Communication-Efficient Distributed Inverse Quantum Fourier Transform

arXiv:2605.10710 · quant-ph · Submitted 2026-05-11 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: Today's paper: "Communication-Efficient Distributed Inverse Quantum Fourier Transform".

Mira: The gist The proposed work introduces a communication-efficient variant of the distributed iQFT that reduces global entanglement complexity from quadratic O(P 2) to linear O(P) by employing a threshold-driven pruning…

Kai: First, who's behind it and why it matters.

Title and authors: Kai: So, we’re looking at the title and authors for this piece, "Communication-Efficient Distributed Inverse Quantum Fourier Transform," and it sets the stage for what they're trying to achieve.

Mira: The paper is by F. Javier Cardamaa, Jorge Vazquez-Pérez, Tomas F. Pena, and Andrés Gómez Cácer from CiTIUS at the University of Santiago de Compostela in Spain.

Lev: That team has a background in quantum error correction research, which is interesting because distributed systems are inherently noisy environments where those codes become crucial for survival.

Kai: And the title itself immediately tells you the focus: it’s about making the inverse quantum Fourier transform communication-efficient when it’s happening across a network.

Mira: It signals that they aren't just looking at running a standard algorithm on multiple machines; they are specifically engineering how those machines talk to each other to minimize the cost of that interaction.

Lev: They’re aiming to address the inherent communication overhead that arises when you have many smaller quantum processing units linked together.

Kai: It suggests they are tackling the challenge head-on, moving past just running an exact simulation and focusing on what is actually practical for a distributed setup.

Mira: The authors clearly recognize that the standard theoretical limits for exact implementations were already formalized by Ebnenasir in reference twenty showing this work is building on existing complexity bounds <ref:2605.10710#pg2>.

Lev: That connection to prior work gives the entire proposal a solid theoretical foundation before they dive into their specific communication-efficient variant.

Kai: So, they’ve established the baseline problem—the quadratic complexity—and are now proposing a solution that fundamentally changes how we view distributed iQFTs on these networks.

Mira: The paper is setting up the framework to move away from the naive expectation of quadratic scaling toward something much more manageable for large-scale quantum computing.

Lev: It’s about finding a way to keep the required communication low enough that you don't lose your quantum advantage just because you added a few more nodes.

Kai: This paper is about taking a very dense, all-to-all interaction pattern and restructuring it systematically into local and distributed dependencies.

The paper's summary: Kai: Now, let’s look at what the abstract actually summarizes for us in "Communication-Efficient Distributed Inverse Quantum Fourier Transform."

Mira: Essentially, they break down the inverse quantum Fourier transform across P nodes, each with Q qubits, which gives you a total global register size of n = P times Q.

Lev: The standard iQFT on that big register requires quadratic two-qubit controlled-phase gates and has this all-to-all interaction pattern that’s the bottleneck.

Kai: They propose a systematic decomposition into local, intra-node operations and internode, or distributed, dependencies.

Mira: The key is introducing a communication horizon based on a threshold pruning strategy, which successfully reduces the global entanglement complexity from quadratic O(P two) to linear O(P) scaling <ref:2605.10710#pg2,successfully reduces the global entanglement complexity>.

Lev: That's the big claim—that by establishing this maximum communication horizon, they cut down on the number of required non-local quantum operations significantly.

Kai: They define a rotation angle theta(i times, i) = theta i - i times = -pi/two(i - i times), and the total number of controlled-phase gates, NCP(n), is determined by summing these interactions across the whole circuit <ref:2605.10710#pg2>.

Mira: The resulting gate complexity is still O(n two) in that initial calculation, but they are showing how pruning changes that practical requirement on the network <ref:2605.10710#pg2>.

Lev: So what this means for someone building a distributed setup is that you can design your network topology around this horizon rather than just assuming everything needs to be connected perfectly.

Kai: It’s about finding the sweet spot between achieving an exact transform and keeping the communication cost low enough to run it on real hardware.

The paper's improvements: Mira: The authors introduce several specific improvements, primarily focusing on how they define and utilize that communication horizon.

Kai: They formalize the maximum required interaction distance, d max, based on the algorithmic tolerance epsilon and node capacity Q.

Lev: Proposition one states this bound is strictly limited by d max = - two(epsilon) - one/Q + one which is a precise way to control the maximum distance between nodes <ref:2605.10710#pg3>.

Mira: That formula is crucial because it gives you a concrete parameter—the communication horizon—that lets you decide how far apart nodes can be while still maintaining the required approximation quality epsilon.

Lev: And then they have Corollary one which proves that in this communication-efficient distributed iQFT, the global entanglement complexity scales linearly O(P) with respect to the total number of nodes P <ref:2605.10710#pg3>.

Kai: They also validate this by looking at performance metrics like Fidelity vs. Threshold and Expected State Probability vs. Threshold to show accuracy is maintained under these constraints.

Mira: And look at resource scaling: the number of EPR pairs per node goes from linear scaling with P down to a constant saturation level, which means your entanglement overhead stops growing with the network size P.

Lev: That constant saturation is a very strong result because it shows that for large systems, you aren't being penalized linearly for adding more nodes in terms of EPR pairs.

Kai: They also show the coupling ratio eta approaches zero when thresholds are less than or equal to seven which suggests a fundamental decoupling between the nodes' communication needs <ref:2605.10710#pg3>.

Conclusion: Mira: So, to wrap up, "Communication-Efficient Distributed Inverse Quantum Fourier Transform" shows that you can drastically reduce the entanglement complexity by employing a threshold-driven pruning strategy.

Kai: The main result is moving the global entanglement complexity from quadratic O(P two) scaling down to linear O(P) scaling by establishing that communication horizon <ref:2605.10710#pg2>.

Lev: It gives us a tangible control parameter, d max, which dictates the maximum required interaction distance based on your required accuracy epsilon and node size Q.

Mira: The implication is that you can design distributed systems where long-range interactions are structurally dispensable for achieving a good approximation of the transform.

Kai: This work provides a scalable pathway for implementing large-scale quantum primitives on networked processors by effectively localizing the network overhead.

Lev: For running this on real hardware, knowing that the resource overhead per node saturates to O(one) regardless of how many nodes you add is a very practical piece of information <ref:2605.10710#pg3>.

Mira: The paper demonstrates that you can keep high algorithmic fidelity while statistically lowering accumulated phase error by selectively omitting remote gates with negligible impact.

Kai: It’s a solid contribution to making these large-scale Fourier transforms feasible on near-term networked systems right now.

Centro Singular de Investigación en Tecnologías Intelixentes (CiTIUS) · Departamento de Electrónica e Computación, Universidade de Santiago de Compostela · Galicia Supercomputing Center (CESGA)

quant-ph

Submitted: 2026-05-11

Updated: 2026-07-10

DOI: 10.1016/j.future.2026.108815

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 78/100

The gist: The gist The proposed work introduces a communication-efficient variant of the distributed iQFT that reduces global entanglement complexity from quadratic O(P 2) to linear O(P) by employing a

Key concepts

Distributed iQFT Formulation
This describes how the standard iQFT is broken down across multiple quantum processors (nodes). The circuit is split into local operations happening within a single node and internode operations between different nodes. This decomposition is essential because it allows the algorithm to manage dependencies locally where possible.
Communication Horizon
This is a pruning strategy used to reduce communication costs. It sets a maximum distance or range for necessary quantum interactions between nodes based on an algorithmic tolerance. Interactions beyond this horizon are safely omitted because their contribution to the final result becomes negligible, effectively limiting long-range communication.
Linear Global Entanglement Scaling
This is the main finding regarding resource consumption. Instead of entanglement requirements growing quadratically with the number of nodes (P^2), this new approach shows that the required entanglement per node stays constant (O(1)) relative to P. This means scaling up a distributed system becomes much more manageable in terms of required quantum resources.
Coupling Ratio ($\eta$)
The coupling ratio measures how strongly nodes are coupled or interacting with each other. The paper shows that for certain thresholds, this ratio approaches zero as the network grows. This indicates a fundamental decoupling between nodes, meaning the global communication overhead is drastically reduced compared to a fully connected distributed implementation.

Terminology

Summary

The gist The proposed work introduces a communication-efficient variant of the distributed iQFT that reduces global entanglement complexity from quadratic O(P 2) to linear O(P) by employing a threshold-driven pruning strategy, thereby significantly lowering quantum communication requirements while maintaining bounded approximation error.

Distributed iQFT Formulation

The paper presents a systematic decomposition of the iQFT across a quantum network composed of P nodes, each with Q qubits, enabling the execution of the transform over a global register of size n = P · Q The standard iQFT on an n-qubit register requires O(n 2) two-qubit controlled-phase gates and exhibits an all-to-all interaction pattern This quadratic gate complexity and dense connectivity pose significant challenges for both monolithic and distributed quantum architectures The circuit is restructured into a sequence of operations that distinguishes between intra-node (local) and internode (distributed) dependencies Local blocks are defined as interactions where both the control and target qubits reside within the same node p (so, p□ = p•), which can be executed entirely within the QPU without utilizing the quantum network

Communication-Efficient Pruning Strategy

The communication-efficient variant is based on a threshold-driven pruning strategy referred to as a communication horizon By establishing a maximum communication horizon, this approach successfully reduces the global entanglement complexity of the network from quadratic O(P 2) to linear O(P) scaling The rotation angle applied to a target qubit i□, controlled by qubit i•, is determined by the logical index difference k between them, denoted as θ(i•, i□) = θi□−i• = −π/2i□−i• The total number of controlled-phase gates, denoted as NCP(n), is determined by the summation of these interactions across the entire circuit: NCP(n) = Xn−1j=1j=n(n − 1)2

Communication Horizon and Scaling

The goal shifts from simply reducing NCP to minimizing the number of active inter-node links The pruning strategy leverages the geometric decay of the rotation angles derived in Section 2.1 to define a communication horizon Based on this truncation condition, we can formalize the maximum interaction range required in the distributed architecture Proposition 1 (Communication Horizon) states that for a distributed quantum register of node capacity Q and a target algorithmic tolerance ε, the maximum required interaction distance between nodes, denoted as the communication horizon dmax, is strictly bounded by: dmax = ⌈− log2(ε) − 1/Q + 1 Corollary 1 (Linear Global Entanglement Scaling) proves that in the communication efficient distributed iQFT, the global entanglement complexity scales linearly O(P) with respect to the total number of nodes P, rather than the quadratic O(P 2) scaling of the exact distributed implementation

Performance Metrics and Validation

The paper evaluates performance using several metrics including Fidelity vs. Threshold, Expected State Probability vs. Threshold, Scalability of entanglement resources (EPR per Node), Accuracy under connectivity constraints, and Coupling Ratio The analysis shows that the number of EPR pairs per node transitions from a linear scaling O(P) with respect to the network size to a constant saturation level O(1), effectively making the resource overhead independent of the system size P The Coupling Ratio η is shown to approach asymptotic zero (η → 0) for thresholds t ≤ 7, signifying a fundamental decoupling of the nodes

Conclusion and Future Directions

Ultimately, this approach provides a scalable pathway for implementing large-scale Quantum Phase Estimation and other Fourier-based primitives on near-term networked quantum processors The communication horizon dmax serves as a decisive control parameter that allows for a drastic reduction in the consumption of entanglement resources This work demonstrates that long-range interactions are structurally dispensable, successfully localizing the network overhead Future work should address the integration of this optimized iQFT schedule with quantum error correction codes suitable for distributed environments The stability implies that the application of the threshold does not alter the fundamental architectural efficiency of the distributed protocol

The paper is 2605.10710.

Improvements for AI systems

  1. textbf Communication-Efficient Distributed iQFT Implementation in Quantum Algorithms: The system can execute global quantum transforms with linear communication scaling O(P) instead of quadratic O(P 2). This is achieved by introducing a communication horizon based on threshold-driven pruning, which reduces the global entanglement complexity from quadratic O(P 2) to linear O(P).

  2. textbf Scalable Quantum Phase Estimation (QPE): The system can factor large integers in polynomial time using a distributed approach where the iQFT is implemented with a communication horizon dmax, ensuring that the entanglement resource consumption per node saturates to a constant value regardless of the total number of nodes P.

  3. textbf Robustness Against NISQ Noise: The system maintains high algorithmic fidelity by selectively omitting remote gates with negligible impact, which statistically lowers the accumulated phase error, as evidenced by results showing that the actual accumulated phase error is statistically lower than the sum of the absolute magnitudes of the discarded angles.

Abstract

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 times 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 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 O(P 2) 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.

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