Rewrites the fidelity function for clarity #226
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## master #226 +/- ##
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- Hits 1191 1188 -3
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thewalrus/quantum/gaussian_checks.py
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| sigma2 = cov2 / hbar | ||
| deltar = (mu1 - mu2) / np.sqrt(hbar) | ||
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| Omega = sympmat(n0 // 2) # The symplectic matrix |
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I would recommend using lowercase for these variables, since capitalization would be used for classes, and thus get highlighted differently. Any reason for changing to capitalized versions?
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I knew this would come up! So I am just trying to follow the paper and LaTeX naming, i.e., Omega is meant to be
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But if you feel strongly about this I am happy to change it.
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Sorry about this. It's a case of programming vs. academic conventions. I would say it's still better to keep lowercase, and follow Python syntax rules here. Either having it as omega or even big_omega (but I think the former is probably better).
thewalrus/quantum/gaussian_checks.py
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| f = np.sqrt(np.linalg.det(Sigma_inv) * np.linalg.det(det_arg)) * np.exp( | ||
| -0.5 * deltar @ Sigma_inv @ deltar |
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No transpose on the first deltar? It seems like the paper writes it np.exp(-0.5 * deltar.T @ Sigma_inv @ deltar), but maybe that's the same in this case. 🤔
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It makes no difference, although it could be added. If you do a @ b and a and b are 1D arrays the numpy is smart enough to know that what you want is mathematically speaking a^T \cdot b
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Fair enough. That's what I suspected, just wanted to clarify. Thanks!
| The actual implementation used here corresponds to the *square* of Eq. 96 of | ||
| `'Gaussian states and operations - a quick reference', Brask <https://arxiv.org/abs/2102.05748>`_. |
Co-authored-by: Theodor <theodor@xanadu.ai>
Co-authored-by: Theodor <theodor@xanadu.ai>
The fidelity function in
quantum/gaussian_checks.pyis rewritten to add clarity and also a reference and test are added.This should clarify the (non-) bug posited in #223