Optimized implementation of GF2Inverse
#1459
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| References: | ||
| [Efficient quantum circuits for binary elliptic curve arithmetic: | ||
| reducing T -gate complexity](https://arxiv.org/abs/1209.6348) | ||
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| section 2.3 |
| result = new_result | ||
| x = bb.add(GF2Square(self.bitsize), x=x) | ||
| return {'x': x, 'result': result} | ({'junk': np.array(junk)} if junk else {}) | ||
| beta = bb.allocate(dtype=self.qgf) |
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| beta = bb.allocate(dtype=self.qgf) | |
| # The algorithm is descriped on page 4 and 5 of https://arxiv.org/abs/1209.6348 and resembles binary exponentiation. | |
| # The inverse is computed as (B_{n-1})^2. Where B_1 = x and B_{i+j} = B_i B_j^{2^i}. | |
| beta = bb.allocate(dtype=self.qgf) |
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cool, yeah. I'd see if this could make its way to the class docstring so it shows up in the docs
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Added to the class docstring and regenerated the docs
| bloq = GF2Inverse(m) | ||
| GFM = GF(2**m) | ||
| assert_consistent_classical_action(bloq, x=GFM.elements[1:]) | ||
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can you add a test for symbolic cost?
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The test for symbolic cost exists above in test_gf2_inverse_symbolic_toffoli_complexity
mpharrigan
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mpharrigan
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lgtm modulo nits and nour's nits
| $$ | ||
| Thus, the inverse can be obtained via $m - 1$ squaring and multiplication operations. | ||
| The exponential $a^{2^m - 2}$ using $\mathcal{O}(m)$ squaring and $\mathcal{O}(\log_2(m))$ |
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this is no longer a sentence. I think you're missing a verb of some sort
| results from intermediate multiplications. | ||
| References: | ||
| [Efficient quantum circuits for binary elliptic curve arithmetic: |
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Can you keep these links on one line? https://qualtran.readthedocs.io/en/latest/Autodoc.html#references
| result = new_result | ||
| x = bb.add(GF2Square(self.bitsize), x=x) | ||
| return {'x': x, 'result': result} | ({'junk': np.array(junk)} if junk else {}) | ||
| beta = bb.allocate(dtype=self.qgf) |
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cool, yeah. I'd see if this could make its way to the class docstring so it shows up in the docs
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Addressed all nits. Merging now |
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This PR improves the T complexity of
GF2Inversefrom O(m^3) to O(m^2log(m)) following construction from https://arxiv.org/pdf/1209.6348Updates the tests and adds references.