Expval kernels for LightningQubit

[Alex-Preciado]

Important Note

⚠️ This issue is part of an internal assignment and not meant for external contributors.

Details

The expectation value of a quantum gate $U$ for a circuit in the state $| \psi \rangle$ is $\langle \psi | U | \psi \rangle$. In PennyLane-Lightning this is calculated by first applying $U$ to $| \psi \rangle$ to get $| \psi' \rangle$ and then take the inner product with $| \psi \rangle$. That is not optimal since one needs to allocate a copy of $| \psi \rangle$.

Implementation

Modify the expval method in MeasurementsLQubit.hpp (only the one with a const std::string &operation argument) to mimic the Lightning-Kokkos implementation, i.e. write specialized kernels that do not rely on applyMatrix/applyOperation+innerProdC but perform all operations at once. That will be done in a loop over the state vector entries (have a look at the PauliX functor in ExpValFunctors.hpp for example). That loop is embarrassingly parallelizable and should be parallelized as such.

Requirements

A PR must satisfy the following:

• Write expval kernels for the Identity, PauliX, PauliY, PauliZ, Hadamard observables.
• Parallelize the kernels with C++ threads or OpenMP.
• Validate the implementation with C++ & Python tests (you may reuse existing tests, but add some if coverage requires it).
• Pass clang-tidy, black and pylint checks.
• Include a changelog entry under "Improvements".
• Gather benchmark data using the Python interface of PennyLane (old versus new implementation & time versus number of threads for different qubits count) and discuss the performance trends. Put the benchmarking scripts in a Github gist and share the gist in the PR comments.

[sbohloul]

@Alex-Preciado I was wondering if I could directly push a branch to the repo.

[Alex-Preciado]

Hey @sbohloul 👋 , external contributions can only be made through forks. You will need to fork the repo to submit a pull request with your changes. You can find more details here: https://github.com/PennyLaneAI/pennylane-lightning#contributing. Let me know if you any other questions.