From 7772ec6cd64355379a678c618afa554b06943477 Mon Sep 17 00:00:00 2001
From: Jim Garrison <garrison@ibm.com>
Date: Wed, 4 Oct 2023 16:53:38 -0400
Subject: [PATCH 1/2] Swap register order, removing need to pass `num_qpd_bits`

---
 .../cutting/cutting_evaluation.py             | 10 +--
 .../cutting/cutting_experiments.py            | 69 +++++++++++++++----
 .../cutting/cutting_reconstruction.py         | 36 ++--------
 circuit_knitting/cutting/qpd/qpd.py           | 12 ++--
 .../how-tos/how_to_specify_cut_wires.ipynb    |  3 -
 ...gate_cutting_to_reduce_circuit_width.ipynb |  8 +--
 ...gate_cutting_to_reduce_circuit_depth.ipynb |  7 +-
 ...03_wire_cutting_via_move_instruction.ipynb |  8 +--
 ...gister_order_swapped-5b07fb661c6250f9.yaml |  9 +++
 test/cutting/test_cutting_evaluation.py       | 10 +--
 test/cutting/test_cutting_experiments.py      | 46 +++++++++++--
 test/cutting/test_cutting_reconstruction.py   | 60 +++-------------
 test/cutting/test_cutting_roundtrip.py        |  3 -
 test/cutting/test_cutting_workflows.py        |  4 --
 14 files changed, 139 insertions(+), 146 deletions(-)
 create mode 100644 releasenotes/notes/register_order_swapped-5b07fb661c6250f9.yaml

diff --git a/circuit_knitting/cutting/cutting_evaluation.py b/circuit_knitting/cutting/cutting_evaluation.py
index 225cd716b..9993d17f0 100644
--- a/circuit_knitting/cutting/cutting_evaluation.py
+++ b/circuit_knitting/cutting/cutting_evaluation.py
@@ -132,15 +132,15 @@ def execute_experiments(
         assert isinstance(samplers, dict)
         samplers_dict = samplers
 
-    # Make sure the first two cregs in each circuit are for QPD and observable measurements
+    # Make sure the first two cregs in each circuit are for observable and QPD measurements, respectively.
     # Run a job for each partition and collect results
     results = {}
     for label in subexperiments_dict.keys():
         for circ in subexperiments_dict[label]:
             if (
                 len(circ.cregs) != 2
-                or circ.cregs[1].name != "observable_measurements"
-                or circ.cregs[0].name != "qpd_measurements"
+                or circ.cregs[0].name != "observable_measurements"
+                or circ.cregs[1].name != "qpd_measurements"
                 or sum([reg.size for reg in circ.cregs]) != circ.num_clbits
             ):
                 # If the classical bits/registers are in any other format than expected, the user must have
@@ -150,10 +150,6 @@ def execute_experiments(
                 )
         results[label] = samplers_dict[label].run(subexperiments_dict[label]).result()
 
-    for label, result in results.items():
-        for i, metadata in enumerate(result.metadata):
-            metadata["num_qpd_bits"] = len(subexperiments_dict[label][i].cregs[0])
-
     # If the input was a circuit, the output results should be a single SamplerResult instance
     results_out = results
     if isinstance(circuits, QuantumCircuit):
diff --git a/circuit_knitting/cutting/cutting_experiments.py b/circuit_knitting/cutting/cutting_experiments.py
index e8ebdc41c..2746b6fe8 100644
--- a/circuit_knitting/cutting/cutting_experiments.py
+++ b/circuit_knitting/cutting/cutting_experiments.py
@@ -148,12 +148,13 @@ def generate_cutting_experiments(
             subcircuit = subcircuit_dict[label]
             if is_separated:
                 map_ids_tmp = tuple(map_ids[j] for j in subcirc_map_ids[label])
-            decomp_qc = decompose_qpd_instructions(
-                subcircuit, subcirc_qpd_gate_ids[label], map_ids_tmp
-            )
             for j, cog in enumerate(so.groups):
-                meas_qc = _append_measurement_circuit(decomp_qc, cog)
-                subexperiments_dict[label].append(meas_qc)
+                new_qc = _append_measurement_register(subcircuit, cog)
+                decompose_qpd_instructions(
+                    new_qc, subcirc_qpd_gate_ids[label], map_ids_tmp, inplace=True
+                )
+                _append_measurement_circuit(new_qc, cog, inplace=True)
+                subexperiments_dict[label].append(new_qc)
 
     # If the input was a single quantum circuit, return the subexperiments as a list
     subexperiments_out: list[QuantumCircuit] | dict[
@@ -231,6 +232,35 @@ def _get_bases(circuit: QuantumCircuit) -> tuple[list[QPDBasis], list[list[int]]
     return bases, qpd_gate_ids
 
 
+def _append_measurement_register(
+    qc: QuantumCircuit,
+    cog: CommutingObservableGroup,
+    /,
+    *,
+    inplace: bool = False,
+):
+    """Append a new classical register for the given ``CommutingObservableGroup``.
+
+    The new register will be named ``"observable_measurements"`` and will be
+    the final register in the returned circuit, i.e. ``retval.cregs[-1]``.
+
+    Args:
+        qc: The quantum circuit
+        cog: The commuting observable set for which to construct measurements
+        inplace: Whether to operate on the circuit in place (default: ``False``)
+
+    Returns:
+        The modified circuit
+    """
+    if not inplace:
+        qc = qc.copy()
+
+    obs_creg = ClassicalRegister(len(cog.pauli_indices), name="observable_measurements")
+    qc.add_register(obs_creg)
+
+    return qc
+
+
 def _append_measurement_circuit(
     qc: QuantumCircuit,
     cog: CommutingObservableGroup,
@@ -239,15 +269,15 @@ def _append_measurement_circuit(
     qubit_locations: Sequence[int] | None = None,
     inplace: bool = False,
 ) -> QuantumCircuit:
-    """Append a new classical register and measurement instructions for the given ``CommutingObservableGroup``.
+    """Append measurement instructions for the given ``CommutingObservableGroup``.
 
-    The new register will be named ``"observable_measurements"`` and will be
-    the final register in the returned circuit, i.e. ``retval.cregs[-1]``.
+    The measurement results will be placed in a register with the name
+    ``"observable_measurements"``.  Such a register can be created by calling
+    :func:`_append_measurement_register` before calling the current function.
 
     Args:
         qc: The quantum circuit
-        cog: The commuting observable set for
-            which to construct measurements
+        cog: The commuting observable set for which to construct measurements
         qubit_locations: A ``Sequence`` whose length is the number of qubits
             in the observables, where each element holds that qubit's corresponding
             index in the circuit.  By default, the circuit and observables are assumed
@@ -273,12 +303,27 @@ def _append_measurement_circuit(
                 f"qubit_locations has {len(qubit_locations)} element(s) but the "
                 f"observable(s) have {cog.general_observable.num_qubits} qubit(s)."
             )
+
+    # Find observable_measurements register
+    for reg in qc.cregs:
+        if reg.name == "observable_measurements":
+            obs_creg = reg
+            break
+    else:
+        raise ValueError('Cannot locate "observable_measurements" register')
+
+    if obs_creg.size != len(cog.pauli_indices):
+        raise ValueError(
+            '"observable_measurements" register is the wrong size '
+            "for the given commuting observable group "
+            f"({obs_creg.size} != {len(cog.pauli_indices)})"
+        )
+
     if not inplace:
         qc = qc.copy()
 
     # Append the appropriate measurements to qc
-    obs_creg = ClassicalRegister(len(cog.pauli_indices), name="observable_measurements")
-    qc.add_register(obs_creg)
+    #
     # Implement the necessary basis rotations and measurements, as
     # in BackendEstimator._measurement_circuit().
     genobs_x = cog.general_observable.x
diff --git a/circuit_knitting/cutting/cutting_reconstruction.py b/circuit_knitting/cutting/cutting_reconstruction.py
index 51902e3d7..90c87257f 100644
--- a/circuit_knitting/cutting/cutting_reconstruction.py
+++ b/circuit_knitting/cutting/cutting_reconstruction.py
@@ -66,8 +66,6 @@ def reconstruct_expectation_values(
     Raises:
         ValueError: ``observables`` and ``results`` are of incompatible types.
         ValueError: An input observable has a phase not equal to 1.
-        ValueError: ``num_qpd_bits`` must be set for all result metadata dictionaries.
-        TypeError: ``num_qpd_bits`` must be an integer.
     """
     if isinstance(observables, PauliList) and not isinstance(results, SamplerResult):
         raise ValueError(
@@ -111,21 +109,7 @@ def reconstruct_expectation_values(
             for k, cog in enumerate(so.groups):
                 quasi_probs = results_dict[label].quasi_dists[i * len(so.groups) + k]
                 for outcome, quasi_prob in quasi_probs.items():
-                    try:
-                        num_qpd_bits = results_dict[label].metadata[
-                            i * len(so.groups) + k
-                        ]["num_qpd_bits"]
-                    except KeyError as ex:
-                        raise ValueError(
-                            "The num_qpd_bits field must be set in each subexperiment "
-                            "result metadata dictionary."
-                        ) from ex
-                    else:
-                        subsystem_expvals[k] += quasi_prob * _process_outcome(
-                            num_qpd_bits,
-                            cog,
-                            outcome,
-                        )
+                    subsystem_expvals[k] += quasi_prob * _process_outcome(cog, outcome)
 
             for k, subobservable in enumerate(subobservables_by_subsystem[label]):
                 current_expvals[k] *= np.mean(
@@ -138,16 +122,12 @@ def reconstruct_expectation_values(
 
 
 def _process_outcome(
-    num_qpd_bits: int, cog: CommutingObservableGroup, outcome: int | str, /
+    cog: CommutingObservableGroup, outcome: int | str, /
 ) -> np.typing.NDArray[np.float64]:
     """
     Process a single outcome of a QPD experiment with observables.
 
     Args:
-        num_qpd_bits: The number of QPD measurements in the circuit. It is
-            assumed that the second to last creg in the generating circuit
-            is the creg  containing the QPD measurements, and the last
-            creg is associated with the observable measurements.
         cog: The observable set being measured by the current experiment
         outcome: The outcome of the classical bits
 
@@ -156,15 +136,11 @@ def _process_outcome(
         this vector correspond to the elements of ``cog.commuting_observables``,
         and each result will be either +1 or -1.
     """
+    num_meas_bits = len(cog.pauli_indices)
+
     outcome = _outcome_to_int(outcome)
-    try:
-        qpd_outcomes = outcome & ((1 << num_qpd_bits) - 1)
-    except TypeError as ex:
-        raise TypeError(
-            f"num_qpd_bits must be an integer, but a {type(num_qpd_bits)} was passed."
-        ) from ex
-
-    meas_outcomes = outcome >> num_qpd_bits
+    meas_outcomes = outcome & ((1 << num_meas_bits) - 1)
+    qpd_outcomes = outcome >> num_meas_bits
 
     # qpd_factor will be -1 or +1, depending on the overall parity of qpd
     # measurements.
diff --git a/circuit_knitting/cutting/qpd/qpd.py b/circuit_knitting/cutting/qpd/qpd.py
index fd4068b24..c40084d31 100644
--- a/circuit_knitting/cutting/qpd/qpd.py
+++ b/circuit_knitting/cutting/qpd/qpd.py
@@ -500,6 +500,8 @@ def decompose_qpd_instructions(
     circuit: QuantumCircuit,
     instruction_ids: Sequence[Sequence[int]],
     map_ids: Sequence[int] | None = None,
+    *,
+    inplace: bool = False,
 ) -> QuantumCircuit:
     r"""
     Replace all QPD instructions in the circuit with local Qiskit operations and measurements.
@@ -529,7 +531,9 @@ def decompose_qpd_instructions(
         ValueError: Length of ``map_ids`` does not equal the number of decompositions in the circuit.
     """
     _validate_qpd_instructions(circuit, instruction_ids)
-    new_qc = circuit.copy()
+
+    if not inplace:
+        circuit = circuit.copy()  # pragma: no cover
 
     if map_ids is not None:
         if len(instruction_ids) != len(map_ids):
@@ -540,12 +544,12 @@ def decompose_qpd_instructions(
         # If mapping is specified, set each gate's mapping
         for i, decomp_gate_ids in enumerate(instruction_ids):
             for gate_id in decomp_gate_ids:
-                new_qc.data[gate_id].operation.basis_id = map_ids[i]
+                circuit.data[gate_id].operation.basis_id = map_ids[i]
 
     # Convert all instances of BaseQPDGate in the circuit to Qiskit instructions
-    _decompose_qpd_instructions(new_qc, instruction_ids)
+    _decompose_qpd_instructions(circuit, instruction_ids)
 
-    return new_qc
+    return circuit
 
 
 _qpdbasis_from_instruction_funcs: dict[str, Callable[[Instruction], QPDBasis]] = {}
diff --git a/docs/circuit_cutting/how-tos/how_to_specify_cut_wires.ipynb b/docs/circuit_cutting/how-tos/how_to_specify_cut_wires.ipynb
index 806d2a264..b4ea9eda8 100644
--- a/docs/circuit_cutting/how-tos/how_to_specify_cut_wires.ipynb
+++ b/docs/circuit_cutting/how-tos/how_to_specify_cut_wires.ipynb
@@ -348,9 +348,6 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "for label in results:\n",
-    "    for i, subexperiment in enumerate(subexperiments[label]):\n",
-    "        results[label].metadata[i][\"num_qpd_bits\"] = len(subexperiment.cregs[0])\n",
     "reconstructed_expvals = reconstruct_expectation_values(\n",
     "    results,\n",
     "    coefficients,\n",
diff --git a/docs/circuit_cutting/tutorials/01_gate_cutting_to_reduce_circuit_width.ipynb b/docs/circuit_cutting/tutorials/01_gate_cutting_to_reduce_circuit_width.ipynb
index ff85dd277..778b32a6b 100644
--- a/docs/circuit_cutting/tutorials/01_gate_cutting_to_reduce_circuit_width.ipynb
+++ b/docs/circuit_cutting/tutorials/01_gate_cutting_to_reduce_circuit_width.ipynb
@@ -307,9 +307,7 @@
    "source": [
     "### Reconstruct the expectation values\n",
     "\n",
-    "Use the subexperiment results, subobservables, and sampling coefficients to reconstruct the expectation value of the original circuit.\n",
-    "\n",
-    "Include the number of bits used for cutting measurements in the results metadata. This will be automated in a future release, but users must specify it manually for now."
+    "Use the subexperiment results, subobservables, and sampling coefficients to reconstruct the expectation value of the original circuit."
    ]
   },
   {
@@ -321,10 +319,6 @@
    "source": [
     "from circuit_knitting.cutting import reconstruct_expectation_values\n",
     "\n",
-    "for label, circuits in subexperiments.items():\n",
-    "    for i, circuit in enumerate(circuits):\n",
-    "        results[label].metadata[i][\"num_qpd_bits\"] = len(circuit.cregs[0])\n",
-    "\n",
     "reconstructed_expvals = reconstruct_expectation_values(\n",
     "    results,\n",
     "    coefficients,\n",
diff --git a/docs/circuit_cutting/tutorials/02_gate_cutting_to_reduce_circuit_depth.ipynb b/docs/circuit_cutting/tutorials/02_gate_cutting_to_reduce_circuit_depth.ipynb
index 1b61a456d..7539f4605 100644
--- a/docs/circuit_cutting/tutorials/02_gate_cutting_to_reduce_circuit_depth.ipynb
+++ b/docs/circuit_cutting/tutorials/02_gate_cutting_to_reduce_circuit_depth.ipynb
@@ -346,9 +346,7 @@
    "source": [
     "### Reconstruct the expectation values\n",
     "\n",
-    "Use the subexperiment results, subobservables, and sampling coefficients to reconstruct the expectation value of the original circuit.\n",
-    "\n",
-    "Include the number of bits used for cutting measurements in the results metadata. This will be automated in a future release, but users must specify it manually for now."
+    "Use the subexperiment results, subobservables, and sampling coefficients to reconstruct the expectation value of the original circuit."
    ]
   },
   {
@@ -360,9 +358,6 @@
    "source": [
     "from circuit_knitting.cutting import reconstruct_expectation_values\n",
     "\n",
-    "for i in range(len(subexperiments)):\n",
-    "    results.metadata[i][\"num_qpd_bits\"] = len(subexperiments[i].cregs[0])\n",
-    "\n",
     "reconstructed_expvals = reconstruct_expectation_values(\n",
     "    results,\n",
     "    coefficients,\n",
diff --git a/docs/circuit_cutting/tutorials/03_wire_cutting_via_move_instruction.ipynb b/docs/circuit_cutting/tutorials/03_wire_cutting_via_move_instruction.ipynb
index 85ef550c5..768d0865e 100644
--- a/docs/circuit_cutting/tutorials/03_wire_cutting_via_move_instruction.ipynb
+++ b/docs/circuit_cutting/tutorials/03_wire_cutting_via_move_instruction.ipynb
@@ -403,9 +403,7 @@
    "source": [
     "### Reconstruct the expectation values\n",
     "\n",
-    "Use the subexperiment results, subobservables, and sampling coefficients to reconstruct the expectation value of the original circuit.\n",
-    "\n",
-    "Include the number of bits used for cutting measurements in the results metadata. This will be automated in a future release, but users must specify it manually for now."
+    "Use the subexperiment results, subobservables, and sampling coefficients to reconstruct the expectation value of the original circuit."
    ]
   },
   {
@@ -417,10 +415,6 @@
    "source": [
     "from circuit_knitting.cutting import reconstruct_expectation_values\n",
     "\n",
-    "for label, circuits in subexperiments.items():\n",
-    "    for i, circuit in enumerate(circuits):\n",
-    "        results[label].metadata[i][\"num_qpd_bits\"] = len(circuit.cregs[0])\n",
-    "\n",
     "reconstructed_expvals = reconstruct_expectation_values(\n",
     "    results,\n",
     "    coefficients,\n",
diff --git a/releasenotes/notes/register_order_swapped-5b07fb661c6250f9.yaml b/releasenotes/notes/register_order_swapped-5b07fb661c6250f9.yaml
new file mode 100644
index 000000000..5b902b466
--- /dev/null
+++ b/releasenotes/notes/register_order_swapped-5b07fb661c6250f9.yaml
@@ -0,0 +1,9 @@
+---
+upgrade:
+  - |
+    The order of the classical registers in the generated experiments
+    has been swapped.  The ``"observable_measurements"`` register now
+    comes first, and the ``"qpd_measurements"`` register now comes
+    second.  As a result of this change, it is no longer necessary to
+    manually insert ``num_qpd_bits`` into the ``metadata`` for each
+    experiment's result.
diff --git a/test/cutting/test_cutting_evaluation.py b/test/cutting/test_cutting_evaluation.py
index 80dc1d7fc..312be1f11 100644
--- a/test/cutting/test_cutting_evaluation.py
+++ b/test/cutting/test_cutting_evaluation.py
@@ -66,7 +66,7 @@ def test_execute_experiments(self):
             )
             self.assertEqual(
                 quasi_dists,
-                SamplerResult(quasi_dists=[{3: 1.0}], metadata=[{"num_qpd_bits": 0}]),
+                SamplerResult(quasi_dists=[{3: 1.0}], metadata=[{}]),
             )
             self.assertEqual([(1.0, WeightType.EXACT)], coefficients)
         with self.subTest("Basic test with dicts"):
@@ -101,12 +101,8 @@ def test_execute_experiments(self):
                 samplers={"A": self.sampler, "B": deepcopy(self.sampler)},
             )
             comp_result = {
-                "A": SamplerResult(
-                    quasi_dists=[{1: 1.0}], metadata=[{"num_qpd_bits": 0}]
-                ),
-                "B": SamplerResult(
-                    quasi_dists=[{1: 1.0}], metadata=[{"num_qpd_bits": 0}]
-                ),
+                "A": SamplerResult(quasi_dists=[{1: 1.0}], metadata=[{}]),
+                "B": SamplerResult(quasi_dists=[{1: 1.0}], metadata=[{}]),
             }
             self.assertEqual(quasi_dists, comp_result)
             self.assertEqual([(1.0, WeightType.EXACT)], coefficients)
diff --git a/test/cutting/test_cutting_experiments.py b/test/cutting/test_cutting_experiments.py
index 46efeda66..6d435f34a 100644
--- a/test/cutting/test_cutting_experiments.py
+++ b/test/cutting/test_cutting_experiments.py
@@ -15,7 +15,7 @@
 import pytest
 import numpy as np
 from qiskit.quantum_info import PauliList, Pauli
-from qiskit.circuit import QuantumCircuit, ClassicalRegister
+from qiskit.circuit import QuantumCircuit
 from qiskit.circuit.library.standard_gates import CXGate
 
 from circuit_knitting.cutting.qpd import (
@@ -27,7 +27,10 @@
 from circuit_knitting.cutting import generate_cutting_experiments
 from circuit_knitting.cutting.qpd import WeightType
 from circuit_knitting.cutting import partition_problem
-from circuit_knitting.cutting.cutting_experiments import _append_measurement_circuit
+from circuit_knitting.cutting.cutting_experiments import (
+    _append_measurement_register,
+    _append_measurement_circuit,
+)
 
 
 class TestCuttingExperiments(unittest.TestCase):
@@ -154,23 +157,37 @@ def test_generate_cutting_experiments(self):
                 == "SingleQubitQPDGates are not supported in unseparable circuits."
             )
 
+    def test_append_measurement_register(self):
+        qc = QuantumCircuit(2)
+        qc.h(0)
+        qc.cx(0, 1)
+        cog = CommutingObservableGroup(Pauli("XZ"), list(PauliList(["IZ", "XI", "XZ"])))
+        with self.subTest("In place"):
+            qcx = qc.copy()
+            assert _append_measurement_register(qcx, cog, inplace=True) is qcx
+        with self.subTest("Out of place"):
+            assert _append_measurement_register(qc, cog) is not qc
+        with self.subTest("Correct number of bits"):
+            assert _append_measurement_register(qc, cog).num_clbits == len(
+                cog.pauli_indices
+            )
+
     def test_append_measurement_circuit(self):
         qc = QuantumCircuit(2)
         qc.h(0)
         qc.cx(0, 1)
-        qc.add_register(ClassicalRegister(1, name="qpd_measurements"))
         cog = CommutingObservableGroup(Pauli("XZ"), list(PauliList(["IZ", "XI", "XZ"])))
-        qc2 = qc.copy()
-        qc2.add_register(ClassicalRegister(2, name="observable_measurements"))
+        _append_measurement_register(qc, cog, inplace=True)
         with self.subTest("In place"):
             qcx = qc.copy()
             assert _append_measurement_circuit(qcx, cog, inplace=True) is qcx
         with self.subTest("Out of place"):
             assert _append_measurement_circuit(qc, cog) is not qc
         with self.subTest("Correct measurement circuit"):
-            qc2.measure(0, 1)
+            qc2 = qc.copy()
+            qc2.measure(0, 0)
             qc2.h(1)
-            qc2.measure(1, 2)
+            qc2.measure(1, 1)
             assert _append_measurement_circuit(qc, cog) == qc2
         with self.subTest("Mismatch between qubit_locations and number of qubits"):
             with pytest.raises(ValueError) as e_info:
@@ -179,6 +196,21 @@ def test_append_measurement_circuit(self):
                 e_info.value.args[0]
                 == "qubit_locations has 1 element(s) but the observable(s) have 2 qubit(s)."
             )
+        with self.subTest("No observable_measurements register"):
+            with pytest.raises(ValueError) as e_info:
+                _append_measurement_circuit(QuantumCircuit(2), cog)
+            assert (
+                e_info.value.args[0]
+                == 'Cannot locate "observable_measurements" register'
+            )
+        with self.subTest("observable_measurements register has wrong size"):
+            cog2 = CommutingObservableGroup(Pauli("XI"), list(PauliList(["XI"])))
+            with pytest.raises(ValueError) as e_info:
+                _append_measurement_circuit(qc, cog2)
+            assert (
+                e_info.value.args[0]
+                == '"observable_measurements" register is the wrong size for the given commuting observable group (2 != 1)'
+            )
         with self.subTest("Mismatched qubits, no qubit_locations provided"):
             cog = CommutingObservableGroup(Pauli("X"), [Pauli("X")])
             with pytest.raises(ValueError) as e_info:
diff --git a/test/cutting/test_cutting_reconstruction.py b/test/cutting/test_cutting_reconstruction.py
index 4bb4eab7a..3a3c4ca04 100644
--- a/test/cutting/test_cutting_reconstruction.py
+++ b/test/cutting/test_cutting_reconstruction.py
@@ -30,15 +30,6 @@
 @ddt
 class TestCuttingReconstruction(unittest.TestCase):
     def setUp(self):
-        qc = QuantumCircuit(2)
-        qc.h(0)
-        qc.cx(0, 1)
-        self.qc0 = qc.copy()
-        qc.add_register(ClassicalRegister(1, name="qpd_measurements"))
-        self.qc1 = qc.copy()
-        qc.add_register(ClassicalRegister(2, name="observable_measurements"))
-        self.qc2 = qc
-
         self.cog = CommutingObservableGroup(
             Pauli("XZ"), list(PauliList(["IZ", "XI", "XZ"]))
         )
@@ -48,11 +39,10 @@ def test_cutting_reconstruction(self):
             results = SamplerResult(
                 quasi_dists=[QuasiDistribution({"0": 1.0})], metadata=[{}]
             )
-            results.metadata[0]["num_qpd_bits"] = 1
             weights = [(1.0, WeightType.EXACT)]
             subexperiments = [QuantumCircuit(2)]
-            creg1 = ClassicalRegister(1, name="qpd_measurements")
-            creg2 = ClassicalRegister(2, name="observable_measurements")
+            creg1 = ClassicalRegister(2, name="observable_measurements")
+            creg2 = ClassicalRegister(1, name="qpd_measurements")
             subexperiments[0].add_register(creg1)
             subexperiments[0].add_register(creg2)
             observables = PauliList(["ZZ"])
@@ -62,7 +52,6 @@ def test_cutting_reconstruction(self):
             results = SamplerResult(
                 quasi_dists=[QuasiDistribution({"0": 1.0})], metadata=[{}]
             )
-            results.metadata[0]["num_qpd_bits"] = 1
             weights = [(0.5, WeightType.EXACT), (0.5, WeightType.EXACT)]
             subexperiments = {"A": QuantumCircuit(2)}
             observables = {"A": PauliList(["Z"]), "B": PauliList(["Z"])}
@@ -84,11 +73,10 @@ def test_cutting_reconstruction(self):
             results = SamplerResult(
                 quasi_dists=[QuasiDistribution({"0": 1.0})], metadata=[{}]
             )
-            results.metadata[0]["num_qpd_bits"] = 1
             weights = [(0.5, WeightType.EXACT)]
             subexperiments = [QuantumCircuit(2)]
-            creg1 = ClassicalRegister(1, name="qpd_measurements")
-            creg2 = ClassicalRegister(2, name="observable_measurements")
+            creg1 = ClassicalRegister(2, name="observable_measurements")
+            creg2 = ClassicalRegister(1, name="qpd_measurements")
             subexperiments[0].add_register(creg1)
             subexperiments[0].add_register(creg2)
             observables = PauliList(["iZZ"])
@@ -107,49 +95,23 @@ def test_cutting_reconstruction(self):
                 e_info.value.args[0]
                 == "An input observable has a phase not equal to 1."
             )
-        with self.subTest("Test num_qpd_bits"):
-            results = SamplerResult(
-                quasi_dists=[QuasiDistribution({"0": 1.0})], metadata=[{}]
-            )
-            results.metadata[0]["num_qpd_bits"] = 1.0
-            weights = [(0.5, WeightType.EXACT)]
-            subexperiments = [QuantumCircuit(2)]
-            creg1 = ClassicalRegister(1, name="qpd_measurements")
-            creg2 = ClassicalRegister(2, name="observable_measurements")
-            subexperiments[0].add_register(creg1)
-            subexperiments[0].add_register(creg2)
-            observables = PauliList(["ZZ"])
-            with pytest.raises(TypeError) as e_info:
-                reconstruct_expectation_values(results, weights, observables)
-            assert (
-                e_info.value.args[0]
-                == "num_qpd_bits must be an integer, but a <class 'float'> was passed."
-            )
-            results.metadata[0] = {}
-            with pytest.raises(ValueError) as e_info:
-                reconstruct_expectation_values(results, weights, observables)
-            assert (
-                e_info.value.args[0]
-                == "The num_qpd_bits field must be set in each subexperiment result metadata dictionary."
-            )
 
     @data(
         ("000", [1, 1, 1]),
-        ("001", [-1, -1, -1]),
-        ("010", [-1, 1, -1]),
-        ("011", [1, -1, 1]),
-        ("100", [1, -1, -1]),
-        ("101", [-1, 1, 1]),
-        ("110", [-1, -1, 1]),
+        ("001", [-1, 1, -1]),
+        ("010", [1, -1, -1]),
+        ("011", [-1, -1, 1]),
+        ("100", [-1, -1, -1]),
+        ("101", [1, -1, 1]),
+        ("110", [-1, 1, 1]),
         ("111", [1, 1, -1]),
     )
     @unpack
     def test_process_outcome(self, outcome, expected):
-        num_qpd_bits = len(self.qc2.cregs[-2])
         for o in (
             outcome,
             f"0b{outcome}",
             int(f"0b{outcome}", 0),
             hex(int(f"0b{outcome}", 0)),
         ):
-            assert np.all(_process_outcome(num_qpd_bits, self.cog, o) == expected)
+            assert np.all(_process_outcome(self.cog, o) == expected)
diff --git a/test/cutting/test_cutting_roundtrip.py b/test/cutting/test_cutting_roundtrip.py
index 867ff6fdc..59ba44331 100644
--- a/test/cutting/test_cutting_roundtrip.py
+++ b/test/cutting/test_cutting_roundtrip.py
@@ -168,9 +168,6 @@ def test_cutting_exact_reconstruction(example_circuit):
         label: sampler.run(subexperiments[label]).result()
         for label, sampler in samplers.items()
     }
-    for label in results:
-        for i, subexperiment in enumerate(subexperiments[label]):
-            results[label].metadata[i]["num_qpd_bits"] = len(subexperiment.cregs[0])
     simulated_expvals = reconstruct_expectation_values(
         results, coefficients, subobservables
     )
diff --git a/test/cutting/test_cutting_workflows.py b/test/cutting/test_cutting_workflows.py
index e743e8f00..e144b3afc 100644
--- a/test/cutting/test_cutting_workflows.py
+++ b/test/cutting/test_cutting_workflows.py
@@ -90,10 +90,6 @@ def test_exotic_labels(label1, label2):
         for label, sampler in samplers.items()
     }
 
-    for label in results:
-        for i, subexperiment in enumerate(subexperiments[label]):
-            results[label].metadata[i]["num_qpd_bits"] = len(subexperiment.cregs[0])
-
     simulated_expvals = reconstruct_expectation_values(
         results,
         coefficients,

From f4dec604669fbe3d1103256221cb6d10ea1b32c7 Mon Sep 17 00:00:00 2001
From: Jim Garrison <garrison@ibm.com>
Date: Mon, 23 Oct 2023 16:26:28 -0400
Subject: [PATCH 2/2] Fix reconstruction when subsystem contains no observable

---
 .../cutting/cutting_reconstruction.py         |  3 +-
 test/cutting/test_cutting_roundtrip.py        | 46 +++++++++++++++----
 2 files changed, 39 insertions(+), 10 deletions(-)

diff --git a/circuit_knitting/cutting/cutting_reconstruction.py b/circuit_knitting/cutting/cutting_reconstruction.py
index 90c87257f..40094a1aa 100644
--- a/circuit_knitting/cutting/cutting_reconstruction.py
+++ b/circuit_knitting/cutting/cutting_reconstruction.py
@@ -22,6 +22,7 @@
 from ..utils.observable_grouping import CommutingObservableGroup, ObservableCollection
 from ..utils.bitwise import bit_count
 from .cutting_decomposition import decompose_observables
+from .cutting_experiments import _get_pauli_indices
 from .qpd import WeightType
 
 
@@ -136,7 +137,7 @@ def _process_outcome(
         this vector correspond to the elements of ``cog.commuting_observables``,
         and each result will be either +1 or -1.
     """
-    num_meas_bits = len(cog.pauli_indices)
+    num_meas_bits = len(_get_pauli_indices(cog))
 
     outcome = _outcome_to_int(outcome)
     meas_outcomes = outcome & ((1 << num_meas_bits) - 1)
diff --git a/test/cutting/test_cutting_roundtrip.py b/test/cutting/test_cutting_roundtrip.py
index 9faa796be..ea4944054 100644
--- a/test/cutting/test_cutting_roundtrip.py
+++ b/test/cutting/test_cutting_roundtrip.py
@@ -179,28 +179,56 @@ def test_cutting_exact_reconstruction(example_circuit):
     assert np.allclose(exact_expvals, simulated_expvals, atol=1e-8)
 
 
-def test_sampler_with_identity_subobservable(example_circuit):
-    """This test ensures that the sampler does not throw an error if you pass it a subcircuit with no observable measurements.
+@pytest.mark.parametrize(
+    "sampler,is_exact_sampler", [(Sampler(), False), (ExactSampler(), True)]
+)
+def test_sampler_with_identity_subobservable(sampler, is_exact_sampler):
+    """This test ensures that the sampler works for a subcircuit with no observable measurements.
 
-    Tests temporary workaround to Issue #422.
+    Specifically, that
 
-    This test passes if no exceptions are raised.
+    - ``Sampler`` does not blow up (Issue #422); and
+    - ``ExactSampler`` returns correct results
 
+    This is related to https://github.com/Qiskit-Extensions/circuit-knitting-toolbox/issues/422.
     """
+    # Create a circuit to cut
+    qc = QuantumCircuit(3)
+    append_random_unitary(qc, [0, 1])
+    append_random_unitary(qc, [2])
+    qc.rxx(np.pi / 3, 1, 2)
+    append_random_unitary(qc, [0, 1])
+    append_random_unitary(qc, [2])
 
-    qc = example_circuit
-    observable_to_test = PauliList(
+    # Determine expectation value using cutting
+    observables = PauliList(
         ["IIZ"]
     )  # Without the workaround to Issue #422, this observable causes a Sampler error.
     subcircuits, bases, subobservables = partition_problem(
-        qc, "AAB", observables=observable_to_test
+        qc, "AAB", observables=observables
     )
     subexperiments, coefficients = generate_cutting_experiments(
         subcircuits, subobservables, num_samples=np.inf
     )
-    samplers = {label: Sampler() for label in subexperiments.keys()}
+    samplers = {label: sampler for label in subexperiments.keys()}
     results = {
         label: sampler.run(subexperiments[label]).result()
         for label, sampler in samplers.items()
     }
-    _ = results
+    reconstructed_expvals = reconstruct_expectation_values(
+        results, coefficients, subobservables
+    )
+
+    if is_exact_sampler:
+        # Determine exact expectation values
+        estimator = Estimator()
+        exact_expvals = (
+            estimator.run([qc] * len(observables), list(observables)).result().values
+        )
+
+        logger.info(
+            "Max error: %f", np.max(np.abs(exact_expvals - reconstructed_expvals))
+        )
+
+        # Ensure both methods yielded equivalent expectation values
+        assert np.allclose(exact_expvals, reconstructed_expvals, atol=1e-8)