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arXiv:2603.06387

Quantum Hamlets: Distributed Compilation of Large Algorithmic Graph States

Anthony Micciche, Naphan Benchasattabuse, Andrew McGregor, Michal Hajdušek, Rodney Van Meter, Stefan Krastanov

quant-phSubmitted Mar 6, 2026• Announced Mar 9, 2026• 0 citations
v1 · Mar 6, 2026v2 · May 3, 2026
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Abstract

We investigate the problem of compiling the generation of graph states to arbitrarily many distributed homogeneous quantum processing units (QPUs), providing a scalable partitioning algorithm and graph state generation protocol to minimize the number of Bell pairs required. To this goal, we consider the problem of balanced k graph partitioning with the objective of minimizing the sizes of the maximum matchings between partitions, a more natural measure of entanglement compared to the naive but common metric of cut edges. We show that our heuristic algorithm, BURY, partitions graph states to require fewer Bell pairs for generation than state-of-the-art k partition algorithms. Furthermore, we show that BURY reduces the cut-rank of the partitions, demonstrating that the partitioning found by our algorithm is likely to minimize the Bell pair utilization of any future improved distributed graph state generation protocol. Additionally, we discuss how one could straightforwardly apply our methods to the dynamic case where the graph state generation and measurement are performed concurrently. Our study of the balanced minimum maximum matching k partition problem and the heuristic algorithm we design provides a scalable foundation for reducing quantum network overhead for distributed measurement-based quantum computation (MBQC), as well as any scheme where distributed graph state generation is desired.

Comments
13 pages, 12 figures

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We investigate the problem of compiling the generation of graph states to arbitrarily many distributed homogeneous quantum processing units (QPUs), providing a scalable partitioning algorithm and graph state generation protocol to minimize the number of Bell pairs required. To this goal, we consider the problem of balanced k graph partitioning with the objective of minimizing the sizes of the maximum matchings between partitions, a more natural measure of entanglement compared to the naive but common metric of cut edges. We show that our heuristic algorithm, BURY, partitions graph states to require fewer Bell pairs for generation than state-of-the-art k partition algorithms. Furthermore, we show that BURY reduces the cut-rank of the partitions, demonstrating that the partitioning found by our algorithm is likely to minimize the Bell pair utilization of any future improved distributed graph state generation protocol. Additionally, we discuss how one could straightforwardly apply our methods to the dynamic case where the graph state generation and measurement are performed concurrently. Our study of the balanced minimum maximum matching k partition problem and the heuristic algorithm we design provides a scalable foundation for reducing quantum network overhead for distributed measurement-based quantum computation (MBQC), as well as any scheme where distributed graph state generation is desired.
Scalable quantum computing requires execution models that go beyond the capacity of a single quantum processing unit (QPU). Although current hardware platforms continue to increase in qubit count, large fault-tolerant applications require substantially more physical qubits, stronger connectivity, and lower effective error rates than a monolithic near-term device can provide. Multi-QPU and multi-core architectures therefore form an important route towards larger quantum systems. However, distributing a quantum computation introduces compiler and architecture constraints that do not arise in conventional classical distribution. A partitioned quantum circuit separates gates and qubits that may still be logically entangled or mutually dependent. The system must therefore provide quantum resources that support entanglement between the distributed circuit fragments, while each local subcircuit must remain executable on the hardware topology of its assigned QPU. In this thesis, graph states serve as the explicit interconnection resources for these nonlocal dependences: they encode the entanglement structure required to support teleportation-based operations across QPUs. This thesis studies scalable quantum execution as an architecture-driven compilation problem. It develops a staged framework in which distribution, graph-state-based interconnection, and interconnection robustness are treated as dependent compiler decisions. The framework addresses three connected questions: 1) how a large quantum circuit should be divided when the resulting subcircuits must match real QPU topologies; 2) how the graph states required to entangle and operate across the distributed circuit boundaries can be prepared efficiently on constrained hardware; and 3) how those graph-state resources can remain useful under the loss and fusion failures that arise during preparation and use. These questions define an execution path from a large logical circuit to distributed local workloads connected by explicit entanglement resources. The thesis makes three main technical contributions that instantiate this framework. 1) It introduces hardware-aware circuit cutting, which incorporates the relationship between subcircuit interaction graphs and target QPU topology into the partitioning objective. This stage produces distributed workloads and explicit cut boundaries where quantum entanglement must be supplied across QPUs. 2) It formulates graph-state preparation as the resource-generation stage for those boundaries and develops methods that reduce preparation depth and emitter usage by exploiting graph-state equivalence and divide-and-conquer construction. 3) It develops a robust graph-state interconnection scheme that uses tree-encoded fusion and spin-memory-assisted compilation to tolerate photon loss and probabilistic fusion failures, so that the graph state can serve as a reliable connection between distributed quantum program fragments.
To overcome the physical limitations of scaling monolithic quantum computers, distributed quantum computing (DQC) interconnects multiple smaller-scale quantum processing units (QPUs) to form a quantum network. However, this approach introduces a critical challenge, namely the high cost of quantum communication between remote QPUs incurred by quantum state teleportation and quantum gate teleportation. To minimize this communication overhead, DQC compilers must strategically partition quantum circuits by mapping logical qubits to distributed physical QPUs. Static graph partitioning methods are fundamentally ill-equipped for this task as they ignore execution dynamics and underlying network topology, while metaheuristics require substantial computational runtime. In this work, we propose a heuristic based on beam search to solve the circuit partitioning problem. Our time-aware algorithm incrementally constructs a low-cost sequence of qubit assignments across successive time steps to minimize overall communication overhead. The time and space complexities of the proposed algorithm scale quadratically with the number of qubits and linearly with circuit depth, offering a significant computational speedup over common metaheuristics. We demonstrate that our proposed algorithm consistently achieves significantly lower communication costs than static baselines across varying circuit sizes, depths, and network topologies, providing an efficient compilation tool for near-term distributed quantum hardware.
Measurement-Based Quantum Computing (MBQC) is inherently well-suited for Distributed Quantum Computing (DQC): once a resource state is prepared and distributed across a network of quantum nodes, computation proceeds through local measurements coordinated by classical communication. However, since non-local gates acting on different Quantum Processing Units (QPUs) are a bottleneck, it is crucial to optimize the qubit assignment to minimize inter-node entanglement of the shared resource. For graph state resources shared across two QPUs, this task reduces to finding bipartitions with minimal cut rank. We introduce a simulated annealing-based algorithm that efficiently updates the cut rank when two vertices swap sides across a bipartition, such that computing the new cut rank from scratch, which would be much more expensive, is not necessary. We show that the approach is highly effective for determining qubit assignments in distributed MBQC by testing it on grid graphs and the measurement-based Quantum Approximate Optimization Algorithm (QAOA).
Distributed Quantum Computing (DQC) addresses the physical scaling limitations of monolithic quantum processors by networking modular Quantum Processing Units (QPUs). Efficient execution of quantum algorithms on DQC architectures requires compiling them across QPUs while minimizing inter-QPU communication bottlenecks, primarily through circuit partitioning. However, current evaluations of state-of-the-art partitioning heuristics focus primarily on the total entanglement cost of the partitions, failing to capture the broader structural and temporal overheads introduced by distributed network constraints. This paper addresses this evaluation gap by applying established monolithic benchmarking metrics to partitioned distributed circuits to quantify the performance impact of network constraints. Using an open-source, automated evaluation pipeline, we systematically assess diverse partitioning algorithms across standardized workloads and quantum network topologies. Our empirical results reveal that partitioning algorithms with comparable entanglement costs can still introduce drastically different physical execution penalties. By exposing these hidden trade-offs, such as severe increases in circuit depth and substantial reductions in gate density, this study demonstrates that comprehensive circuit-level metrics are essential for guiding the future design of DQC compilers.
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.
Executing quantum algorithms over distributed quantum systems requires quantum circuits to be divided into sub-circuits which communicate via entanglement-based teleportation. Naively mapping circuits to qubits over multiple quantum processing units (QPUs) results in large communication overhead, increasing both execution time and noise. This can be minimised by optimising the assignment of qubits to QPUs and the methods used for covering non-local operations. Formulations that are general enough to capture the spectrum of teleportation possibilities lead to complex problem instances which can be difficult to solve effectively. This highlights a need to exploit the wide range of heuristic techniques used in the graph partitioning literature. This paper formalises and extends existing constructions for graphical quantum circuit partitioning and designs a new objective function that captures further possibilities for non-local operations via nested state teleportation . We adapt the well-known Fiduccia-Mattheyses heuristic to the constraints and problem objective and explore multilevel techniques that coarsen hypergraphs and partition at multiple levels of granularity. We find that this reduces runtime and improves solution quality of standard partitioning. We place these techniques within a larger framework, through which we can extract full distributed quantum circuits including teleportation instructions. We compare the entanglement requirements and runtimes with state-of-the-art methods, finding that we achieve the lowest entanglement costs in most cases. Averaging over a wide range of circuits, we reduce the entanglement requirements by 35% compared with the next best-performing method. We also find that our techniques can scale to much larger circuit sizes than competing methods, provided the number of partitions is not too large.