on restricted hardware more efficiently.