nit

qualtran/bloqs/comparison_gates.ipynb

@@ -37,7 +37,7 @@
    },
    "source": [
     "## Introduction\n",
-    "The current optimal implementation of a reversible oracle for comparing two quantum numbers of $n$ qubits each is $4n + \\mathcal{O}(1)$ T operations. This is done by reducing the problem to subtraction which takes $4n + \\mathcal{O}(1)$ (see. [Gidney., 2018](https://arxiv.org/abs/1709.06648)). \n",
+    "The current optimal implementation of a reversible oracle for comparing two quantum numbers of $n$ qubits each is $4n + \\mathcal{O}(1)$ T operations. This is done by reducing the problem to subtraction which takes $4n + \\mathcal{O}(1)$ (see. [Gidney, 2018](https://arxiv.org/abs/1709.06648)). \n",
     "\n",
     "This way while optimal in terms of T count has linear depth. The question of whether we can trade some T operations in order to reduce the depth of the circuit is interesting and turns out to have multiple answers.\n",
     "In this notebook, we consider the problem of doing a comparison at a depth logarithmic in the number of qubits $\\mathcal{O}(\\log{n})$. The current best way to do this is given in the supplementary materials of [Berry et al., 2018](https://doi.org/10.1038/s41534-018-0071-5) and leverages the divide and conquer technique. \n",