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STMC: Small-Tile Multiple-Copy Compilation for Reliable Measurement-Based Quantum Computing

Rongchao Dong, Zewei Mo, Yingheng Li, Aditya Pawar, Jun Yang, Youtao Zhang, Xulong Tang

Published Oct 26, 2025• 0 citations
Publisher

Abstract

Measurement-based Quantum Computing (MBQC) achieves universal quantum computing by applying measurements on the photonic architectures. While it has many advantages, such as long qubit decoherence time and strong scalability, the success rate of MBQC execution is constrained by imperfect photon control, measurement, and fusion operations. Both fusion failure and photon loss necessitate the re-execution of the entire quantum circuit, leading to significant overhead in terms of additional execution time and increased consumption of resource state layers. Recent studies mainly focus on mitigating fusion failures and little attention has been paid to photon loss. In this paper, we propose STMC (Small-Tile Multiple-Copy) compilation framework to reduce the re-execution overhead caused by both the fusion failure and photon loss. Specifically, STMC first transforms a quantum circuit into a fusion graph and partitions the fusion graph into subgraphs. Then, STMC generates compact subgraph mappings that are appropriate for the size of a subportion in the resource state layer, referred to as a tile. Finally, STMC employs multiple copies of each subgraph when mapping to tiles, duplicates the execution of tiles in parallel, and finishes the whole circuit execution in order. The experimental results demonstrate that STMC achieves an average execution time speedup of 65.68× for successfully executing the circuit under a 75% fusion success rate, compared to prior work. Additionally, STMC reduces the number of resource state layers by three orders of magnitude and decreases the number of resource states by an average of 36.40×.

DOI
10.1109/iccad66269.2025.11240760

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Measurement-based Quantum Computing (MBQC) achieves universal quantum computing by applying measurements on the photonic architectures. While it has many advantages, such as long qubit decoherence time and strong scalability, the success rate of MBQC execution is constrained by imperfect photon control, measurement, and fusion operations. Both fusion failure and photon loss necessitate the re-execution of the entire quantum circuit, leading to significant overhead in terms of additional execution time and increased consumption of resource state layers. Recent studies mainly focus on mitigating fusion failures and little attention has been paid to photon loss. In this paper, we propose STMC (Small-Tile Multiple-Copy) compilation framework to reduce the re-execution overhead caused by both the fusion failure and photon loss. Specifically, STMC first transforms a quantum circuit into a fusion graph and partitions the fusion graph into subgraphs. Then, STMC generates compact subgraph mappings that are appropriate for the size of a subportion in the resource state layer, referred to as a tile. Finally, STMC employs multiple copies of each subgraph when mapping to tiles, duplicates the execution of tiles in parallel, and finishes the whole circuit execution in order. The experimental results demonstrate that STMC achieves an average execution time speedup of 65.68× for successfully executing the circuit under a 75% fusion success rate, compared to prior work. Additionally, STMC reduces the number of resource state layers by three orders of magnitude and decreases the number of resource states by an average of 36.40×.
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 7.46×7.46\times7.46× improvement on required photon lifetime and 6.82×6.82\times6.82× 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.
Photonic quantum computing provides a promising route toward quantum computation by naturally supporting the measurement-based quantum computation (MBQC) model. In MBQC, programs are executed through measurements on a pre-generated graph state, whose construction largely depends on probabilistic fusion operations. However, fusion operations in PQC are vulnerable to two major error sources: fusion failure and fusion erasure. As a result, MBQC compilation must account for both error mechanisms to generate reliable and efficient photonic executions. Prior state-of-the-art MBQC compilation, represented by OneAdapt, is designed for all-photonic architectures and mainly focuses on handling fusion failures. Nevertheless, it does not explicitly model fusion erasures induced by photon loss, which can be substantially more damaging than fusion failures. To mitigate fusion erasure errors, we introduce a new MBQC compilation scheme built upon the spin qubit quantum memory. We propose tree-encoded fusion, an encoding strategy that suppresses erasure errors during graph-state generation. We further incorporate this scheme into a compiler framework with algorithms that reduce the execution overhead of quantum programs. We evaluate the proposed framework using a realistic PQC simulator on six representative quantum algorithm benchmarks across multiple program scales. The results show that tree-encoded fusion achieves better robustness than alternative fusion-encoding strategies, and that our compiler provides exponential improvement over OneAdapt. In addition, we validate the feasibility of our approach through a proof-of-concept demonstration on real PQC hardware.
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 a7.46×7.46 \times7.46×improvement on required photon lifetime and6.82×6.82 \times6.82×speedup with 8 fully-connected QPUs, which further confirm the advantage of distributed quantum computing in photonic systems.
Measurement-based quantum computing relies on the generation of large entangled cluster states that act as a universal resource on which logical circuits can be imprinted and executed through local measurements. A number of strategies for constructing sufficiently large photonic cluster states propose fusing many smaller resource states generated by a series of quantum emitters. However, the fusion process is inherently probabilistic with a 50% success probability in standard guise. A recent proposal has shown that, in the limit of low loss, the probability of achieving successful fusion may be boosted to near unity by redundantly encoding the vertices of linear graph states using Greenberger-Horne-Zeilinger states [Quantum 7, 992 (2023)]. Here we present a protocol for deterministically generating redundantly encoded photonic resource states using single quantum emitters, and study the impact of protocol errors and photonic losses on the generated resource states and type-II photonic fusion. Our work provides a route for efficiently constructing complex entangled photonic qubit states for photonic quantum computing and quantum repeaters.
Quantum computing has rapidly evolved in recent years and has established its supremacy in many application domains. While matter-based qubit platforms such as superconducting qubits have received the most attention so far, there is a rising interest in photonic qubits lately, which show advantages in parallelism, speed, and scalability. Photonic qubits are best served by the paradigm of measurement-based quantum computation (MBQC). To deliver the promise of measurement-based photonic quantum computing (MBPQC), the photon cluster state depth and photon utilization are two of the most important metrics. However, little attention has been paid to optimizing the depth and utilization when mapping quantum circuits to the photon clusters. In this paper, we propose a compiler framework that achieves automatic and dynamic depth and utilization optimizations. Our approach consists of an MBPQC mapping mechanism that maps optimized measurement patterns on a cluster state and a cluster state pruning strategy that removes all possible redundancies without impacting the circuit functions. Experimental results on five quantum benchmark with three different qubit numbers indicate our approach achieves an average of 63.4% cluster depth reduction and 22.8% photon utilization improvements.
Measurement-based quantum computing (MBQC) is a promising quantum computing paradigm that carries out computation through one-way measurements on entangled photon qubits. Practical photonic hardware first generates a 2D mesh of resource states with each being a small number of entangled photon qubits and then exploits fusion operations to connect resource states to scale up the computation. Given that the fusion operation is highly error-prone, it is important to reduce the number of fusions for an MBQC circuit.