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If you're talking about simulating a hamiltonian on a regular computer then you may want to check out Qutip. It's a python module where a lot of this stuff has already been worked out, including simulating time dependent hamiltonians. I did an undergrad project on QC and this helped me get past a lot of the roadblocks like this and freed up more time to learn about the field, it also becomes a useful toy to play around with and get an intuition for a lot of stuff.
NOTE:
The number of mentions on this list indicates mentions on common posts plus user suggested alternatives.
Hence, a higher number means a more popular project.
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