The rapid advancement of quantum computing has highlighted the need for scalable and efficient software infrastructures to fully exploit its potential. Current quantum processors face significant scalability constraints due to the limited number of qubits per chip. In response, distributed quantum computing (DQC) —achieved by networking multiple quantum processor units (QPUs)— is emerging as a promising solution. To support this paradigm, robust intermediate representations (IRs) are needed to translate high-level quantum algorithms into executable instructions suitable for distributed systems. This paper presents NetQIR, an extension of Microsoft’s Quantum Intermediate Representation (QIR), specifically designed to facilitate DQC by incorporating new instruction specifications. NetQIR was developed in response to the lack of abstraction at the network and hardware layers identified in the existing literature as a significant obstacle to effectively implementing distributed quantum algorithms. Based on this analysis, NetQIR introduces new essential abstraction features to support compilers in DQC contexts. It defines network communication instructions independent of specific hardware, abstracting the complexities of inter-QPU communication. Although the proposed work allows abstraction of the underlying network, it is important to note that it is intended for the development of high-performance code on future modular quantum architectures. Leveraging the QIR framework, NetQIR aims to bridge the gap between high-level quantum algorithm design and low-level hardware execution, thus promoting modular and scalable approaches to quantum software infrastructures for distributed applications. Furthermore, its design may serve as a foundational component for future implementations of distributed quantum standards such as the Quantum Message Passing Interface (QMPI).

Abstract Intermediate representations (IRs) are fundamental to classical and quantum computing, bridging high-level quantum programming languages and the hardware-specific instructions required for execution. This paper reviews the development of quantum IRs, focusing on their evolution and the need for abstraction layers that facilitate portability and optimization. Monolithic quantum IRs, such as QIR (Lubinski et al. in Front Phys 10:940293, 2022. https://doi.org/10.3389/fphy.2022.940293), QSSA (Peduri et al. in Proceedings of the 31st ACM SIGPLAN international conference on compiler construction. CC 2022. Association for Computing Machinery, New York, 2022), or Q-MLIR (McCaskey and Nguyen in Proceedings-2021 IEEE International Conference on Quantum Computing and Engineering, QCE, 2021), their effectiveness in handling abstractions, and their hybrid support between quantum-classical operations are evaluated. However, a key limitation is their inability to address qubit locality, an essential feature for distributed quantum computing (DQC). To overcome this, InQuIR (Nishio and Wakizaka in InQuIR: Intermediate Representation for Interconnected Quantum Computers, 2023. https://arxiv.org/abs/2302.00267) was introduced as an IR specifically designed for distributed systems, providing explicit control over qubit locality and inter-node communication. While effective in managing qubit distribution, InQuIR’s dependence on manual manipulation of communication protocols increases complexity for developers. NetQIR (Vázquez-Pérez et al. in NetQIR: An Extension of QIR for Distributed Quantum Computing, 2024. https://arxiv.org/abs/2408.03712), an extension of QIR for DQC, emerges as a solution to achieve the abstraction of quantum communications protocols. This review emphasizes the need for further advancements in IRs for distributed quantum systems, which will play a crucial role in the scalability and usability of future quantum networks.

Abstract Quantum computing is a rapidly evolving field, with almost every aspect open to change or improvement. This includes moving from using a single quantum processing unit to interconnecting multiple quantum processing units (or several of them), establishing a new paradigm called distributed quantum computing and increasing the overall computing capability. Some research is already underway in this area to prepare the ground for an eventual architecture with these characteristics. This is the case of InQuIR (Nishio and Wakizaka in arXiv:2302.00267 2023) and NetQASM (Dahlberg et al in QST 7:035023 2022), two languages developed for distributed quantum computing. This paper presents the development of the InQASM compiler with the aim of translating code from the InQuIR language to NetQASM, establishing a compilation stack for the new distributed paradigm. An example of this compilation and a simulation of the compiled code are shown to showcase it.

Abstract The integration of quantum processing units (QPUs) in a heterogeneous high-performance computing environment requires solutions that facilitate hybrid classical–quantum programming. Standards such as OpenCL facilitate the programming of heterogeneous environments, consisting of CPUs and hardware accelerators. This study presents an innovative method that incorporates QPU functionality into OpenCL, standardizing quantum processes within classical environments. By leveraging QPUs within OpenCL, hybrid quantum–classical computations can be sped up, impacting domains like cryptography, optimization problems, and quantum chemistry simulations. Using Portable Computing Language (Jääskeläinen et al. in Int J Parallel Program 43(5):752–785, 2014. https://doi.org/10.1007/s10766-014-0320-y ) and the Qulacs library (Suzuki et al. in Quantum 5:559, 2021. https://doi.org/10.22331/q-2021-10-06-559 ), results demonstrate, for instance, the successful execution of Shor’s algorithm (Nielsen and Chuang in Quantum computation and quantum information, 10th anniversary edn. Cambridge University Press, Cambridge, 2010), serving as a proof of concept for extending the approach to larger qubit systems and other hybrid quantum–classical algorithms. This integration approach bridges the gap between quantum and classical computing paradigms, paving the way for further optimization and application to a wide range of computational problems.