Implement QFT as a gate in Lightning-Qubit

[tomlqc]

Important Note

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

Context

PennyLane has support for many quantum gates natively at the Python level, but often we may require faster implementations. lightning.qubit is a fully C++ backed simulator library that can be called from PennyLane, with optimal implementations of many highly-used gates. Implementing gates or templates in the C++ backend can boost their performance.

Requirements

The QFT template has to be implemented in the lightning.qubit C++ backend as a gate.

• Add a method for the QFT gate to the lightning_qubit/gates/cpu_kernels/GateImplementationsLM.hpp file. Implement by using the decomposition approach outlined in compute_decomposition() in pennylane/templates/subroutines/qft.py.

• Add a GateOpToMemberFuncPtr struct in lightning_qubit/gates/OpToMemberFuncPtr.hpp.

• Add C++ tests for the QFT gate to Test_GateImplementations_Nonparam.cpp. You can follow the same style used for other gates in this test file.

• Update the list of supported gates in pennylane_lightning/lightning_qubit/lightning_qubit.py.

• Add Python tests in tests/test_gates.py to check the correctness of this gate against PennyLane qml.QFT. (you may reuse existing tests, but add some if coverage requires it)

• Create a pull-request in the PennyLane Lightning repository and ensure to complete all the steps outlined in the PR template. Please keep the checklist at the top of the PR description.

• Create a script defining a basic circuit that uses qml.QFT.compute_matrix() passed to QubitUnitary, and benchmark this against the qml.QFT that you have just implemented for different number of qubits. Upload the results to the pull-request for further discussions.

• Mark the PR ready for review.

Don't hesitate to ask for clarification or raise any concerns regarding the issue. We'll be happy to discuss with you!

[gzquse]

Dear Thomas,

Please refer to Solution Nov 8 Ziqing
There might be some CI issues related to my forked branch pennylane-lightning.

I am using NERSC HPC env.
Could you help me check the files thanks!

Kind regards,
Ziqing

[tomlqc]

Thanks @gzquse, I'll take a look.