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Qubit allocation in modular quantum architectures via reinforcement learning

Victor Carballo Araruna

Published Jan 28, 2026• 0 citations
OpenAlex

Abstract

The scaling of quantum processors is currently limited by technical challenges such as decoherence and cross- talk. As the number of qubits grows, the interference between them adds more noise to the computations. Distributed quantum computing addresses this limitation by interconnecting smaller, easier-to-handle quantum cores, but it introduces the challenge of minimizing slow, error-prone inter-core communication. The task of distributing quantum circuits across cores to minimize communication costs is known as the Qubit Allocation problem. This work is centered on finding a deep learning approach to this problem, focusing on scalability and improving the state-of-the-art performance. Classical algorithms like the Hungarian Qubit Allocation (HQA) currently represent the state of the art, but they suffer from poor scalability with circuit size. In contrast, existing Deep Learning optimizations like Reinforcement Learning (RL) approaches often lack flexibility, requiring retraining if hardware configurations change, and are far from the solution quality of classical methods. However, these are worth exploring due to the good scalability and execution times. To overcome these limitations, this thesis proposes a flexible, transformer-based architecture capable of handling arbitrary numbers of qubits and cores without retraining. The policy is trained using a combination of REINFORCE and Group Relative Policy Optimization, two well-known RL algorithms. Furthermore, to explore the test-time compute paradigm applied to this problem, we introduce QAllocZero, an AlphaZero-inspired tree search algorithm we implemented in C++ that utilizes the trained policy as a heuristic. The results show that the trained policy achieves up to 33% improvement in allocation cost with respect to the state of the art (HQA) for the Cuccaro Adder and narrows the gap between RL and HQA for the most common circuits while maintaining scalable execution time. These findings show that learning-based approaches can effectively break the computational bottlenecks of classical algorithms, a crucial step for managing future systems with millions of qubits. All the code is open source and can be found in the porject's repository (https://github.com/Vicara12/MAI-TFM_RL_Qubit_Allocation).

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The scaling of quantum processors is currently limited by technical challenges such as decoherence and cross- talk. As the number of qubits grows, the interference between them adds more noise to the computations. Distributed quantum computing addresses this limitation by interconnecting smaller, easier-to-handle quantum cores, but it introduces the challenge of minimizing slow, error-prone inter-core communication. The task of distributing quantum circuits across cores to minimize communication costs is known as the Qubit Allocation problem. This work is centered on finding a deep learning approach to this problem, focusing on scalability and improving the state-of-the-art performance. Classical algorithms like the Hungarian Qubit Allocation (HQA) currently represent the state of the art, but they suffer from poor scalability with circuit size. In contrast, existing Deep Learning optimizations like Reinforcement Learning (RL) approaches often lack flexibility, requiring retraining if hardware configurations change, and are far from the solution quality of classical methods. However, these are worth exploring due to the good scalability and execution times. To overcome these limitations, this thesis proposes a flexible, transformer-based architecture capable of handling arbitrary numbers of qubits and cores without retraining. The policy is trained using a combination of REINFORCE and Group Relative Policy Optimization, two well-known RL algorithms. Furthermore, to explore the test-time compute paradigm applied to this problem, we introduce QAllocZero, an AlphaZero-inspired tree search algorithm we implemented in C++ that utilizes the trained policy as a heuristic. The results show that the trained policy achieves up to 33% improvement in allocation cost with respect to the state of the art (HQA) for the Cuccaro Adder and narrows the gap between RL and HQA for the most common circuits while maintaining scalable execution time. These findings show that learning-based approaches can effectively break the computational bottlenecks of classical algorithms, a crucial step for managing future systems with millions of qubits. All the code is open source and can be found in the porject's repository (https://github.com/Vicara12/MAI-TFM_RL_Qubit_Allocation).
The scaling of quantum processors is currently limited by technical challenges such as decoherence and cross-talk. As the number of qubits grows, interference increases the computational noise. Distributed quantum computing addresses these limitations by interconnecting smaller, easier-to-handle quantum processors (cores), but it introduces the challenge of minimizing slow, error-prone inter-core communication. The task of distributing quantum circuits across cores while minimizing communication costs is known as the Qubit Allocation problem. This work focuses on developing a deep learning approach to this problem, emphasizing flexibility to quantum hardware topology and improving state-of-the-art performance. Heuristic and non-learning algorithms, such as the Hungarian Qubit Allocation (HQA), currently represent the state of the art. Reinforcement Learning (RL) approaches leverage learned allocation policies but often lack flexibility, requiring retraining when hardware configurations change, and they fall short of the solution quality achieved by non-learning methods. However, learning mechanisms could outperform human-crafted heuristics. To overcome these limitations, this work proposes a flexible, transformer-based architecture that can handle arbitrary numbers of qubits and cores without retraining. Results show that the trained policy consistently outperforms the previous RL state of the art and narrows the gap between RL and HQA for the most common circuits. It achieves a 33% reduction in allocation cost relative to the HQA for the Cuccaro Adder and 25% on average for random circuits. These findings show that learning-based approaches can effectively match the performance of hand-crafted heuristics, a crucial step towards their application in real-world scenarios.
Quantumcomputers exhibit significant potential for addressing problems that are intractable by classical computing. Nevertheless, the scalability of quantum architectures remains a pivotal challenge within the field. Current efforts for increasing the number of qubits. However, using these architectures implies dealing with new hardware and algorithmic challenges. The primary focus of this thesis is the partitioning of quantum circuits across multiple cores; a task classified as an NP-hard problem. While classical algorithms often struggle with execution time and scalability, Machine Learning (ML) has emerged as a promising, faster yet powerful alternative. This thesis presents a novel approach for circuit partitioning in multi-core quantum architectures using Deep Reinforcement Learning (DRL) with graph neural networks (GNN). This methodology provides a flexible and efficient framework, enabling the partitioning of circuits with varying numbers of qubits while maintaining high performance and scalability.
Abstract Modular quantum architectures have emerged as a promising approach for scaling quantum computing systems by connecting multiple Quantum Processing Units (QPUs). However, this approach introduces significant challenges due to costly inter-core operations between chips and quantum state transfers, which contribute to noise and quantum decoherence. This paper presents QARMA, a novel Qubit mapping using Attention-based deep Reinforcement learning (DRL) for Modular quantum Architectures, along with its extension QARMA-R that incorporates dynamic qubit reuse capabilities. Our approach combines an attention-based mechanism with Graph Neural Networks (GNN) to learn optimal qubit allocation, routing, and reuse strategies that minimize inter-core communications.Our experimental results show significant improvements over state-of-the-art approaches. Compared to highly-optimized Qiskit with modular architecture configuration, QARMA-R reduces inter-core communications by up to 100% (on average 86%), while QARMA maintains 15-40% improvement for larger circuits without reuse. Against traditional modular qubit mapping, our approach achieves 97-100% reduction in inter-core operation.The proposed methods advance quantum circuit compilation techniques and enable the execution of more extensive quantum algorithms on resource-constrained modular quantum systems, contributing to the growing body of research on scalable quantum computing architectures.
Modular, distributed and multi-core architectures are currently considered a promising approach for scalability of quantum computing systems. The integration of multiple Quantum Processing Units necessitates classical and quantum-coherent communication, introducing challenges related to noise and quantum decoherence in quantum state transfers between cores. Optimizing communication becomes imperative, and the compilation and mapping of quantum circuits onto physical qubits must minimize state transfers while adhering to architectural constraints. The compilation process, inherently an NP-hard problem, demands extensive search times even with a small number of qubits to be solved to optimality. To address this challenge efficiently, we advocate for the utilization of heuristic mappers that can rapidly generate solutions. In this work, we propose a novel approach employing Deep Reinforcement Learning (DRL) methods to learn these heuristics for a specific multi-core architecture. Our DRL agent incorporates a Transformer encoder and Graph Neural Networks. It encodes quantum circuits using self-attention mechanisms and produce outputs through an attention-based pointer mechanism that directly signifies the probability of matching logical qubits with physical cores. This enables the selection of optimal cores for logical qubits efficiently. Experimental evaluations show that the proposed method can outperform baseline approaches in terms of reducing inter-core communications and minimizing online time-to-solution. This research contributes to the advancement of scalable quantum computing systems by introducing a novel learning-based heuristic approach for efficient quantum circuit compilation and mapping.
The practical implementation of quantum algorithms on noisy intermediate-scale quantum devices encounters operational limitations due to decoherence and other sources of noise inherent in real hardware. To mitigate these errors while preserving the original functionality of the algorithm, shorter quantum circuits are therefore preferred. This motivates the development of effective quantum circuit optimization algorithms. Learning-based approaches have emerged as a leading candidate, yet existing autonomous agents remain inefficient, spending most of their training capacity rediscovering elementary reductions that deterministic rule-based methods already handle reliably. To address this challenge, we propose a reinforcement learning framework that embeds a deterministic Commutation-and-Reduction (CR) algorithm directly into the training environment. After every agent action, the CR algorithm automatically resolves elementary commutations and cancellations, enabling the agent to focus its learning capacity on the non-trivial optimizations where reinforcement learning adds real value. Empirical evaluation across two gate sets, the universal Clifford+T basis and the CNOT+Pauli basis, shows that RL+CR produces shorter circuits than a standard RL agent at all tested scales. We demonstrate that RL trained on smaller quantum circuits can be applied to larger quantum circuits. On 20-qubit Clifford+T circuits, five times larger than the training circuits, RL+CR removes twice as many gates as standard RL. This work provides a robust approach that could accelerate the compilation and optimization processes for future fault-tolerant and utility-scale quantum systems.
Distributed quantum computing provides a scalable route for executing quantum circuits beyond the capacity limits of a single quantum processing unit (QPU), but it introduces a communication-aware compilation problem involving strict hardware constraints and circuit dependencies. This paper presents an architecture-aware reinforcement-learning framework that formulates distributed quantum compilation as a constrained Markov Decision Process (MDP). The compiler-level communication actions dynamically update logical-qubit placement and enable subsequent gate execution. A heterogeneous graph model represents interactions among hardware, logical qubits, and circuit operations, while a policy trained via Proximal Policy Optimization optimizes EPR-pair consumption and communication makespan. Evaluation across benchmark circuits shows that our policy matches state-of-the-art heuristics on structured workloads, with lookahead reward shaping yielding modest improvements on unstructured circuits. These results demonstrate that reinforcement learning is a flexible alternative to manual heuristics, though scalability remains a key bottleneck for practical use.