Within Quantum Error Correction and stabilizer codes, toric codes/surface codes are very tempting, mainly for their high error threshold. For more background please check up, in our Physics sister (aunt?) site: Quantum Error Correction: Surface code vs. color code.
However, these codes require fairly specific measurements in specific bases, which I find hard to translate in practice, especially into my language of interest which is spin states in a solid-state few-spin collection. To see my motivation, here is a not-quite successful attept from a few years ago, using a more naïve QEC scheme: "Quantum Error Correction with magnetic molecules".
So, the problem:
- I am designing a realistic (molecular/supramolecular) network of 7 spins 1/2 (or something almost equivalent, see Is qubit/qudit terms, where is the experimental limit between an S=3/2 and 2·S=1/2?)
- a necessary first: what are the operations/measurements that I need to be able to do? here assume I'm able to do Pulsed electron paramagnetic resonance to address every transition coherently
- and, as a consequence, what is a good coupling scheme between my spins so that the required number of physical operations is reasonable?
Related: How does the size of a toric code torus affect its ability to protect qubits?