diff --git a/qualtran/bloqs/gf_arithmetic/gf2_inverse.ipynb b/qualtran/bloqs/gf_arithmetic/gf2_inverse.ipynb index 789ba01cd..dec031115 100644 --- a/qualtran/bloqs/gf_arithmetic/gf2_inverse.ipynb +++ b/qualtran/bloqs/gf_arithmetic/gf2_inverse.ipynb @@ -58,8 +58,10 @@ " a^{-1} = a^{2^m - 2}\n", "$$\n", "\n", - "The exponential $a^{2^m - 2}$ using $\\mathcal{O}(m)$ squaring and $\\mathcal{O}(\\log_2(m))$\n", - "multiplications via Itoh-Tsujii inversion. See Ref[1, 2] for more details.\n", + "The exponential $a^{2^m - 2}$ is computed using $\\mathcal{O}(m)$ squaring and\n", + "$\\mathcal{O}(\\log_2(m))$ multiplications via Itoh-Tsujii inversion. The algorithm is described on\n", + "page 4 and 5 of Ref[1] and resembles binary exponentiation. The inverse is computed as $B_{n-1}^2$,\n", + "where $B_1 = x$ and $B_{i+j} = B_i B_j^{2^i}$.\n", "\n", "#### Parameters\n", " - `bitsize`: The degree $m$ of the galois field $GF(2^m)$. Also corresponds to the number of qubits in the input register whose inverse should be calculated. \n", @@ -70,8 +72,8 @@ " - `junk`: Output RIGHT register of size $m$ and shape ($m - 2$) that stores results from intermediate multiplications. \n", "\n", "#### References\n", - " - [Efficient quantum circuits for binary elliptic curve arithmetic: reducing T -gate complexity](https://arxiv.org/abs/1209.6348). \n", - " - [Structure of parallel multipliers for a class of fields GF(2^m)](https://doi.org/10.1016/0890-5401(89)90045-X)\n" + " - [Efficient quantum circuits for binary elliptic curve arithmetic: reducing T -gate complexity](https://arxiv.org/abs/1209.6348). Section 2.3\n", + " - [Structure of parallel multipliers for a class of fields GF(2^m)](https://doi.org/10.1016/0890-5401(89)90045-X)\n" ] }, {