Communication-Efficient Distributed Inverse Quantum Fourier Transform
The scalability of quantum computing is currently limited by physical, technological, and architectural constraints that hinder the integration of a large number of qubits within a single quantum processor. Distributed quantum computing (DQC) has therefore emerged as a viable alternative, aiming to interconnect multiple smaller quantum processing units (QPUs) to jointly operate on a global quantum state. While this paradigm enables scalable architectures, it introduces significant communication overhead due to the cost of non-local quantum operations across distant nodes. In this work we propose a distributed formulation of the iQFT over a quantum network composed of $P$ nodes, each hosting $Q$ qubits, enabling the execution on a logical register of size $n = P \cdot Q$. Furthermore, we introduce a communication-efficient variant based on a threshold-driven pruning strategy, referred to as a \emph{communication horizon}, which exploits the exponentially decreasing significance of controlled-phase rotations to safely omit remote gates with negligible impact. By reducing the number of inter-node quantum interactions, the proposed approach significantly lowers the quantum communication requirements of the distributed iQFT while preserving its functional correctness. Crucially, we show that this approach fundamentally alters the scaling of the algorithm: the entanglement resource consumption per node saturates to a constant value, reducing the global communication complexity from quadratic $\mathcal{O}(P^2)$ to linear $\mathcal{O}(P)$. As the iQFT constitutes a critical building block in many quantum algorithms, the techniques presented in this paper directly contribute to improving the practicality and scalability of distributed quantum computation.