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arXiv:2610.38914

High-Threshold Fusion-Based Quantum Computation with Optical Hybrid Qubits

Seong-Yeop Lim, Jaehak Lee, Nuri Kang, Seung-Woo Lee

quant-phSubmitted Oct 28, 2026• Announced Oct 30, 2026• 0 citations
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Abstract

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.

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14 pages, including Supplementary Materials

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Hybridizing different degrees of freedom or physical platforms potentially offers various advantages in building scalable quantum architectures. Here, we introduce a fault-tolerant hybrid quantum computation by building on the advantages of both discrete-variable (DV) and continuous-variable (CV) systems. In particular, we define a CV-DV hybrid qubit with a bosonic cat code and a single photon, which is implementable in current photonic platforms. Due to the cat code encoded in the CV part, the predominant loss errors are readily correctable without multiqubit encoding, while the logical basis is inherently orthogonal due to the DV part. We design fault-tolerant architectures by concatenating hybrid qubits and an outer DV quantum error-correction code such as a topological code, exploring their potential merit in developing scalable quantum computation. We demonstrate by numerical simulations that our scheme is at least an order of magnitude more resource efficient compared to all previous proposals in photonic platforms, allowing us to achieve a record-high loss threshold among existing CV and hybrid approaches. We discuss the realization of our approach not only in all-photonic platforms but also in other hybrid platforms including superconducting and trapped-ion systems, which allows us to find various efficient routes toward fault-tolerant quantum computing. Published by the American Physical Society 2024
Fault-tolerant photonic quantum computing schemes have suffered low photon-loss thresholds and heavy resource requirements particularly when using single-photon qubits. Recently, several approaches utilizing both discrete and continuous variables of light have been proposed to reach high photon-loss thresholds with relatively low resource requirements. Here we present two schemes that outperform known previous schemes in terms of photon-loss thresholds and resource overheads. The first one is a hybrid scheme that combines discrete-variable (DV) and continuous-variable (CV) states of light. This scheme is nearly ballistic in the sense that passive measurements with hybrid entangled states are sufficient with little feedforwards. The second scheme is based on the parity-based encoding and Bayesian error tracking that enables one to reach a significantly high photon-loss threshold of ~8.5% with moderate resource requirements compared to previous known schemes.
Fusion-based quantum computation is a promising quantum computing model where small-sized photonic resource states are simultaneously entangled and measured by fusion gates. Such operations can be readily implemented with scalable photonic hardware: resource states can be deterministically generated by quantum emitters and fusions require only shallow linear-optical circuits. Here, we propose fusion-based architectures tailored to the capabilities and noise models in quantum emitters. We show that high tolerance to dominant physical error mechanisms can be achieved, with fault-tolerance thresholds of 8% for photon loss, 4% for photon distinguishability between emitters, and spin noise thresholds well above memory-induced errors for typical spin-photon interfaces. Our construction and analysis provide guidelines for the development of photonic quantum hardware targeting fault-tolerant applications with quantum emitters.
Bell state measurements (BSMs) play a significant role in quantum information and quantum computing, in particular in fusion-based quantum computing (FBQC). The FBQC model is a framework for universal quantum computing, provided that we are able to perform entangling measurements, called fusions, on qubits within small entangled resource states. Here, we analyze the usage of different linear-optical BSM circuits as fusions in the FBQC schemes and numerically evaluate hardware requirements for fault-tolerance in this framework. We examine and compare the performance of several BSM circuits with varying additional resources and estimate the requirements on losses for every component of the linear-optical realization of fusions under which errors in fusion networks caused by these losses can be corrected. Our results show that fault-tolerant quantum computing in the FBQC model is possible with currently achievable levels of optical losses in an integrated photonic implementation, provided that we can create and detect single photons of the resource states with a total marginal efficiency higher than 0.973.
Quantum error correction is an essential tool for performing reliable quantum information processing tasks under noisy circumstances, and is attracting growing attention today as a crucial element for realizing the fault-tolerant quantum computer. In this article, we introduce two cutting-edge quantum error correction techniques for implementing fault-tolerant quantum computation: the hybrid approach and the fusion-based quantum computation. The hybrid quantum computing utilizes hybrid qubits which combine the advantages of continuous-variable and discrete-variable qubits. The fusion-based quantum error correction offers a way, specialized for photonic quantum information processing, toward fault tolerance based on two-qubit measurement, known as fusion. We demonstrate by numerical simulations that our methods achieve the increased loss threshold and the improved resource efficiency compared to previous photonic proposals.
We propose a fault-tolerant quantum computation scheme in a measurement-based manner with finite-sized entangled resource states and encoded-fusion scheme with linear optics. The encoded fusion is an entangled measurement devised to enhance the fusion success probability in the presence of losses and errors based on a quantum error-correcting code. We apply an encoded-fusion scheme, which can be performed with linear optics and active feedforwards to implement the generalized Shor code, to construct a fault-tolerant network configuration in a three-dimensional Raussendorf-Harrington-Goyal lattice based on the surface code. Numerical simulations show that our scheme allows us to achieve up to 10 times higher loss thresholds than nonencoded fusion approaches with limited numbers of photons used in fusion. Our scheme paves an efficient route toward fault-tolerant quantum computing with finite-sized entangled resource states and linear optics.