Cp/qda vqe cpg

learning/courses/quantum-diagonalization-algorithms/vqe.ipynb

@@ -345,7 +345,7 @@
     "$$\n",
     "where $h_\\alpha$ is a Pauli string acting on all the qubits describing your system like `IZZX…XIYX`, or several such strings that commute with each other. Recall that Qiskit uses *little endian* notation, in which the $n^\\text{th}$ Pauli operator from the right acts on the $n^\\text{th}$ qubit. So we can measure our operator by measuring a series of Pauli operators.\n",
     "\n",
-    "But we cannot measure all those Pauli operators simultaneously. Pauli operators (excluding I) do not commute with each other if they are associated with the same qubit. For example, we can measure `IZIZ` and `ZZXZ` simultaneously, because we can measure I and Z simultaneously for the 3rd qubit, and we can know I and X simultaneously for the 1st qubit. But we cannot measure ZZZZ and ZZZX simultaneously, because Z and X do not commute, and both act on the 0th qubit.\n",
+    "But we cannot measure all those Pauli operators simultaneously. Pauli operators (excluding I) do not commute with each other if they are associated with the same qubit. For example, we can measure `IZIZ` and `ZZXZ` simultaneously, because we can measure I and Z simultaneously for the third qubit, and we can know I and X simultaneously for the first qubit. But we cannot measure `ZZZZ` and `ZZZX` simultaneously, because Z and X do not commute, and both act on the 0th qubit. Experienced readers might recall that two groups of Pauli operators might commute as a set even though each individual qubit's measurements do not commute. Estimator assumes tensor-product Pauli measurements (via basis rotations), corresponding to grouping operators that are qubit-wise commuting. So to simultaneously estimate two strings (A and B) of Pauli operators using Estimator, the Pauli operators of each qubit in A and B must commute. This means we also cannot measure `ZZZZ` and `ZZXX` simultaneously.\n",
     "\n",
     "![A table of different Pauli strings, some of which commute and others which do not.](/learning/images/courses/quantum-diagonalization-algorithms/vqe/vqe-fig4.svg)\n",
     "\n",