Notepad/enter/Machine Tips (Quantum)/Resources/Concepts Review/Error Correction.md

# Error Correction 

Quantum error  correction is a huge part of why current quantum  computers are still being improved today. Understanding the quantum error correction problem will get you on your way to be a QC whiz! 

-  Here are  a brief set of [Notes](obsidian://open?vault=Coding%20Tips&file=Careers%2FCurrent%20Occupations%2FQRG%2Fmore-qrg%2FThe%20Quantum%20Research%20Group%207150bc7f5d7e4ba384212a9816ce928b%2FZe%20Quantum%20Papers%2FQuantum%20Error%20Correction%20-%20Notes) on Error Correction 
- Here's an [article](https://spectrum.ieee.org/quantum-error-correction) written by Michael Biercuk himself. 
- Steane code tool ([wiki](https://en.wikipedia.org/wiki/Steane_code)) for error correction 
- This[ paper on QEC side effects](https://drive.google.com/file/d/1_5nlZResIkD5RsbEUV2loKYa655n7cwk/view?usp=share_link) and sensors report (2022)

---

### Software & Tools
- A [Github](https://github.com/cgranade/python-quaec) scientific software library for working with quantum error correction
- A [medium article](https://medium.com/qiskit/heres-how-to-test-error-correction-on-an-ibm-quantum-computer-ecb086606e7) that shows how to test error correction on a quantum computer. 
- the qiskit chapter on error corrections using [repetition codes](https://qiskit.org/textbook/ch-quantum-hardware/error-correction-repetition-code.html)
- [Q-CTRL's software ](https://docs.q-ctrl.com/boulder-opal/tutorials/design-robust-single-qubit-gates-using-computational-graphs)is always excellent 
- Another software repo with fantastic visualization of topological codes, stabilizers, error models and more is found at [panqec repository](https://github.com/panqec/panqec)
- This is a fantastic [youtube tutorial](https://www.youtube.com/watch?v=sprDaLxPVNI) on simulating a quantum error correcting circuit using Stim 
- [Gate Set Tomography python implementation](https://github.com/sandialabs/pyGSTi) used for error mitigation 
	- for a more about GST, [read this paper](https://ar5iv.labs.arxiv.org/html/2009.07301)


---
## Research 
-  QEC scheme called measurement-based estimator scheme for continuous quantum error correction ([MBE-CQEC](https://www.oist.jp/news-center/news/2022/9/15/mbe-cqec-new-scheme-correct-quantum-errors)), which could quickly and efficiently detect and correct errors from partial, noisy syndrome measurements. They set up a powerful classical computer to act as an outside controller (or estimator) that estimates errors in the quantum system, filters out the noise perfectly, and applies feedback to correct them![[Pasted image 20221217144843.png]]

- **Quantum Low-Density Parity-Check (QLDPC)  Code** - Also called a sparse quantum code. Family of [[n,k,d]] stabilizer codes for which the number of sites (either qubit or qudit) participating in each stabilizer generator and the number of stabilizer generators that each site participates in are both bounded by a constant as <73>→∞. A geometrically local stabilizer code is a QLDPC code where the sites involved in any syndrome bit are contained in a fixed volume that does not scale with <68>. As opposed to general stabilizer codes, syndrome extraction of the constant-weight check operators of a QLDPC codes can be done using a constant-depth circuit. More info can be [found here](https://errorcorrectionzoo.org/c/qldpc). 
![[Pasted image 20230224122914.png]]


----

Check out the [code graph](https://errorcorrectionzoo.org/code_graph) as well. 

More Error correction Papers: 
- https://www.arxiv-vanity.com/papers/2111.07029/ 
- Error correction continues to be a field that gets furthered each and every year with better performance metrics. 
- It is currently (as of 2024 August) at 99.5% accuracy. However, for quantum computing to be scalable, it needs to have an accuracy of **at worst** 0.1% meaning at the very least 99.9 percent and it is simply not that right now especially as qubits continue to scale.