An Evolutionary Approach to Optimizing Teleportation Cost in Distributed Quantum Computation

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.

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.

Precise time synchronization is a fundamental challenge in distributed quantum systems, with direct implications for secure communication, sensing, and next-generation network technologies. In this study, we present a Field Programmable Gate Array (FPGA)-based implementation of a Time-Correlated Entangled Photons (TCEP) source-based synchronization system, achieving <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sub-nanosecond</i> accuracy with timing jitter consistently below 200 ps for a distance up to 20 km. The system leverages the strong temporal correlations inherent in entangled photon pairs to compute synchronization offsets between spatially separated nodes. The design features a modular architecture with optimized kernels for temporal correlation, data aggregation, and normalization, enabling efficient resource utilization and high-throughput performance. Experimental validation demonstrates the FPGA's ability to process photon timestamp data and compute cross-correlation functions significantly faster than traditional CPU-based approaches, achieving execution times in the millisecond range even for large datasets. Our FPGA implementation achieved a consistent <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\sim$</tex-math></inline-formula> 800 times speedup over CPU, with performance largely unaffected by channel length. Resource utilization analysis highlights the scalability of the design, with the fully integrated system operating at a clock frequency of 397.5 MHz while maintaining efficient use of logic elements, registers, and memory blocks. This hardware-efficient approach provides the timing backbone for next-generation technologies, facilitating advancements in ultra-reliable low-latency communication, distributed quantum computing, quantum-enhanced sensing, navigation, and lays a foundation for forthcoming 6G networks and the quantum internet.

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 (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%.

Quantum computing simulation platform can simulate the computation results of the quantum computer based on traditional computers, which is an effective way to promote the development of quantum computing software, algorithms and hardware at the current immature stage of the real quantum computer. Since quantum computers have exponential calculation acceleration compared with traditional computers, the main problems in implementing quantum computing simulation on traditional computers are low computational efficiency and long time-consuming. A quantum circuit which is a sequence of quantum gates acting on a collection of qubits is the general quantum computing model. So by the means of quantum circuit optimization, the calculation speed can be significantly increased while keeping the calculation result unchanged. The existing empirical rules of quantum circuit optimization methods have limitations and there is no common and automatic quantum circuit optimization method. In this paper, a general and automatic quantum circuit optimization method based on the genetic algorithm is proposed, by which the equivalent optimal quantum circuit is obtained through a finite number of searching in a large searching space. This method is not limited by the hardware of the quantum computing simulation and the composition of the quantum circuit. The experimental results show that for the QFT algorithm of 29 qubits, the running time can be shortened by 41.4% and for the variational circuit of 6 qubits, the running time can be shortened by 18.8% compared with the state-of-the-art quantum circuit optimization method. So this method can improve the quantum computing simulation capability and operating efficiency and provide a rapid development way for quantum algorithms and applications.

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.

This paper designs quantum testing circuit to detect intermediate malicious node and achieve message integrity in the distributed quantum computing. The proposed mechanism has several improvements shown as follows. The random key generation between Alice and Bob such that an attack cannot break this deriving process. Local unitary operations and quantum teleportation in the entangled particles can be used to transfer quantum information in a secure way. For intermediate node has no capability to differentiate which qubit is quantum superposition state or quantum entangled state. In regard to node detection, the receiver has the capability to judge whether intermediate node is honest or not by using quantum testing circuit. Based on this physical property, quantum circuit could be detect malicious node and achieve message integrity. The proposed circuit is scalable.

Genetic Algorithm (GA) is a widely used search method, and Quantum Genetic Algorithm (QGA) has been pointed out for several years. While common QGA only refers to the concept of quantum mechanics, and still uses mathematical representations of quantum states to simulate quantum entanglement and superposition, it can’t be realized on a quantum computer. This paper presents an implementable quantum circuit for a genetic algorithm, named as Planar-Weibull Quantum Circuit Genetic Algorithm (PW-QCGA), employing the Weibull function and excitation function through planar matrix coding. It is not only a self-adaptive algorithm that adjusts parameters dynamically, but it can also be executed on quantum computers by constructing parameterized quantum circuits. Experiments on three typical applications show that PW-QCGA not only has obvious advantages on convergence accuracy, search ability, convergence speed, and robustness, but also has higher fidelity on a quantum computer. We hope this work can bring inspiration to other quantum intelligent algorithms.

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.

In the present work, a novel approach was proposed to optimize the teleportation cost in Distributed Quantum Circuits (DQCs) by applying a new approach. To overcome the difficulty with keeping a large number of qubits next to each other, DQCs, as a well-known solution, have always been employed. In a distributed quantum system, qubits are transferred from a subsystem to another subsystem by a quantum protocol such as teleportation. First, we proposed a heuristic approach through which we could replace the equivalent circuits in the initial quantum circuit. Then, we used a genetic algorithm to partition the placement of qubits so that the number of teleportations could be optimized for the communications of a DQC. Finally, results showed that the proposed approach could impressively work.

Simulation of the dynamics of quantum materials is emerging as a promising scientific application for noisy intermediate-scale quantum (NISQ) computers. Due to their high gate-error rates and short decoherence times, however, NISQ computers can only produce high-fidelity results for those quantum circuits smaller than some given circuit size. Dynamic simulations, therefore, pose a challenge as current algorithms produce circuits that grow in size with each subsequent time-step of the simulation. This underscores the crucial role of quantum circuit compilers to produce executable quantum circuits of minimal size, thereby maximizing the range of physical phenomena that can be studied within the NISQ fidelity budget. Here, we present two domain-specific (DS) quantum circuit compilers for the Rigetti and IBM quantum computers, specifically designed to compile circuits simulating dynamics under a special class of time-dependent Hamiltonians. The compilers outperform state-of-the-art general-purpose compilers in terms of circuit size reduction by around 25%–30% as well as wall-clock compilation time by around 40% (dependent on system size and simulation time-step). Drawing on heuristic techniques commonly used in artificial intelligence, both compilers scale well with simulation time-step and system size. Code for both compilers is open-source and packaged into a full-stack quantum simulation software with tutorials included for ease of use for future researchers wishing to perform dynamic simulations of quantum materials on quantum computers. As our DS compilers provide significant improvements in both compilation time and simulation fidelity, they provide a building block for accelerating progress toward physical quantum supremacy.

While current quantum computers, referred to as Noisy Intermediate-Scale Quantum (NISQ) computers, are expected to be beneficial for different applications, they are prone to different types of errors. In order to enhance the reliability of quantum systems, noise-aware quantum compilers are used to generate physical quantum circuits to be executed on NISQ computers. The quantum hardware is calibrated very frequently and its error rates are computed accordingly. Based on the hardware error rates, a quantum compiler allocates physical qubits and schedules quantum operations. However, error rates may change post-calibration. To incorporate dynamic error rates into quantum circuit compilation with minimum cost, we propose a Machine Learning (ML)-based scheme to detect the incorrect output of the quantum circuit and predict the Probability of Successful Trials (PST) with high accuracy. Our approach can verify the error rates of the quantum hardware and validate the correctness of the extracted quantum circuit output. We provide a case study of our ML-based reliability models using IBM Q16 Melbourne quantum computer. Our results show that the proposed scheme achieves a very high prediction accuracy.

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)