Implement two qubit unitary to operations algorithm from https://arxiv.org/abs/quant-ph/0406176

[NoureldinYosri]

The paper https://arxiv.org/abs/quant-ph/0406176 introduces an algorithm for performing quantum shannon decomposition. We have this algorithm implemented in Cirq in

Cirq/cirq-core/cirq/transformers/analytical_decompositions/quantum_shannon_decomposition.py

Line 44 in 351a08e

def quantum_shannon_decomposition(

However, one of the base cases of the algorithms is not implemented. Namely A.2 the base case for a two qubit unitary, instead cirq uses another decomposition

Cirq/cirq-core/cirq/transformers/analytical_decompositions/quantum_shannon_decomposition.py

Lines 101 to 113 in 351a08e

	if n == 4:
	operations = tuple(
	two_qubit_matrix_to_cz_operations(
	qubits[0], qubits[1], u, allow_partial_czs=True, clean_operations=True, atol=atol
	)
	)
	yield from operations
	i, j = np.unravel_index(np.argmax(np.abs(u)), u.shape)
	new_unitary = unitary_protocol.unitary(FrozenCircuit.from_moments(*operations))
	global_phase = np.angle(u[i, j]) - np.angle(new_unitary[i, j])
	if np.abs(global_phase) > 1e-9:
	yield ops.global_phase_operation(np.exp(1j * global_phase))
	return

Which is not as efficient as the decompositin described in A.2. It would be nice to implement A.2 and uses it in QSD.

What is the urgency from your perspective for this issue? Is it blocking important work?

P2 - we should do it in the next couple of quarters

[RahilJain1366]

Hi @NoureldinYosri, can I take this up too since I am trying to find a solution for #6770?

[senecameeks]

Cirq Cynq: This will improve the performance by reducing the number of rotations and depth of the circuit.

[senecameeks]

@RahilJain1366, thanks for offering, let's discuss after #6770 is complete