✨ Shor's 9-qubit code

[adnathanail]

Problem Statement

Shor's 9-qubit code was the first quantum error correcting code, proposed by Shor in 1995.

It involves encoding a single logical qubit in 9 physical qubits. It can then detect up to 1 bit-flip and 1 phase-flip error, using a mid-circuit measurement, and a correcting Z or X gate can be applied, to correct the state.

Original paper:
https://journals.aps.org/pra/abstract/10.1103/PhysRevA.52.R2493
https://www.cs.miami.edu/home/burt/learning/Csc670.052/pR2493_1.pdf

Error correction zoo page:
https://errorcorrectionzoo.org/c/shor_nine

Proposed Solution

As a key piece of the journey towards fault tolerant quantum computing, and one of the first ocurrences of the idea of mid-circuit measurements, I think it would make a good addition as a benchmark