Short answer: Fusion-based quantum computation (FBQC) is a model for fault-tolerant photonic computing built from entangling measurements called fusions, performed on small entangled resource states. Because photons are easily lost, a central question is how much loss the scheme can tolerate. A 2023 Nature Communications paper reports a ballistic scheme that tolerates a 10.4% probability of photon loss in each fusion, which corresponds to a 2.7% loss probability for each individual photon. These are theoretical and numerical results.
Why photonics needs a different model
The 2023 paper says standard quantum computing primitives include deterministic unitary entangling gates, which are not natural operations in many systems including photonics. FBQC is presented as a fault-tolerant model built from primitives readily accessible in photonic systems. The primitives are fusions, which are entangling measurements on qubits of small constant-sized entangled resource states. The error correction protocol deals directly with probabilistic photonic gates as well as errors.
Reported thresholds
The authors state three main results: introducing FBQC with a stabilizer formalism, evaluating specific fusion networks, and defining a physical photonic architecture. With a hardware-agnostic fusion error model they report a threshold of 11.98% against erasure in each fusion measurement and 1.07% against Pauli error. With a linear optical error model that accounts for photon loss and non-deterministic fusions, they report the 10.4% per-fusion loss figure above, equal to 2.7% for each photon. They say the model can achieve a higher threshold than schemes reported in the literature and that the architecture is highly modular with reduced classical processing requirements compared with earlier photonic architectures.
A closer look at loss in fusions
A 2024 analysis on arXiv (2403.14811), also published in AVS Quantum Science, studies linear-optical Bell state measurement circuits used as fusions. Bell state measurements are central to FBQC. The authors compare circuits with varying additional resources and numerically estimate the loss requirements for each component of the linear-optical realization under which loss-caused errors in fusion networks can be corrected. They report that fault-tolerant computation in this model is possible with currently achievable levels of optical loss in an integrated photonic implementation, provided single photons of the resource states can be created and detected with a total marginal efficiency higher than 0.973. That is the authors' numerical conclusion, with the efficiency condition attached.
What this does not tell you
These are design and simulation studies. They do not say that a fault-tolerant photonic computer has been built, and the efficiency condition above is a requirement that hardware would still need to meet. Different architectures and error models give different thresholds, so the numbers should not be compared across papers without checking the assumptions.
FAQ
What is a fusion?
An entangling measurement performed on qubits of small entangled resource states, per the 2023 paper.
Why is photon loss the main concern?
Loss causes errors in fusions. The papers quantify how much loss the error correction can tolerate.
How much loss can the scheme tolerate?
In the 2023 ballistic scheme, 10.4% per fusion, which corresponds to 2.7% per photon.
What is a Bell state measurement?
An entangling measurement central to FBQC, studied in linear-optical form in the 2024 analysis.
Has this been built?
These papers are theoretical and numerical. They do not report a built fault-tolerant machine.
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