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IEEE Access

Hybrid Circuit and Measurement-Based Quantum Computing Architecture With Encoded-Fusion-Assisted Teleportation

Harashta Tatimma Larasati, Byung-Soo Choi

Published Jan 1, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.1109/access.2026.3690417

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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.
Hybrid discrete- and continuous-variable (DV-CV) encodings have been developed to overcome operational drawbacks of each individual encoding, while fusion-based quantum computation (FBQC) has emerged to address the practical challenges of scalability toward fault-tolerant photonic quantum computation. Here we introduce hybrid FBQC using small optical DV-CV hybrid resource states connected through hybrid fusions, to combine the advantages of both approaches. We develop protocols for directly generating these resource states without requiring local hybrid logic such as the Hadamard gate, together with a tailored decoding strategy that exploits the error information contained in individual hybrid-fusion outcomes. We demonstrate that hybrid FBQC achieves a photon loss threshold of 2.231% while requiring only 12 hybrid fusions per surface-code unit cell, substantially improving upon the 0.89% threshold and 60-fusion requirement of previous hybrid measurement-based scheme. These results establish optical hybrid FBQC as a high-threshold resource-efficient route to scalable fault-tolerant photonic quantum computation.
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.
We propose a measurement-based fault-tolerant quantum computing (MB-FTQC) architecture for high-connectivity platforms, targeting early-FTQC devices with thousands to tens of thousands of physical qubits. Unlike earlier teleportation-based architectures that rely on code concatenation for scalability, MB-FTQC operates in a zero-concatenation regime with compact fixed-distance codes, keeping the qubit overhead within reach of such devices. MB-FTQC combines offline-verified logical resource states with Knill's error-correcting teleportation, allowing each online step to use single-round syndrome extraction and independent lookup-table decoding. Under circuit-level depolarizing noise, we study a Steane-code implementation with partially fault-tolerant analog RZ(θ)R_Z(θ)RZ​(θ) rotations and a Golay-code implementation with higher-order zero-level distillation for fault-tolerant TTT-state preparation. At a physical error rate of 10−410^{-4}10−4, our estimates give a megaquop-scale equivalent TTT-count of 1.89×1061.89\times10^{6}1.89×106 for the Steane implementation and a gigaquop-scale characteristic TTT-count of 1.87×1091.87\times10^{9}1.87×109 for the Golay implementation. With sufficient parallel resource supply, MB-FTQC achieves a short online critical path, while resource estimates including verification failures and retries show competitive spacetime costs. These results show that compact, fixed-distance codes can support fault-tolerant computation at substantial scales in the early-FTQC regime, without code concatenation.
The realisation of a fault-tolerant universal quantum computer requires the ability to implement and control large scale quantum systems while maintaining physical noise levels sufficiently low to avoid errors in the computation. Fusion-Based Quantum Computation (FBQC) – a framework in which entangling fusion measurements are performed between constant-size entangled resource states – has emerged as a promising approach to achieve this, especially in the context of Linear Optical Quantum Computing (LOQC). Most FBQC schemes proposed so far use physical fusions between two qubits. In this thesis, we study the impact of using multi-way fusions, which act on more physical qubits simultaneously, on the error tolerance and resource overhead of linear optical FBQC architectures. The main challenge of LOQC is that entangling operations are inherently non-deterministic, leading to large resource overheads. The success probability is known to decrease exponentially with the number of input qubits. We introduce novel fusion circuits which succeed at higher rates and/or entangle subsets of inputs upon failure. We present a framework to analyse the impact of noise on these circuits and describe the resulting errors as effective Pauli error channels on the input qubits. We also examine the application of multi-way fusion circuits within a linear optical FBQC architecture. We find that they can be used to generate resource states with significantly reduced Pauli error rates and footprint compared to two-way fusions alone, in turn resulting in linear optical FBQC architectures with higher error tolerance and lower resource overheads. We also investigate their use as primitives of the computation, applied between different resource states, and find evidence that two-way fusions remain preferable in this context due to their lower erasure rate.
Networking matter-based quantum processing units (QPUs) offers a promising route to scaling fault-tolerant quantum computers. This requires distributed logical operations to be performed across photonic links, where noise is characteristically different from and stronger than in local QPUs owing to photon loss and probabilistic linear-optical operations. Measurement- and fusion-based quantum computing are designed to be robust against loss and probabilistic photonic operations, suggesting they could complement circuit-based error correction at the interface between networked QPUs. We use ZX calculus transformations to construct hybrid syndrome extraction protocols and apply them to distributed rotated surface code lattice surgery, demonstrating that several protocols attain a 50%50\%50% interface-erasure threshold when local noise is absent, including circuit-based lattice surgery using fused Bell pairs and hybrid protocols using linear cluster states. Relative to a straight Bell-pair interface geometry, the hybrid protocols increase the merge-observable interface distance from d+1d+1d+1 to 2d+12d+12d+1 and restore the perpendicular-observable interface distance from ⌊(d+1)/2⌋\lfloor(d+1)/2\rfloor⌊(d+1)/2⌋ to ddd. We calculate how the threshold decreases when using truncated resource states and map correctable regions under resource-state errors, local circuit noise, and fusion erasure. We then convert these erasure thresholds into photon-loss thresholds and probe subthreshold performance using fusion boosting. At circuit and resource-state error rates of 10−310^{-3}10−3, local errors largely mask the interface-distance advantage. As local noise is reduced to 10−410^{-4}10−4 and below, the linear-chain protocols improve more rapidly with decreasing erasure, suggesting that interface distance enhancements are effective in low local noise regimes.
We present a hybrid scheme for quantum computation that combines the modular structure of elementary building blocks used in the circuit model with the advantages of a measurement-based approach to quantum computation. We show how to construct optimal resource states of minimal size to implement elementary building blocks for encoded quantum computation in a measurement-based way, including states for error correction and encoded gates. The performance of the scheme is determined by the quality of the resource states, where within the considered error model a threshold of the order of 10% local noise per particle for fault-tolerant quantum computation and quantum communication.