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 global register of size 𝑛=𝑃⋅𝑄. Furthermore, we introduce a communication-efficient variant based on a threshold-driven pruning strategy, referred to as a 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 operating within a strictly bounded approximation error. 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 O(P²) to linear 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.

Palabras clave: Distributed Quantum Computing, Quantum Fourier Transform, Quantum computing, Quantum communication, Quantum algorithm, Quantum internet