Fusion-based quantum computing (FBQC) code[1] 


Code whose codewords are resource states used in an FBQC scheme. Related to a cluster state via Hadamard transformations.

FBQC is a fault tolerant way to produce fusion networks, or large entangled resource states starting from small constant-sized entangled resource states along with destructive measurements called fusions. These large states can be produced asychronously in the fusion framework and can be used as resources, as in measurement-based quantum computation (MBQC), or as logical states of topological codes. The difference from ordinary MBQC is that error-correction two-qubit measurements are performed, which requires a foliation with more qubits. The use of two-qubit measurements makes FBQC more compatible with photonic platforms.


Protects against erasure, Pauli errors, photon loss, fusion failure from non-determinism, and faulty resource states. Redundancy in fusion outcomes is captured by the check operator group. Fusion measurement outcomes form a syndrome that allows to correct for Pauli errors. There is no physical error correction, and decoding output is simply used to update the Pauli frame.


Resource state generators, which produce small constant size cluster states, and Fusion measurements (Bell fusions).


Clifford gates are performed by creating topological features such as boundaries, defects, or twists, which can be done by single qubit measurements. Logical gates can also be performed by code deformation. Non Clifford gates are perfomed by magic-state injection.

Fault Tolerance

Fusion networks are constructed in a fault tolerant way (as a stabilizer code), and they can be created in a way that naturally encodes topological fault tolerance.


\(11.98\%\) against erasure in fusion measurements.\(1.07\%\) against Pauli error.In linear optical systems, can tolerate \(10.4\%\) probability of photon loss in each fusion.\(43.2\%\) against fusion failure.FBQC applied to the surface code yields thresholds for logical gates that is consistent with the code capacity threshold [2].


  • Qubit stabilizer code — The resource states in FBQC are small stabilizer states, and after fusion measurements, the outputs are stabilizers (conditioned on measurement outcomes).


  • Topological code — Arbitrary topological codes can be created using FBQC, as can topological features such as defects and boundaries, by modifying fusion measurements or adding single qubit measurements.
  • Dual-rail quantum code — FBQC resource states are concatenated with dual-rail codes to increase loss detection.
  • Dynamically-generated QECC — Building a fusion network is done using a measurement-based dynamical process.
  • Cluster-state code — FBQC and MBQC are both computational models in which computation is done by measuring resource states (which are qubit stabilizer states). The difference between the two is in how the states are constructed. FBQC is based exclusively on two-qubit measurements tailored to photonic platforms. These measurements require a foliation with more qubits but one which can be built by fusing smaller modules.


S. Bartolucci et al., “Fusion-based quantum computation”, (2021) arXiv:2101.09310
H. Bombín et al., “Logical Blocks for Fault-Tolerant Topological Quantum Computation”, PRX Quantum 4, (2023) arXiv:2112.12160 DOI
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Zoo Code ID: fusion

Cite as:
“Fusion-based quantum computing (FBQC) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/fusion
@incollection{eczoo_fusion, title={Fusion-based quantum computing (FBQC) code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/fusion} }
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Cite as:

“Fusion-based quantum computing (FBQC) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/fusion

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/stabilizer/mbqc/fusion.yml.