Compressed Sparse Row (CSR) representation for Hamiltonians and Tensors

[AmintorDusko]

Context:
This PR changes the Pennylane sparse representation to Compressed Sparse Row (CSR) representation.

Description of the Change:
When converting a Hamiltonian to a sparse format, this format will be CSR.
The COO format previously used in all parts of PennyLane was left as an internal format in parts of the code where it will be beneficial.

Benefits:
The expval calculation speed of Sparse Hamiltonians has increased by 20%-30%.

Possible Drawbacks:

Related GitHub Issues:

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[AmintorDusko]

Some benchmarks below:

The sparse Hamiltonian representation shows an increase of ~25% in speed with the CSR representation.
As expected, we observe just a slight improvement in time for dense Hamiltonian cases.

[codecov]

Codecov Report

Merging #2561 (dfaf3f3) into master (da89442) will not change coverage.
The diff coverage is 100.00%.

@@           Coverage Diff           @@
##           master    #2561   +/-   ##
=======================================
  Coverage   99.58%   99.58%           
=======================================
  Files         243      243           
  Lines       19596    19596           
=======================================
  Hits        19515    19515           
  Misses         81       81           

Impacted Files	Coverage Δ
pennylane/devices/default_qubit.py	100.00% <100.00%> (ø)
pennylane/operation.py	96.73% <100.00%> (ø)
pennylane/ops/qubit/observables.py	100.00% <100.00%> (ø)
pennylane/ops/qubit/qchem_ops.py	100.00% <100.00%> (ø)
pennylane/utils.py	100.00% <100.00%> (ø)

---

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[soranjh]

The sparse Hamiltonian representation shows an increase of ~25% in speed with the CSR representation. As expected, we observe just a slight improvement in time for dense Hamiltonian cases.

Thanks @AmintorDusko. I am curious how CRS compares with COO in terms of the time needed to create the sparse Hamiltonian matrix and also the size of the sparse matrix.

[AmintorDusko]

The sparse Hamiltonian representation shows an increase of ~25% in speed with the CSR representation. As expected, we observe just a slight improvement in time for dense Hamiltonian cases.

Thanks @AmintorDusko. I am curious how CRS compares with COO in terms of the time needed to create the sparse Hamiltonian matrix and also the size of the sparse matrix.

Hi @soranjh, thanks for asking.
The time to create the sparse Hamiltonians is essentially the same. Mainly because I kept the COO representation internally to build the Hamiltonian and convert to CSR after the Hamiltonian is built. Scipy conversion from COO to CSR is very efficient.
Regarding the size, CSR, due to its internal structure, will usually be smaller or in the worst case have the COO size.
I'm attaching some images to illustrate what I'm saying.

[antalszava]

Looks good 🎉 The changes look good, though it would be great to get an extra pair of eyes here before merging.

[AmintorDusko]

Looks good tada The changes look good, though it would be great to get an extra pair of eyes here before merging.

Thank you, @antalszava! I will wait for one more approval before merging.

[soranjh]

Looks good to me @AmintorDusko, just left two questions.

[AmintorDusko]

Thank you, @soranjh, @antalszava and @josh146!