DC-MBQC: A Distributed Compilation Framework for Measurement-Based Quantum Computing

TL;DR

This paper addresses the challenge of scaling MBQC by proposing DC-MBQC, a distributed compilation framework tailored for photonic MBQC. It formalizes the required photon lifetime as a central hardware-aware metric and two core subproblems—adaptive graph partitioning and layer scheduling—that enable efficient distributed compilation across multiple QPUs. The approach yields substantial practical gains, achieving up to 7.46× reduction in photon storage requirements and 6.82× faster execution on 8 QPUs across standard benchmarks, demonstrating the viability of distributed MBQC for photonic platforms. The framework is modular and compatible with existing single-QPU MBQC compilers, and the authors provide public source code to facilitate further development and adoption.

Abstract

Distributed quantum computing (DQC) is a promising technique for scaling up quantum systems. While significant progress has been made in DQC for quantum circuit models, there exists much less research on DQC for measurement-based quantum computing (MBQC), which is a universal quantum computing model that is essentially different from the circuit model and particularly well-suited to photonic quantum platforms. In this paper, we propose DC-MBQC, the first distributed quantum compilation framework tailored for MBQC. We identify and address two key challenges in enabling DQC for MBQC. First, for task allocation among quantum processing units (QPUs), we develop an adaptive graph partitioning algorithm that preserves the structure of the graph state while balancing the workload across QPUs. Second, for inter-QPU communication, we introduce the layer scheduling problem and propose an algorithm to solve it. Regrading realistic hardware requirements, we optimize the execution time of running quantum programs and the corresponding required photon lifetime to avoid fatal failures caused by photon loss. Our experiments demonstrate a $7.46\times$ improvement on required photon lifetime and $6.82\times$ speedup with 8 fully-connected QPUs, which further confirm the advantage of distributed quantum computing in photonic systems. The source code is publicly available at https://github.com/qfcwj/DC-MBQC.

Figures (10)

• Figure 1: Demonstration of the effect of different resource state clock rates on photon loss probability. The probability is estimated as $1-e^{-\alpha L}$, where $\alpha=0.2$ dB/km is the attenuation rate in state-of-the-art optical fibers and $L$ is the distance a photon traveled with $2/3$ speed of light in delay lines.
• Figure 2: An overview of our approach for minimizing the required photon lifetime in distributed MBQC.
• Figure 3: MBQC architecture with $1$-dimensional arranged Resource State Generators (RSGs).
• Figure 4: (a) Different resource state graphs; (b) Consequence of fusion on resource states; (c) Illustration of routing. After the fusion process, the photon $u$ and $v$ are connected, forming an entangled pair.
• Figure 5: Illustration of primary sources of required photon lifetime. (a) A fusee (photon B) must wait for its fusion partner (photon A) when they are generated in different execution layers. (b) A measuree (photon B) must be stored while waiting for classical information. This wait occurs because its measurement basis depends on measurement outcomes of other photons (A and C).

Theorems & Definitions (3)

• Definition 4.1: Layer Scheduling Problem
• Theorem 4.2: NP-hardness of Layer Scheduling
• proof