Circuit-based vs. measurement-based quantum computing: a comparative analysis, layered metrics, and decision flow for approach selection

Abstract

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.