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arXiv:2501.11816

Binary integer programming for optimizing ebit cost in distributed quantum circuits with fixed module allocation

Cha, Hyunho, Lee, Jungwoo

Published Jan 21, 2025• 1 citation
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Abstract

Modular and networked quantum architectures can scale beyond the qubit count of a single device, but executing a circuit across modules requires implementing non-local two-qubit gates using shared entanglement (ebits) and classical communication, making ebit cost a central resource in distributed execution. The resulting distributed quantum circuit (DQC) problem is combinatorial, motivating prior heuristic approaches such as hypergraph partitioning. In this work, we decouple module allocation from distribution. For a fixed module allocation (i.e., assignment of each qubit to a specific Quantum Processing Unit), we formulate the remaining distribution layer as an exact binary integer programming (BIP). This yields solver-optimal distributions for the fixed-allocation subproblem and can be used as a post-processing step on top of any existing allocation method. We derive compact BIP formulations for four or more modules and a tighter specialization for three modules. Across a diverse benchmark suite, BIP post-processing reduces ebit cost by up to 20\% for random circuits and by more than an order of magnitude for some arithmetic circuits. While the method incurs offline classical overhead, it is amortized when circuits are executed repeatedly.

DOI
10.48550/arxiv.2501.11816

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Modular and networked quantum architectures can scale beyond the qubit count of a single device, but executing a circuit across modules requires implementing non-local two-qubit gates using shared entanglement (ebits) and classical communication, making ebit cost a central resource in distributed execution. The resulting distributed quantum circuit (DQC) problem is combinatorial, motivating prior heuristic approaches such as hypergraph partitioning. In this work, we decouple module allocation from distribution. For a fixed module allocation (i.e., assignment of each qubit to a specific Quantum Processing Unit), we formulate the remaining distribution layer as an exact binary integer programming (BIP). This yields solver-optimal distributions for the fixed-allocation subproblem and can be used as a post-processing step on top of any existing allocation method. We derive compact BIP formulations for four or more modules and a tighter specialization for three modules. Across a diverse benchmark suite, BIP post-processing reduces ebit cost by up to 20% for random circuits and by more than an order of magnitude for some arithmetic circuits. While the method incurs offline classical overhead, it is amortized when circuits are executed repeatedly.
Abstract Modular and networked quantum architectures can scale beyond the qubit count of a single device, but executing a circuit across modules requires implementing non-local two-qubit gates using shared entanglement (ebits) and classical communication, making ebit cost a central resource in distributed execution. The resulting distributed quantum circuit (DQC) problem is combinatorial, motivating prior heuristic approaches such as hypergraph partitioning. In this work, we decouple module allocation from distribution. For a fixed module allocation (i.e., assignment of each qubit to a specific quantum processing unit), we formulate the remaining distribution layer as an exact binary integer programming (BIP). This yields solver optimal distributions for the fixed allocation subproblem and can be used as a post-processing step on top of any existing allocation method. We derive compact BIP formulations for four or more modules and a tighter specialization for three modules. Across a diverse benchmark suite, BIP post-processing reduces ebit cost by up to 20% for random circuits and by more than an order of magnitude for some arithmetic circuits. While the method incurs offline classical overhead, it is amortized when circuits are executed repeatedly.
Distributed Quantum Computing (DQC) enables the execution of quantum circuits across multiple interconnected quantum processing units (QPUs), but requiring efficient qubit allocation and network topology design to optimize computational performance. Proper qubit allocation minimizes entanglement costs across QPUs, balances computational workload, and ensures efficient execution of quantum computing tasks. Meanwhile, network topology plays a crucial role in reducing entanglement routing complexity and communication overhead for remote quantum gate operations. In this paper, we propose a joint optimization framework for network topology design and qubit allocation in DQC to minimize the communication overhead. We formulate the problem as a tractable integer nonlinear programming model that explicitly incorporates entanglement routing, thereby ensuring a more tractable optimization process. To further improve computational efficiency, we present a partially linearized version of the problem, making it solvable using any classical optimization solver. Extensive simulations on both random and real-world quantum circuits validate the effectiveness of our proposed approach, demonstrating its capability to handle complex quantum circuits while reducing communication costs in DQC.
Modular quantum computing architectures are a promising alternative to monolithic QPU (Quantum Processing Unit) designs for scaling up quantum devices. They refer to a set of interconnected QPUs or cores consisting of tightly coupled quantum bits that can communicate via quantum-coherent and classical links. In multi-core architectures, it is crucial to minimize the amount of communication between cores when executing an algorithm. Therefore, mapping a quantum circuit onto a modular architecture involves finding an optimal assignment of logical qubits (qubits in the quantum circuit) to different cores with the aim to minimize the number of expensive inter-core operations while adhering to given hardware constraints. In this paper, we propose for the first time a Quadratic Unconstrained Binary Optimization (QUBO) technique to encode the problem and the solution for both qubit allocation and inter-core communication costs in binary decision variables. To this end, the quantum circuit is split into slices, and qubit assignment is formulated as a graph partitioning problem for each circuit slice. The costly inter-core communication is reduced by penalizing inter-core qubit communications. The final solution is obtained by minimizing the overall cost across all circuit slices. To evaluate the effectiveness of our approach, we conduct a detailed analysis using a representative set of benchmarks having a high number of qubits on two different multi-core architectures. Our method showed promising results and performed exceptionally well with very dense and highly-parallelized circuits that require on average 0.78 inter-core communications per two-qubit gate.
This paper addresses the challenge of scaling quantum computing by employing distributed quantum algorithms across multiple processors. As quantum circuits grow in complexity, efficiently managing the entanglement resources required for communication between quantum processing units (QPUs) becomes increasingly critical. We propose novel methods to optimize entanglement consumption while accounting for network constraints. Our approach leverages graph partitioning techniques to optimize both qubit teleportation and gate teleportation, minimizing the number of Einstein-Podolsky-Rosen (EPR) pairs required to execute general quantum circuits. Additionally, we formulate an integer linear program (ILP) to further reduce entanglement requirements by mapping the logical resources of partitioned circuits to the physical constraints of the underlying quantum network. Finally, we analyze the entanglement cost for implementing the Quantum Fourier Transform (QFT) across multiple QPUs, employing an approach that exploits the circuit's structure to minimize total entanglement consumption. These contributions provide a pathway to scalable and resource-efficient distributed quantum computing.
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.
This paper addresses the challenge of scaling quantum computing by employing distributed quantum algorithms across multiple processors. We propose a novel circuit partitioning method that leverages graph partitioning to optimize both qubit and gate teleportation, minimizing the required Einstein-Podolsky-Rosen (EPR) pairs for executing general quantum circuits. Additionally, we formulate an integer linear program to further reduce entanglement requirements by mapping the logical resources of partitioned circuits to the physical constraints of the quantum network. Finally, we analyze the entanglement cost of implementing the Quantum Fourier Transform (QFT) across multiple QPUs, exploiting the circuit's structure to minimize total entanglement consumption.