# Fusion-based quantum computation

**Authors:** Sara Bartolucci, Patrick Birchall, Hector Bombin, Hugo Cable, Chris Dawson, Mercedes Gimeno-Segovia, Eric Johnston, Konrad Kieling, Naomi Nickerson, Mihir Pant, Fernando Pastawski, Terry Rudolph, Chris Sparrow  
**arXiv:** [2101.09310](https://arxiv.org/abs/2101.09310)  
**Date:** 2021-01-22  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2101.09310v1/

## Key points

- Introduction of fusion-based quantum computing (FBQC)
- FBQC uses entangling measurements called fusions on qubits of small entangled resource states
- Proposal of stabilizer formalism for analyzing fault tolerance and computation in FBQC
- Advantages of FBQC: architectural simplifications, hardware made up of identical modules, low depth of operations on each physical qubit
- Presentation of two pedagogical examples of fault-tolerant schemes within the FBQC framework
- Numerical evaluation of threshold under a hardware-agnostic fusion error model and linear optical quantum computing error model
- Addressing non-determinism of fusion through quantum error correction protocol and other errors in FBQC
- Higher threshold compared to existing literature by tailoring fault-tolerance framework to the physical system
- Ballistic scheme presented that can tolerate a 10.4% probability of photon loss in each fusion
- Demonstrates robustness and potential practicality of FBQC in real-world implementations

## Summary

The paper introduces fusion-based quantum computing (FBQC), a model of universal quantum computation in which entangling measurements called fusions are performed on the qubits of small constant-sized entangled resource states. The authors propose a stabilizer formalism for analyzing fault tolerance and computation in these schemes. One of the key advantages of FBQC is that it offers significant architectural simplifications; it enables hardware made up of many identical modules and requires an extremely low depth of operations on each physical qubit, thereby reducing classical processing requirements. The paper presents two pedagogical examples of fault-tolerant schemes constructed within the FBQC framework. The authors numerically evaluate the threshold of these schemes under a hardware-agnostic fusion error model, which includes both erasure and Pauli errors. They also study an error model specific to linear optical quantum computing, considering probabilistic fusion and photon loss. In FBQC, the non-determinism of fusion is directly addressed by the quantum error correction protocol along with other errors. The authors find that tailoring the fault-tolerance framework to the physical system allows for a higher threshold compared to schemes reported in existing literature. The paper concludes by presenting a ballistic scheme that can tolerate a 10.4% probability of suffering photon loss in each fusion; this demonstrates the robustness and potential practicality of FBQC in real-world implementations. Overall, this research contributes to advancing understanding and development of fusion-based quantum computing as a promising approach for achieving fault-tolerant universal quantum computation with simplified architecture and reduced classical processing requirements.