Add 2-CNOT decomposition for qml.QubitUnitary

[lillian542]

Important Note

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

Context

We would like to add a 2-CNOT decomposition for the qml.QubitUnitary operation. This will be more efficient for some cases that currently decompose to 3 CNOT gates unnecessarily.

Implementation Details

This task is to add a new decomposition, _decompose_2_cnots, for the two-qubit decomposition for QubitUnitary. Once added, the logic in two_qubit_decomposition should be updated to dispatch to this decomposition when relevant.

The implementation should:

• Define a decomposition using 2 CNOT gates, based on this paper
• Update the logic in _compute_num_cnots to determine if the 2 CNOT decomposition is the best option.
• Update the logic in the dispatch in the function two_qubit_decomposition to link to the 2 CNOT case instead of the 3 CNOT case when applicable.

All functions added or modified for this task belong in the pennylane/ops/op_math/decompositions/unitary_decompositions file.

Relevant functions include:

• qml.QubitUnitary
• qml.ops.op_math.decompositions.unitary_decompositions._compute_num_cnots
• qml.ops.op_math.decompositions.unitary_decompositions._decompose_3_cnots
• qml.ops.two_qubit_decomposition

Additional Requirements

A completed PR would:

• Include a docstring for the new _decompose_2_cnots function with details about what the function does and a link to the referenced paper
• Update the docstring of _compute_num_cnots to include a correct reference for the logic used for the 2 CNOT case
• Update the docstring of two_qubit_decomposition to reflect the change.
• Include a changelog entry at doc/releases/changelog-dev.md. Make sure to include your name in the list of contributors at the bottom!
• Add tests to the file tests/ops/op_math/test_decompositions.py. The tests should include an adequate suite of both unit and integration tests.
• Pass all existing tests including black and pylint checks

[teotro]

Update the logic in _compute_num_cnots to determine if the 2 CNOT decomposition is the best option.

However, isn't the logic in _compute_num_cnots already there and trace(γ(U)) is able to be identified as real?

[lillian542]

However, isn't the logic in _compute_num_cnots already there and trace(γ(U)) is able to be identified as real?

Thanks, good point - I missed that when looking over the existing functions! There's already logic there for returning 2, two_qubit_decomposition just defaults to the 3-CNOT implementation for num_cnots==2.

That logic is left over from a previous implementation for a 2-CNOTs decomposition that was found to be unreliable and removed. If you've double-checked that the same pre-requisites apply for using the 2-CNOT decomposition in this paper, then you can just proceed with the existing logic in _compute_num_cnots 😄

[teotro]

Please check PR #8717. I pushed the changes. Could you please approve the workflows so the tests can run?