From 473479bf0d684b940742115feca060d826fa2c10 Mon Sep 17 00:00:00 2001 From: christopherporter1 Date: Thu, 11 Jun 2026 13:22:16 -0400 Subject: [PATCH 1/3] Fixed groups of commuting Paulis --- .../quantum-diagonalization-algorithms/vqe.ipynb | 10 ++++------ 1 file changed, 4 insertions(+), 6 deletions(-) diff --git a/learning/courses/quantum-diagonalization-algorithms/vqe.ipynb b/learning/courses/quantum-diagonalization-algorithms/vqe.ipynb index 4f62d53361b..e9b695d73fa 100644 --- a/learning/courses/quantum-diagonalization-algorithms/vqe.ipynb +++ b/learning/courses/quantum-diagonalization-algorithms/vqe.ipynb @@ -378,15 +378,13 @@ "\n", "\n", "\n", - "It can be done in 5 groups. Note that such solutions are typically not unique.\n", + "It can be done in 4 groups. Note that such solutions are typically not unique.\n", "\n", - "`IIXX`, `XXXX`\n", + "`IIXX`, `XXXX`, `IIZZ`, `ZZZZ`\n", "\n", - "`IIXZ`, `IZXZ`, `ZZXZ`\n", + "`IIXZ`, `IZXZ`, `ZIXZ`, `ZZXZ`\n", "\n", - "`IIZZ`, `ZZZZ`\n", - "\n", - "`IXXZ`, `ZIXZ`\n", + "`IXXZ`\n", "\n", "`XZXZ`\n", "\n", From 04e8ae6e15a7d3940b60ebef885b57021b5bc9da Mon Sep 17 00:00:00 2001 From: christopherporter1 Date: Thu, 11 Jun 2026 15:56:40 -0400 Subject: [PATCH 2/3] corrected wording to clarify commuting vs simultaneous measurement --- .../quantum-diagonalization-algorithms/vqe.ipynb | 12 +++++++----- 1 file changed, 7 insertions(+), 5 deletions(-) diff --git a/learning/courses/quantum-diagonalization-algorithms/vqe.ipynb b/learning/courses/quantum-diagonalization-algorithms/vqe.ipynb index e9b695d73fa..3557c5107b5 100644 --- a/learning/courses/quantum-diagonalization-algorithms/vqe.ipynb +++ b/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 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. Experienced readers may 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), which corresponds to grouping operators that are qubit-wise commuting. So for two strings (A and B) of Pauli operators to be simultaneously estimated using Estimator, the Pauli operators 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", @@ -378,13 +378,15 @@ "\n", "\n", "\n", - "It can be done in 4 groups. Note that such solutions are typically not unique.\n", + "It can be done in 5 groups. Note that such solutions are typically not unique.\n", "\n", - "`IIXX`, `XXXX`, `IIZZ`, `ZZZZ`\n", + "`IIXX`, `XXXX`\n", "\n", - "`IIXZ`, `IZXZ`, `ZIXZ`, `ZZXZ`\n", + "`IIXZ`, `IZXZ`, `ZZXZ`\n", "\n", - "`IXXZ`\n", + "`IIZZ`, `ZZZZ`\n", + "\n", + "`IXXZ`, `ZIXZ`\n", "\n", "`XZXZ`\n", "\n", From 6760cfa3cd305e7f60c57d73111ac06ab45a6282 Mon Sep 17 00:00:00 2001 From: christopherporter1 <125992427+christopherporter1@users.noreply.github.com> Date: Fri, 12 Jun 2026 10:36:41 -0400 Subject: [PATCH 3/3] Update learning/courses/quantum-diagonalization-algorithms/vqe.ipynb Co-authored-by: abbycross --- learning/courses/quantum-diagonalization-algorithms/vqe.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/learning/courses/quantum-diagonalization-algorithms/vqe.ipynb b/learning/courses/quantum-diagonalization-algorithms/vqe.ipynb index 3557c5107b5..d13e44176d8 100644 --- a/learning/courses/quantum-diagonalization-algorithms/vqe.ipynb +++ b/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. Experienced readers may 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), which corresponds to grouping operators that are qubit-wise commuting. So for two strings (A and B) of Pauli operators to be simultaneously estimated using Estimator, the Pauli operators each qubit in A and B must commute. This means we also cannot measure `ZZZZ` and `ZZXX` simultaneously.\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",