[Paper] Distributed Quantum Computing with Fan-Out Operations and Qudits: the Case of Distributed Global Gates (a Preliminary Study)

Source: arXiv - 2512.03685v1

Overview

Seng W. Loke’s preliminary study investigates how multipartite entanglement (e.g., GHZ states) and four‑level quantum systems (qudits) can be harnessed to perform distributed fan‑out operations and to compress quantum circuits across a network of quantum processors. By focusing on “global” two‑qubit gates—operations that simultaneously act on many qubits, such as the Mølmer‑Sørensen gate—the paper shows a pathway to dramatically reduce communication overhead and circuit depth in distributed quantum computing (DQC) architectures, especially those built from trapped‑ion hardware.

Key Contributions

• Distributed fan‑out via GHZ resources: Demonstrates how a single multipartite entangled state can replace many Bell‑pair links for broadcasting a qubit’s value across nodes.
• Qudit‑based circuit compression: Introduces a scheme that encodes two logical qubits into a single four‑dimensional qudit, cutting the number of inter‑node swaps needed for certain gate patterns.
• Application to global Mølmer‑Sørensen (MS) gates: Shows that fan‑out + qudit tricks enable the implementation of MS‑style global gates in a distributed setting with only a handful of entanglement resources.
• Preliminary cost analysis: Provides rough estimates of entanglement consumption, communication latency, and circuit depth improvements compared with standard distributed two‑qubit gate approaches.
• Design insights for quantum data‑centre routing: Discusses how the findings could influence the layout of quantum interconnects and compilation pipelines in large‑scale quantum cloud services.

Methodology

1. Resource model: The study assumes a network of quantum nodes, each capable of local single‑ and two‑qubit gates, plus the ability to generate and share GHZ states of arbitrary size.
2. Fan‑out construction: Starting from a GHZ state (|\text{GHZ}\rangle = (|0^{\otimes n}\rangle + |1^{\otimes n}\rangle)/\sqrt{2}), the author shows how a controlled‑NOT cascade can broadcast a control qubit’s value to all nodes with a single round of local CNOTs and a final measurement‑based correction.
3. Qudit encoding: By treating a four‑level system as two logical qubits ((|00\rangle, |01\rangle, |10\rangle, |11\rangle)), the protocol maps pairs of qubits that would otherwise need a swap across nodes onto a single qudit, thereby eliminating that swap.
4. Global gate simulation: The paper builds a circuit that mimics a global MS gate using the fan‑out primitive to distribute a control phase, then applies local two‑qubit interactions, and finally reverses the fan‑out.
5. Analytical cost comparison: The author derives formulas for the number of entangled pairs, GHZ size, and communication rounds required, contrasting them with the baseline approach that uses only Bell pairs and point‑to‑point teleportation.

Results & Findings

• Entanglement savings: For a network of (k) nodes, the fan‑out method reduces the required Bell‑pair count from (O(k^2)) (pairwise teleportation) to (O(k)) (one GHZ per global operation).
• Depth reduction: The combined fan‑out + qudit scheme collapses what would be a depth‑(O(k)) sequence of swaps into a constant‑depth subroutine, cutting overall circuit depth by up to 70 % in simulated benchmarks.
• Error propagation: Because the GHZ distribution is a single shot, the protocol’s error model is dominated by the fidelity of the GHZ generation; however, the subsequent local operations are unchanged, meaning existing error‑mitigation techniques can still be applied.
• Hardware alignment: Trapped‑ion platforms, which naturally support high‑fidelity global MS gates, can implement the proposed distributed MS gate with only modest modifications to their photonic interconnects.

Practical Implications

• Quantum cloud providers: The approach offers a concrete recipe for reducing the bandwidth needed between quantum processing units (QPUs) in a multi‑node cloud offering, potentially lowering latency and cost.
• Compiler optimizations: Quantum compilers can now target a “global‑gate” primitive that automatically expands into fan‑out + qudit blocks, enabling more aggressive depth‑compression passes for distributed workloads.
• Hardware design: Engineers designing quantum interconnects may prioritize high‑fidelity multipartite entanglement distribution (e.g., GHZ‑state photonic links) over a large pool of point‑to‑point Bell‑pair channels.
• Algorithmic impact: Algorithms that heavily rely on collective operations—variational quantum eigensolvers, quantum approximate optimization, and certain quantum machine‑learning kernels—could see speed‑ups when run on a distributed ion‑trap cluster using this technique.

Limitations & Future Work

• Preliminary nature: The study is largely theoretical; experimental validation on a real multi‑node ion‑trap system is still pending.
• GHZ generation overhead: Creating large‑scale GHZ states remains challenging; the paper assumes idealized generation and does not fully account for decoherence during distribution.
• Qudit control complexity: Operating on four‑level systems requires hardware that can reliably address and read out qudit states, which many current platforms lack.
• Scalability analysis: While asymptotic savings are promising, concrete scaling curves for networks beyond a handful of nodes need empirical measurement.

Future research directions suggested include:

1. Building a prototype GHZ‑based interconnect.
2. Extending the qudit compression idea to higher‑dimensional systems.
3. Integrating the primitives into existing quantum compilation toolchains to assess end‑to‑end performance gains.

Authors

• Seng W. Loke

Paper Information

• arXiv ID: 2512.03685v1
• Categories: quant-ph, cs.DC, cs.ET
• Published: December 3, 2025
• PDF: Download PDF