$O(N^3)$ Pauli-flow finding algorithm #337
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## master #337 +/- ##
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+ Coverage 79.59% 79.63% +0.03%
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Files 40 41 +1
Lines 5892 5858 -34
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- Hits 4690 4665 -25
+ Misses 1202 1193 -9 ☔ View full report in Codecov by Sentry. 🚀 New features to boost your workflow:
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| import numpy.typing as npt | ||
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| class MatGF2: |
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Let's use inheritance if possible, as MatGF2 seems to be exactly the same as the implementation type (that of .data).
| for k in range(m): | ||
| if mat_data[k, j] == 1 and k != p: | ||
| for l in range(n): | ||
| mat_data[k, l] ^= mat_data[p, l] |
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Let's use numpy 's element-wise operation if possible (though for is also efficient here due to the jit decorator)
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Indeed, numpy element-wise operations are used everywhere but in the two jit-decorated functions in linalg.
| meas_planes = self.get_meas_plane() | ||
| flow, l_k = find_gflow(g, vin, vout, meas_planes=meas_planes) | ||
| if not flow: | ||
| if flow is None or l_k is None: # We check both to avoid typing issues with `get_layers`. |
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MEMO: Let's return None rather than tuple[None, None] for better typing.
| def __getitem__(self, key) -> MatGF2: | ||
| """Allow numpy-style slicing.""" | ||
| return MatGF2(self.data.__getitem__(key)) | ||
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| def __setitem__(self, key, value: gt.ElementLike | gt.ArrayLike | MatGF2) -> None: |
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Let's annotate key. I know it's very difficult but still we need it (or improve current design so that we don't have to annotate by ourselves).
| iset: AbstractSet[int], | ||
| oset: AbstractSet[int], | ||
| meas_planes: Mapping[int, Plane], | ||
| mode: str = "single", # noqa: ARG001 Compatibility with old API |
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Let's remove it. I believe we need to prioritize simplicity over compatibility in v0 developments.
| import galois | ||
| import numpy as np | ||
| import numpy.typing as npt | ||
| import sympy as sp |
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Let's prune sympy from the requirements.
| ) | ||
| pf = _find_pflow(og) | ||
| if pf is None: | ||
| return None, None # This is to comply with old API. It will be change in the future to `None`` |
| self.non_outputs_optim = deepcopy(self.non_outputs) | ||
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| def _get_reduced_adj(ogi: OpenGraphIndex) -> MatGF2: |
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This could be a method (many other occurrences)
| self.non_outputs_optim = deepcopy(self.non_outputs) | ||
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| def _get_reduced_adj(ogi: OpenGraphIndex) -> MatGF2: |
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Please do not use the word get (and also set) for ordinary functions. This is only allowed for getters.
| """ | ||
| adj_mat = ordering_matrix.data | ||
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| indegree_map = {} |
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General remark: could you annotate untyped literals, especially when you add something completely new? It greatly improves DX in the future as...
- we can readily detect type mismatches
- we are benefited by better intellisense
- it makes
pyrightoutputs less noisy
This PR introduces the$O(N^3)$ Pauli flow-finding algorithm presented in [1] which improves the previous version with $O(N^5)$ complexity [2]. Since a Pauli flow in an open graph without Pauli measurements defines a gflow, this algorithm also improves the previous implementation of the gflow-finding algorithm with $O(N^4)$ complexity [3].
The implementation proposed here considers the suggestion in [1] to eliminate the rows that are identically 0 in the order-demand matrix to accelerate the flow-finding routine in open graphs with$n_I \neq n_O$ .
Finally, the new algorithm solves the issue discussed in qat-inria#17 , whereby the previous flow-finding functions could return a correction function containing input nodes in the codomain, which is not allowed by the definition of gflow or Pauli flow.
In summary:
graphix.find_pflow, whilegraphix.gflowand related modules are adapted accordingly to avoid modifying the current API in this PR.linalg.pyhas been updated with more efficient functions for gaussian elimination, back substitution, kernel-finding and right-inverse. New implementation isnumba. The dependence onsimpyis dropped. Tests are simplified and updated accordingly, and module is now typed.pytest-benchmarkis incorporated to allow for easier benchmarking between different commits (courtesy of @thierry-martinez).Additional comments
graphix.gflowis currently functioning but rather messy. We leave its restructuration for a future PR to simply the review process.References
[1] Mitosek and Backens, 2024 (arXiv:2410.23439)
[2] Simmons, 2021 (arXiv:2109.05654)
[3] Backens et al., Quantum 5, 421 (2021)