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

## Description

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.

## Protection

## Encoding

## Gates

## Fault Tolerance

## Threshold

## Parent

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

## Cousins

- 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 from ordinary MBQC is that error-correction two-qubit measurements are performed, which requires a foliation with more qubits but one which can be built by fusing smaller modules.

## References

- [1]
- S. Bartolucci et al., “Fusion-based quantum computation”, (2021) arXiv:2101.09310
- [2]
- H. Bombín et al., “Logical Blocks for Fault-Tolerant Topological Quantum Computation”, PRX Quantum 4, (2023) arXiv:2112.12160 DOI

## Page edit log

- Victor V. Albert (2023-03-01) — most recent
- Yaron Jarach (2023-03-01)
- Victor V. Albert (2021-12-30)
- Dhruv Devulapalli (2021-12-17)

## 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/tree/main/codes/quantum/qubits/mbqc/fusion.yml.