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

## Description

Fusion Based Quantum Computing, or FBQC, describes a fault tolerant way to produce fusion networks, or large entangled 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 is baked into the state-generation protocol.

## Protection

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.

## Encoding

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

## Gates

Clifford gates by creating topological features such as boundaries, defects, or twists, which can be done by single qubit measurements.Logical gates can be performed by code deformation.Non Clifford gates by Magic-state injectionLogical Clifford operations can be kept track of using the classical Pauli-frame register and need not be explicitly applied at the quantum level.

## 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.

## Threshold

\(11.98\%\) 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].

## 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.

## References

- [1]
- Sara Bartolucci et al., “Fusion-based quantum computation”. 2101.09310
- [2]
- Hector Bombin et al., “Logical blocks for fault-tolerant topological quantum computation”. 2112.12160

## Page edit log

- Victor V. Albert (2021-12-30) — most recent
- Dhruv Devulapalli (2021-12-17)

## Zoo code information

## 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/properties/fusion.yml.