feat: add Fast Walsh–Hadamard Transform for Pauli-Liouville conversion #1736
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renatomello
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Oct 28, 2025
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| def _fht(vec): | ||
| """In-place 1D Fast Walsh–Hadamard Transform.""" | ||
| n = len(vec) | ||
| h = 1 | ||
| while h < n: | ||
| for i in range(0, n, h * 2): | ||
| for j in range(i, i + h): | ||
| a = vec[j] | ||
| b = vec[j + h] | ||
| vec[j] = a + b | ||
| vec[j + h] = a - b | ||
| h *= 2 | ||
| return vec |
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The 1D FWHT is already implemented in quantum_info.utils
https://qibo.science/qibo/stable/_modules/qibo/quantum_info/utils.html#hadamard_transform
renatomello
reviewed
Oct 28, 2025
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| # Normalize if required (divide by sqrt of dimension) | ||
| if normalize: | ||
| import math |
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This does not need to be outside toplevel
renatomello
reviewed
Oct 28, 2025
Codecov Report❌ Patch coverage is
Additional details and impacted files@@ Coverage Diff @@
## master #1736 +/- ##
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- Coverage 99.09% 98.92% -0.17%
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Files 80 80
Lines 13083 13106 +23
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+ Hits 12964 12965 +1
- Misses 119 141 +22
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This PR introduces a new helper function
_to_pauli_liouville_fhtthat uses the Fast Walsh–Hadamard Transform to convert a Liouville superoperator to its Pauli‑Liouville representation in O(N log N) time. The function applies the transform along rows and columns and optionally normalizes the result. No existing functionality is removed; the new helper can be called by existing conversion routines for improved performance.Resolves or addresses issue #1632 (Fast conversion to and from Pauli basis). Adds 46 lines of code.