Update Hamiltonian Simulation with Block Encoding #1269
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I would flip the 1st and 2nd paragraphs (first motivation, then how people solve it)
"and applications, such as Continouos Quantum Walk. " - not sure if that is actually an application or a primitive. but you can mention GS preparaiton of gibbs sampling.
Promise - I think it is not relevant
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"This will be acheived by implementing a block-encoding for the polynomial approximation of the function" - you don't block encode the function - you block encode the function of the hamiltonian
last sentence is missing a '.'
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Line #1. DATA_SIZE = HAMILTONIAN.num_qubits
you already defined this one above.
Also, be consistent with either capital or lower case
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maybe mention that the need for negative_power is because the expansion in exp(i*theta) include negative powers as well
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Line #7. print(
maybe define some utility function vector_overlap because you do this calculation 3 times?
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Line #36. U(0, 0, np.pi / 2, -np.pi / 2, state.block.block_lcu)
use phase instead of this U
consider using within_apply for the H
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the cx-counts is a bit misleading, maybe add some effective_counts that is the product with the scaling factor. Also the scaling factor is chosen a bit arbitrarily, I would choose it close to 1 so it won't affect the result.
Additionaly, add the approximation ratio or something like that, it also has impact on the comparison
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PR Description
This PR improves the Hamiltonian simulation based on block encoding example: align with new features, use optimized select operation for the Qubitization and QSVT approaches, and include a GQSP example.
Some notes
Please make sure that the notebook runs successfully with the latest Classiq version.
[ x] Please make sure that you placed the files in an appropriate folder