[labs.dla 3] structure_constants_dense #6376
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## dense_util #6376 +/- ##
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Coverage 99.29% 99.29%
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Files 454 454
Lines 43262 43267 +5
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+ Hits 42959 42964 +5
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Qottmann
changed the title
…into structure_constants_dense
| @pytest.mark.parametrize("dla", [Ising3, XXZ3]) | ||
| @pytest.mark.parametrize("use_orthonormal", [False, True]) | ||
| def test_structure_constants_elements(self, dla, use_orthonormal): | ||
| r"""Test relation :math:`[i G_\alpha, i G_\beta] = \sum_{\gamma = 0}^{\mathfrak{d}-1} f^\gamma_{\alpha, \beta} iG_\gamma`.""" | ||
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| d = len(dla) | ||
| dla_dense = np.array([qml.matrix(op, wire_order=range(3)) for op in dla]) | ||
| if use_orthonormal: | ||
| gram_inv = sp.linalg.sqrtm( | ||
| np.linalg.pinv(np.tensordot(dla_dense, dla_dense, axes=[[1, 2], [2, 1]]).real) | ||
| ) | ||
| dla_dense = np.tensordot(gram_inv, dla_dense, axes=1) | ||
| dla = [(scale * op).pauli_rep for scale, op in zip(np.diag(gram_inv), dla)] | ||
| ad_rep = structure_constants_dense(dla_dense, is_orthonormal=use_orthonormal) | ||
| for i in range(d): | ||
| for j in range(d): | ||
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| comm_res = 1j * dla[i].commutator(dla[j]) | ||
| res = sum((c + 0j) * dla[gamma] for gamma, c in enumerate(ad_rep[:, i, j])) | ||
| res.simplify() | ||
| assert set(comm_res) == set(res) # Assert equal keys | ||
| if len(comm_res) > 0: | ||
| assert np.allclose(*zip(*[(comm_res[key], res[key]) for key in res.keys()])) |
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I think the tests are nice. We should add one on a non-orthonormal set of operators, though, that checks exactly this defining property of the structure constants :)
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(Can do this just by applying some random coefficients to the existing DLAs.)
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I guess to be truly non-orthonormal we should also break the orthogonality, so doing some sums of paulis
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Ah yeah, I meant a non-diagonal coefficients matrix :)
Like
coeffs = np.random.random((len(dla), len(dla)))
new_dla = [qml.sum(*(c * op for c, op in zip(_coeffs, dla))) for _coeffs in coeffs]or so
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I added a tested orthonormalize function but somehow the test now fails for the cases where I orthonormalize the basis 🤔 I am confused
edit: talking about the test_structure_constants_elements test, the tests for orthonormalize work as expected
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I think the problem is the inconsistency between the trace inner product for matrices and pauli sentences that is assumed. I.e. the pauli sentence one is normalized whereas in the matrix case we dont. So I think to have consistent adjoint representations we should fix one convention and stick to that. Not sure which one though?
x = X(0) @ X(1)
x = x.pauli_rep
(x @ x).trace()
# 1.0
xm = qml.matrix(x, wire_order=range(2))
np.trace(xm @ xm)
# 4.0
I feel like the normalized one is neater because it should not depend on the (potentially redundant) matrix dimensions. E.g. in the example if you set the wire_order to range(3) the inner product is 8
In particular, I would suggest the matrix inner product to be
xm = qml.matrix(x, wire_order=range(4))
np.trace(xm @ xm)/len(xm)
to match those pauli sentences.
I pushed some suggestions but the sructure_constants test is still failing when the operators are being orthonormalized 🤔
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Fully agree that we should be using
…into structure_constants_dense
Co-authored-by: David Wierichs <[email protected]>
…aneAI/pennylane into structure_constants_dense
Building on top of #6371
An implementation of
structure_constantsusing dense matrices, which sometimes is advantageous in certain scenarios.The projection routine can be optimized still
[sc-75525]