Hardware-Software Co-design for Distributed Quantum Computing

The exploration of distributed quantum computing (DQC) represents a significant frontier in quantum information science, aiming to harness the unique properties of quantum mechanics to solve complex computational problems effectively. This paper discusses the diverse architectures and models that facilitate the distribution of quantum computing tasks across multiple quantum nodes, thereby addressing the limitations inherent in single quantum devices. DQC systems exploit the principles of superposition and entanglement to enhance computational capabilities beyond what classical computing systems can achieve. We examine various DQC architectures, including both quantum-classical hybrid systems and fully quantum distributed systems, highlighting their respective benefits and challenges. Key issues such as coherence, communication overhead, and error correction are discussed in detail, and we analyze specific use cases where DQC demonstrates superior performance relative to classical computing approaches, including optimization problems in logistics and finance, as well as quantum simulations for material science. Furthermore, we identify future research directions aimed at overcoming existing barriers to the practical implementation of DQC systems. By assessing the current landscape and future possibilities of DQC, this paper underscores the transformative potential of distributed quantum computing in various fields, paving the way for realizing more complex quantum algorithms and applications.

Quantum computing continues to face challenges in scaling both qubit quality and quantity, motivating the shift toward Distributed Quantum Computing (DQC), where multiple interconnected Quantum Processing Units (QPUs) collaboratively solve problems too complex for monolithic systems. In a quantum data center, QPUs distributed across racks can perform remote gate operations by creating entanglement between them, enabling circuit execution through DQC. However, generating end-to-end entangled pairs in a quantum data center often causes congestion and resource contention. To mitigate this, we introduce a resource management framework with efficient schedulers that maximize fidelity-guaranteed throughput while preserving the dependency constraints of sub-circuits derived from the original quantum circuit. We benchmark the scheduling problem using a MixedInteger Linear Programming (MILP) model and then propose a set of lightweight schedulers-Least Resource First (LRF) and its extension, Group LRF (GLRF). These lightweight schedulers provide practical, though less optimal, solutions for handling the high volume of remote gates in DQC workloads. Our initial results on a DCell-based quantum data center show that such heuristics perform well under current DQC conditions, balancing runtime and performance while avoiding the heavy overhead of solvers or machine learning approaches, which often struggle to meet the strict timing demands of short-lived entanglement.

Scaling quantum computers, i.e., quantum processing units (QPUs) to enable the execution of large quantum circuits is a major challenge, especially for applications that should provide a quantum advantage over classical algorithms. One approach to scale QPUs is to connect multiple machines through quantum and classical channels to form clusters or even quantum networks. Using this paradigm, several smaller QPUs can collectively execute circuits that each would not be able on its own. However, communication between QPUs is costly as it requires generating and maintaining entanglement, and hence it should be used wisely. In this paper, we evaluate the architectures, and in particular the entanglement patterns, of variational quantum circuits in a distributed quantum computing (DQC) setting. That is, using Qiskit, we simulate the execution of an eight qubit circuit using four QPUs each with two computational and two communication qubits where non-local CX-gates are performed using the remote-CX protocol. We compare the performance of various circuits on a binary classification task where training is executed under ideal and testing under noisy conditions. The study provides initial results on suitable VQC architectures for the DQC paradigm, and indicates that a standard VQC baseline is not always the best choice, and alternative architectures that use entanglement between QPUs sparingly deliver better results under noise.

Distributed quantum computing relies on coordinated operations between remote quantum processing units (QPUs), yet most existing work either assumes full connectivity, unrealistic for large networks, or relies on entanglement swapping. To mitigate the overhead of communication, we propose a scheme for the distribution of collective quantum operations among remote quantum processing units by exploiting distributed fan-out operations to a central node in network architectures similar to those used for high-performance computing, which requires only pre-shared entanglement, local operations and classical communication. We show that a general diagonal gate can be distributed among any number of nodes and provide the ebit cost bounds. For a single distributed multicontrolled gate, this amounts to a single additional Bell pair over the theoretically optimal calculation with all-to-all pre-shared entanglement, demonstrating better scalability when compared to current proposals based on entanglement swapping through a network. We provide a recipe for the lumped distribution of gates such as arbitrarily-sized Toffoli and multicontrolled Z, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$R_{zz}(\theta)$</tex-math></inline-formula> gates. Finally, we provide an exact implementation of a distributed Grover's search algorithm using this protocol to partition the circuit, with Bell pair cost growing linearly with the number of Grover iterations and the number of partitions, and show how these techniques can be applied to other algorithms such as QAOA. Our results show that alternative approaches to entanglement swapping can provide major benefits in distributed quantum computing, pointing to promising avenues for future research.

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.

Distributed quantum computing has been well-known for many years as a system composed of a number of small-capacity quantum circuits. Limitations in the capacity of monolithic quantum computing systems can be overcome by using distributed quantum systems which communicate with each other through known communication links. In our previous study, an algorithm with an exponential complexity was proposed to optimize the number of qubit teleportations required for the communications between two partitions of a distributed quantum circuit (DQC). In this work, a genetic algorithm is used to solve the optimization problem in a more efficient way. The results are compared with the previous study and we show that our approach works almost the same with a remarkable speed-up. Moreover, the comparison of the proposed approach based on GA with a random search over the search space verifies the effectiveness of GA.

Quantum computers may offer significant computational advantages over classical counterparts, revolutionizing the technology landscape in the near future. When networked together, the advantage of quantum computing may be further amplified, and there may emerge innovative applications. Among various active explorations on distributed quantum computing, multiqubit quantum gates between distant networked quantum computers are of particular interest because they offer operational advantages of efficiency and fidelity. Here we report the first experimental demonstration of quantum teleportation for a Toffoli gate, which is a commonly used multiqubit quantum gate, across three spatially distributed parties within a photonic quantum network. Employing the Hofmann method, we estimate the fidelity of the teleported Toffoli gate to be at least 0.706 ± 0.131. This successful demonstration of the quantum teleportation of a Toffoli gate constitutes a critical step toward the ultimate realization of distributed quantum computation.

Distributed quantum computing (DQC) architectures offer a scalable solution for the computational demands of large-scale quantum computing. In near-term DQC architectures, the costly remote quantum communication and the execution cost within quantum chips together significantly limit the execution efficiency of quantum circuits. To comprehensively optimize both costs, we propose DMapS, which consists of end-to-end algorithms for qubit mapping and routing. The qubit mapping component, DMapS-M, adopts a two-stage mapping strategy that decomposes a large quantum circuit into smaller ones and parallelizes the qubit mapping on quantum chips. The qubit routing component, DMapS-R, reduces remote quantum communication overhead by prioritizing the insertion of local SWAP gates and further improves transpilation efficiency by exploiting parallelism within chips. Our experimental results show that DMapS-M reduces overall overhead (including both remote quantum communication overhead and local SWAP gate overhead) by an average of 43.44% and 59.72%, respectively, compared to two baseline algorithms, and achieves an average speedup of 87.05x. DMapS-R, compared to the baseline algorithm, reduces overall overhead by an average of 8.85% and achieves an average transpilation speedup of 2.78×. Moreover, compared to the DQC-oriented quantum compiler, DMapS reduces remote communication overhead by an average of 75.16%.

Charged quantum dots containing an electron or hole spin are bright solid-state qubits suitable for quantum networks and distributed quantum computing. Incorporating such quantum dot spin into a photonic crystal cavity creates a strong spin-photon interface in which the spin can control a photon by modulating the cavity reflection coefficient. However, previous demonstrations of such spin-photon interfaces have relied on quantum dots that are charged randomly by nearby impurities, leading to instability in the charge state, which causes poor contrast in the cavity reflectivity. Here we demonstrate a strong spin-photon interface using a quantum dot that is charged deterministically with a diode structure. By incorporating this actively charged quantum dot in a photonic crystal cavity, we achieve strong coupling between the cavity mode and the negatively charged state of the dot. Furthermore, by initializing the spin through optical pumping, we show strong spin-dependent modulation of the cavity reflectivity, corresponding to a cooperativity of 12. This spin-dependent reflectivity is important for mediating entanglement between spins using photons, as well as generating strong photon-photon interactions for applications in quantum networking and distributed quantum computing.

We explore the concept of distributed quantum computation, discussing the advantages and disadvantages of this approach. We divide its development into three layers and highlight the challenges we face in each stage. With a few examples we explore the scalability of such disturbed quantum systems. © 2020 The Author(s)

This chapter looks at distributed quantum computing from a different perspective. lt looks at computations described by quantum circuits involving multiple qubits, where the qubits reside on multiple nodes, each node hosting one or more of the qubits. The chapter discusses nonlocal gates, or quantum gates for computations over several nodes. In particular, it discusses the distributed CNOT gate, and different ways for its implementation, and discusses distributed control of gates beyond the CNOT gate. The chapter also reviews briefly work on distributing quantum circuits and architectures for distributed control and management for distributed quantum computers. The idea of automating the distribution of a quantum circuit into parts which map to a given topology of quantum processing units brings us to the notion of compilers for distribute quantum programs.

In distributed quantum computing, the final solution of a problem is usually achieved by catenating these partial solutions resulted from different computing nodes, but intolerable errors likely yield in this catenation process. In this paper, we propose a universal error correction scheme to reduce errors and obtain effective solutions. Then, we apply this error correction scheme to designing a distributed phase estimation algorithm that presents a basic tool for studying distributed Shor’s algorithm and distributed discrete logarithm algorithm as well as other distributed quantum algorithms. Our method may provide a universal strategy of error correction for a kind of distributed quantum computing.

In this work, we present a solution to the critical limitation of qubit capacity in near-term quantum hardware by giving a hybrid framework that integrates the spectral element method (SEM) with distributed quantum computing. Using domain decomposition techniques, the additive and multiplicative Schwarz methods, the global problem is divided into smaller subproblems that each require significantly fewer qubits, making them suitable for current quantum devices. The HHL algorithm is applied locally to these subproblems, enabling quantum speedups without exceeding hardware constraints. Numerical results validate the approach, demonstrating a scalable and practical solution for high-accuracy simulations despite qubit limitations.

With their ability to process and transfer quantum information, large-scale entanglement-based quantum networks could be at the heart of a new age of quantum information, enabling fundamentally new applications such as distributed quantum computation, quantum communication, and quantum enhanced sensing. Due to their long spin coherence, controllable local qubit registers and optically active spins, color centers in diamond are prime candidates for nodes of such a network, and have enabled some of the most advanced quantum network demonstrations to date. These demonstrations include the distribution of a 3-node GHZ state across a quantum network, entanglement swapping, entanglement distillation, and memory-enhanced quantum communication. To move beyond current proof-of-principle networks, a further increase of entanglement generation rates is crucial. This thesis presents theoretical and experimental work on enhancing the spin-photon interface of color centers in diamond to achieve this goal, making use of the Purcell effect. The discussed work follows two main directions: embedding of color centers in open, tuneable Fabry-Perot micro-cavities, and in all-diamond photonic crystal cavities. First, we describe theoretical and experimental progress towards cavity-enhanced quantum networks based on nitrogen-vacancy (NV) centers in diamond. Due to their first order sensitivity to electric fields, we choose to embed NV centers in microns-thin diamond membranes that can be integrated into open fiber-based micro-cavities. We develop analytical methods to optimize the design of such open cavity systems for maximum Purcell enhancement of embedded color centers. We demonstrate a method to fabricate optically coherent NV centers in microns-thin diamond membranes, and use such structures to demonstrate the resonant excitation and detection of coherent, Purcell enhanced NV emission. A theoretical model in excellent agreement with our results suggests our system can improve entanglement rates between distant NV centers by two orders of magnitude with near-term improvements to the setup. Second, we describe progress towards an efficient spin-photon interface of group-IV color centers in diamond by coupling them to photonic nanostructures, allowing for large-scale integration. Due to their first-order insensitivity to electric fields, group-IV color centers can be brought in close proximity to surfaces (~ 100 nm), allowing for sub-wavelength mode volumes and thus very high Purcell factors. We numerically optimize photonic crystal cavity designs to maximize the Purcell enhancement of embedded emitters, test the robustness of our designs to real-world fabrication imperfections, and devise a method to efficiently interface nanophotonic structures. We then proceed to fabricate all-diamond photonic crystal cavities, making use of a dry etching technique that is selective to different crystallographic directions, and characterize the resulting optical quality factors. Finally, we marry the developed fabrication methods to fabricate microns-sized diamond platelets that can be transferred from a holding frame in a controlled fashion. This capability could be crucial for the realization of hybrid photonic circuits that we expect to be at the heart of future large-scale quantum networks.

Programmable photonic integrated circuits (PICs) offer practical solutions to the scaling requirements of quantum technologies for quantum communications and distributed quantum computing. Here we present recent advances in piezoelectrically-actuated PICs demonstrating large-scale optical switching and linear-optic operations for the realization of quantum network systems.