Circuit-based quantum computing (CBQC), also known as the gate model, is currently regarded as the leading paradigm for performing quantum computation and has garnered widespread interest due to its relatively better-established implementation and close intuitive resemblance to classical computation. However, an alternative model that solely utilizes single-qubit measurements on entangled states to perform computation, namely the measurement-based quantum computing (MBQC), has started to attract further research interest as it is deemed more naturally suited for certain quantum hardware architectures, though its actual implementation remains largely underexplored. Recently, there have been preliminary efforts to characterize the specific regimes in which MBQC may potentially be more advantageous compared to CBQC. Nevertheless, a more systematic assessment is necessary to assess the suitability of each model across a broader range of more practical cases. In this work, we present a detailed comparative analysis of CBQC and MBQC, beginning with reviewing the theoretical foundations of each model before highlighting its distinguishing features that set the two paradigms apart. Furthermore, building on previous work, we propose a generalized regime analysis that more accurately captures the conditions under which a given quantum algorithm is more favorably executed in MBQC or CBQC. Subsequently, we identify critical parameters that likely determine whether a quantum algorithm is better suited to CBQC or MBQC, categorizing detailed key factors and performance metrics into layers of quantum computation. Next, we propose a decision flow that, given specific hardware constraints and algorithm requirements, guides the selection to the most appropriate model, discussing suitability in two representative worked examples of quantum algorithm applications: Quantum Fourier Transform (QFT) and Variational Quantum Algorithm (VQE). Last, we discuss the potential to combine both models as a hybrid approach to leverage the best of both worlds and explore its benefits for practical quantum computing applications.
Circuit-based quantum computing (CBQC), also known as the gate model, is currently regarded as the leading paradigm for performing quantum computation and has garnered widespread interest due to its relatively better-established implementation and close intuitive resemblance to classical computation. However, an alternative model that solely utilizes single-qubit measurements on entangled states to perform computation, namely the measurement-based quantum computing (MBQC), has started to attract further research interest as it is deemed more naturally suited for certain quantum hardware architectures, though its actual implementation remains largely underexplored. Recently, there have been preliminary efforts to characterize the specific regimes in which MBQC may potentially be more advantageous compared to CBQC. Nevertheless, a more systematic assessment is necessary to assess the suitability of each model across a broader range of more practical cases. In this work, we present a detailed comparative analysis of CBQC and MBQC, beginning with reviewing the theoretical foundations of each model before highlighting its distinguishing features that set the two paradigms apart. Furthermore, building on previous work, we propose a generalized regime analysis that more accurately captures the conditions under which a given quantum algorithm is more favorably executed in MBQC or CBQC. Subsequently, we identify critical parameters that likely determine whether a quantum algorithm is better suited to CBQC or MBQC, categorizing detailed key factors and performance metrics into layers of quantum computation. Next, we propose a decision flow that, given specific hardware constraints and algorithm requirements, guides the selection to the most appropriate model, discussing suitability in two representative worked examples of quantum algorithm applications: Quantum Fourier Transform (QFT) and Variational Quantum Algorithm (VQE). Last, we discuss the potential to combine both models as a hybrid approach to leverage the best of both worlds and explore its benefits for practical quantum computing applications.
Recent advances in quantum technologies are rapidly pushing the boundaries of computational capabilities, with the promise of significant speedups across a variety of applications. However, building large-scale monolithic quantum processors remains an immense engineering challenge, motivating the pursuit of alternative paradigms to realize practical quantum advantage. One such paradigm is Distributed Quantum Computing (DQC), which interconnects multiple quantum nodes via quantum networks to collectively perform complex computations. While Circuit-Based Quantum Computing (CBQC) has traditionally been the dominant model, Measurement-Based Quantum Computing (MBQC), with its one-way computation framework and pre-shared entangled cluster states, introduces distinctive benefits for distributed architectures. Importantly, within DQC, MBQC offers enhanced security over CBQC by naturally supporting protocols such as Blind Quantum Computation (BQC) and secure delegated processing. This study offers an application-oriented perspective on the role of MBQC in DQC, highlighting concrete industrial use cases alongside key implementation challenges. By bridging theoretical potential with practical deployment considerations, it aims to accelerate progress toward secure and scalable distributed quantum systems.
Measurement-based quantum computation (MBQC) is a paradigm for quantum computation where computation is driven by local measurements on a suitably entangled resource state. In this work we show that MBQC is related to a model of quantum computation based on Clifford quantum cellular automata (CQCAs). Specifically, we show that certain MBQCs can be directly constructed from CQCAs which yields a simple and intuitive circuit model representation of MBQC in terms of quantum computation based on CQCA. We apply this description to construct various MBQC-based Ans\"atze for parametrized quantum circuits, demonstrating that the different Ans\"atze may lead to significantly different performances on different learning tasks. In this way, MBQC yields a family of hardware-efficient Ans\"atze that may be adapted to specific problem settings and are particularly well suited for architectures with translationally invariant gates such as neutral atoms.
Circuit-based quantum computing (CBQC) has far remained the most intuitive and experimentally mature model of universal quantum computation, serving as the basis for today’s noisy intermediate-scale quantum (NISQ) devices and emerging fault-tolerant quantum computation (FTQC) due to its well-developed control and error-correction techniques. Nevertheless, scalability challenges and suitability to photonic platforms have motivated the exploration of alternative computational models such as measurement-based quantum computing (MBQC), which separates entanglement generation from actual computation and is considered more natural for scalable and distributed architectures. More recently, fusion-based quantum computation (FBQC), and in particular its encoded variant (EFBQC), have been proposed to alleviate many of the practical limitations of traditional MBQC by using constant-size resource states and encoded fusion operations with controllable failure behavior, thus improving practicality, flexibility, and fault-tolerance. Motivated by these potential advantages of measurement-based approaches while recognizing the continued prominence and circuit-level versatility of CBQC, in this work, we propose a hybrid approach that combines CBQC with (E)FBQC to improve long-range connectivity and Clifford-dominated subroutine execution under threshold-compatible operating conditions, enabling higher performance in the context of fault tolerance and architectural scalability. In detail, we propose an encoded-fusion- assisted teleportation (EFAT) mechanism, with two configurations for different scenarios: (1) the Minimal Hybrid, in which (E)FBQC acts as a logical entanglement bus that supplies encoded Bell pairs for teleportation-based connectivity between CBQC modules, thus replacing distance-dependent routing with teleportation and reducing routing overhead when routing dominates the logical schedule, while remaining compatible with the derived surface-code threshold condition; (2) the Extended Hybrid, in which (E)FBQC additionally participates in the computation alongside CBQC nodes, so that encoded cluster fragments can be used to execute Clifford subroutines in constant depth. Our performance analysis shows that the Minimal Hybrid can reduce routing-dominated logical depth while remaining compatible with the derived fault-tolerance condition, whereas the Extended Hybrid can further compress Clifford-dominated subroutines and may improve the temporal scheduling of magic-state supply, at the expense of higher photonic throughput and tighter synchronization requirements. Together, these results indicate a practical route toward scalable, modular, and fault-tolerant quantum computing based on encoded-fusion-assisted hybrid architectures.
This manuscript is intended for readers who have a general interest in the subject of quantum computation and provides an overview of the most significant developments in the field. It begins by introducing foundational concepts from quantum mechanics—such as superposition, entanglement, and the no-cloning theorem—that underpin quantum computation. The primary computational models are discussed, including gate-based (circuit) quantum computing, adiabatic quantum computing, measurement-based quantum computing and the quantum Turing machine. A selection of significant quantum algorithms are reviewed, notably Grover’s search algorithm, Shor’s factoring algorithm, and Quantum Singular Value Transformation (QSVT), which enables efficient solutions to linear algebra problems on quantum devices. To assess practical performance, we compare quantum and classical implementations of support vector machines (SVMs) using several synthetic datasets. These experiments offer insight into the capabilities and limitations of near-term quantum classifiers relative to classical counterparts. Finally, we review leading quantum programming platforms—including Qiskit, PennyLane, and Cirq—and discuss their roles in bridging theoretical models with real-world quantum hardware. The paper aims to provide a concise yet comprehensive guide for those looking to understand both the theoretical foundations and applied aspects of quantum computing.
Machine Learning (ML) has been widely applied across numerous domains due to its ability to automatically identify informative patterns from data for various tasks. The availability of large-scale data and advanced computational power enables the development of sophisticated models and training strategies, leading to state-of-the-art performance, but it also introduces substantial challenges. Quantum Computing (QC), which exploits quantum mechanisms for computation, has attracted growing attention and significant global investment as it may address these challenges. Consequently, Quantum Machine Learning (QML), the integration of these two fields, has received increasing interest, with a notable rise in related studies in recent years. We are motivated to review these existing contributions regarding quantum circuit-based learning models for classical data analysis and highlight the identified potentials and challenges of this technique. Specifically, we focus not only on QML models, both kernel-based and neural network-based, but also on recent explorations of their integration with classical machine learning layers within hybrid frameworks. Moreover, we examine both theoretical analysis and empirical findings to better understand their capabilities, and we also discuss the efforts on noise-resilient and hardware-efficient QML that could enhance its practicality under current hardware limitations. In addition, we cover several emerging paradigms for advanced quantum circuit design and highlight the adaptability of QML across representative application domains. This study aims to provide an overview of the contributions made to bridge quantum computing and machine learning, offering insights and guidance to support its future development and pave the way for broader adoption in the coming years.
Abstract The paradigm of measurement-based quantum computing (MBQC) starts from a highly entangled resource state on which unitary operations are executed through adaptive measurements and corrections ensuring determinism. This is set in contrast to the more common quantum circuit model, in which unitary operations are directly implemented through quantum gates prior to final measurements. In this work, we incorporate concepts from MBQC into the circuit model to create a hybrid simulation technique, permitting us to split any quantum circuit into a classically efficiently simulatable Clifford-part and a second part consisting of a stabilizer state and local (adaptive) measurement instructions—a so-called standard form—which is executed on a quantum computer. We further process the stabilizer state with the graph state formalism, thus, enabling a significant decrease in circuit depth for certain applications. We show that groups of mutually-commuting operators can be implemented using fully-parallel, i.e. non-adaptive, measurements within our protocol. In addition, we discuss how groups of mutually commuting observables can be simulatenously measured by adjusting the resource state, rather than performing a costly basis transformation prior to the measurement as it is done in the circuit model. Finally, we demonstrate the utility of our technique on two examples of high practical relevance—the Quantum Approximate Optimization Algorithm and the Variational Quantum Eigensolver (VQE) for the ground-state energy estimation of the water molecule. For the VQE, we find a reduction of the depth by a factor of 4 to 5 using measurement patterns vs. the standard circuit model. At the same time, since we incorporate the simultaneous measurements, our patterns allow us to save shots by a factor of at least 3.5 compared to measuring Pauli strings individually in the circuit model.