diff --git a/cirq-core/cirq/study/result.py b/cirq-core/cirq/study/result.py
index 646202e2f65..3eacc6c07be 100644
--- a/cirq-core/cirq/study/result.py
+++ b/cirq-core/cirq/study/result.py
@@ -97,7 +97,8 @@ def __init__(
         self,
         *,  # Forces keyword args.
         params: resolver.ParamResolver,
-        measurements: Dict[str, np.ndarray],
+        measurements: Optional[Dict[str, np.ndarray]] = None,
+        measurements2: Optional[Dict[str, np.ndarray]] = None,
     ) -> None:
         """Inits Result.
 
@@ -108,10 +109,53 @@ def __init__(
                 with the first index running over the repetitions, and the
                 second index running over the qubits for the corresponding
                 measurements.
+            measurements2: A dictionary from measurement gate key to measurement
+                results. The value for each key is a 3D array of booleans,
+                with the first index running over the repetitions, the second
+                index running over "instances" of that key in the circuit, and
+                the last index running over the qubits for the corresponding
+                measurements.
         """
+        if measurements is None and measurements2 is None:
+            measurements2 = {}  # for backwards compatibility, allow constructing with None.
         self.params = params
-        self._data: Optional[pd.DataFrame] = None
         self._measurements = measurements
+        self._measurements2 = measurements2
+        self._data: Optional[pd.DataFrame] = None
+
+    @property
+    def measurements(self) -> Dict[str, np.ndarray]:
+        if self._measurements is None:
+            self._measurements = {}
+            for key, data in self._measurements2.items():
+                reps, instances, qubits = data.shape
+                if instances != 1:
+                    raise ValueError('Cannot extract 2D measurements for repeated keys')
+                self._measurements[key] = data.reshape((reps, qubits))
+        return self._measurements
+
+    @property
+    def measurements2(self) -> Dict[str, np.ndarray]:
+        """Returns mapping from measurement key to 3D data array."""
+        if self._measurements2 is None:
+            self._measurements2 = {
+                key: data[:, np.newaxis, :] for key, data in self._measurements.items()
+            }
+        return self._measurements2
+
+    @property
+    def repetitions(self) -> int:
+        if self._measurements2 is not None:
+            if not self._measurements2:
+                return 0
+            # Get the length quickly from one of the keyed results.
+            return len(next(iter(self._measurements2.values())))
+        else:
+            if not self._measurements:
+                return 0
+            # Get the length quickly from one of the keyed results.
+            return len(next(iter(self._measurements.values())))
+
 
     @property
     def data(self) -> pd.DataFrame:
@@ -119,7 +163,7 @@ def data(self) -> pd.DataFrame:
             # Convert to a DataFrame with columns as measurement keys, rows as
             # repetitions and a big endian integer for individual measurements.
             converted_dict = {}
-            for key, val in self._measurements.items():
+            for key, val in self.measurements.items():
                 converted_dict[key] = [value.big_endian_bits_to_int(m_vals) for m_vals in val]
             # Note that when a numpy array is produced from this data frame,
             # Pandas will try to use np.int64 as dtype, but will upgrade to
@@ -145,17 +189,6 @@ def from_single_parameter_set(
         """
         return Result(params=params, measurements=measurements)
 
-    @property
-    def measurements(self) -> Dict[str, np.ndarray]:
-        return self._measurements
-
-    @property
-    def repetitions(self) -> int:
-        if not self.measurements:
-            return 0
-        # Get the length quickly from one of the keyed results.
-        return len(next(iter(self.measurements.values())))
-
     # Reason for 'type: ignore': https://github.com/python/mypy/issues/5273
     def multi_measurement_histogram(  # type: ignore
         self,
@@ -208,12 +241,12 @@ def multi_measurement_histogram(  # type: ignore
             results.
         """
         fixed_keys = tuple(_key_to_str(key) for key in keys)
-        samples = zip(
+        samples: Iterable[Any] = zip(
             *(self.measurements[sub_key] for sub_key in fixed_keys)
-        )  # type: Iterable[Any]
+        )
         if len(fixed_keys) == 0:
             samples = [()] * self.repetitions
-        c = collections.Counter()  # type: collections.Counter
+        c = collections.Counter()
         for sample in samples:
             c[fold_func(sample)] += 1
         return c
@@ -350,7 +383,7 @@ def _pack_digits(digits: np.ndarray, pack_bits: str = 'auto') -> Tuple[str, bool
     if pack_bits == 'force':
         return _pack_bits(digits), True
     if pack_bits not in ['auto', 'never']:
-        raise ValueError("Please set `pack_bits` to 'auto', " "'force', or 'never'.")
+        raise ValueError("Please set `pack_bits` to 'auto', 'force', or 'never'.")
         # Do error checking here, otherwise the following logic will work
         # for both "auto" and "never".