Add Product block encoding

[charlesyuan314]

Add an instance of BlockEncoding that implements the product of constituent block encodings.

[mpharrigan]

Some minor things to consider, but LGTM

[tanujkhattar]

Please add an explanation of the decomposition to the docstring and consider doing the partitions and unpartitions once outside the for-loop

[charlesyuan314]

I will do the suggested refactor to clean up the circuit diagram in a follow-up PR.

@mpharrigan I've addressed all of the other feedback.

[tanujkhattar]

Why are these not serializable ?

[tanujkhattar]

@charlesyuan314 I'll merge the PR and we can continue this discussion and potentially address in a follow-up PR

[charlesyuan314]

I believe it is because this bloq has an attribute of type Tuple[BlockEncoding, ...]. It results in the following at serialization time:

qualtran.testing.BloqCheckException: Serialization Failed:
Object arrays cannot be saved when allow_pickle=False

Are bloqs contained as attributes something that can be made serializable?

[tanujkhattar]

Object arrays cannot be saved when allow_pickle=False

I think it's because so far we haven't had any bloq that stores a sequence of subbloqs as an attribute.

To support serialization we'll have to update

Qualtran/qualtran/protos/bloq.proto

Line 40 in f8d2db0

int32 subbloq = 7;

to add a new NDArray subbloqs that stores an NDArray of integers corresponding to IDs of each of the subbloqs and then update

Qualtran/qualtran/serialization/bloq.py

Line 349 in f8d2db0

if isinstance(val, Bloq):

to check if the argument is an ndarray of bloqs, then delegate to a different method that serializes it.

Can you please open an issue to track this?