# Analysis of error propagation in time-independent Hamiltonian computations

With a Feynman-Kitaev Hamiltonian, quantum computation does not need to apply any gates; you construct the Hamiltonian, initialize the system, and let it propagate on its own.

However, the Hamiltonian you can actually construct is probably not exactly the Hamiltonian you want. This will cause errors in the resulting computation. Has there been any analysis on how errors propagate in this model? E.g., if you need to apply 2-local terms and there is some model of errors in each term, how the system evolves?

Searching for things like "feynman-kitaev hamiltonian error propagation" doesn't yield anything useful. Is there a different search term I should use?

I can get some basic results analyzing this on my own but I don't want to duplicate effort or miss some good work.

• I think control error might be related? Aug 19, 2022 at 12:52
• If we study two unitary $U$ and $V$, we can study the error from optimization over state, i.e., $max_{|\psi\rangle} ||(U-V)|\psi\rangle||$. This is mentioned in Nielsen and Chuang's book, unitary quantum gates part. Aug 19, 2022 at 14:22
• I'd like to know if, e.g., $U=e^{iHt}$ where $H = \sum_{i=0}^n H_i$, and $H' = H + \sum_{i=0}^n \epsilon_i E_i$ and $V=e^{iH't}$, how $\Vert U-V\Vert$ changes with respect to $\epsilon$, $n$, the distribution of $E_i$, etc. Aug 19, 2022 at 14:31