# Embedding returns energies which are lower than the true minimum energy

In my problem, I coupled many qubits together to form a chain. However, after running QUBO and negleting broken chain,  I still got some energies which are lower than the true minimum energy. Why it would be the case?

As far as I know, if 2 qubits are coupled to form a chain, a penalty function will be added, so if the chain is broken, energies will get higher than the true minimum energy.

But how about the case of coupling many qubits to form a chain?

• Hello,

Regarding why the energies are not higher in results with broken chains, the broken chains are fixed in post-processing using a majority vote method, meaning that the logical qubit resolves to the value of that taken by the majority of qubits in the chain.

I'm not sure how the energy can be lower than the true minimum energy.

How are you determining the true minimum energy?

I hope this helped.

• Hi, thank you for your help.

I know true minimum energy because the problem can be solved exactly analytically. So I just tried to compare Dwave's result with theoretical results. While Dwave result agrees well with theoretical result for most cases, there are some cases which I obtain a lower energy than theoretical energies.