BUG: ArrowExtensionArray(temporal).quantile raising for non-round results

doc/source/whatsnew/v2.1.0.rst

@@ -384,6 +384,7 @@ Sparse
 
 ExtensionArray
 ^^^^^^^^^^^^^^
+- Bug in :meth:`Series.quantile` for pyarrow temporal types raising ArrowInvalid (:issue:`52678`)
 - Bug in :meth:`Series.rank` returning wrong order for small values with ``Float64`` dtype (:issue:`52471`)
 - Bug where the ``__from_arrow__`` method of masked ExtensionDtypes(e.g. :class:`Float64Dtype`, :class:`BooleanDtype`) would not accept pyarrow arrays of type ``pyarrow.null()`` (:issue:`52223`)
 -

pandas/core/arrays/arrow/array.py

@@ -1495,6 +1495,8 @@ def _quantile(self, qs: npt.NDArray[np.float64], interpolation: str) -> Self:
         result = pc.quantile(data, q=qs, interpolation=interpolation)
 
         if pa.types.is_temporal(pa_dtype):
+            if pa.types.is_floating(result.type):
+                result = pc.floor(result)
             nbits = pa_dtype.bit_width
             if nbits == 32:
                 result = result.cast(pa.int32())

pandas/tests/extension/test_arrow.py

@@ -2488,3 +2488,15 @@ def test_describe_numeric_data(pa_type):
         index=["count", "mean", "std", "min", "25%", "50%", "75%", "max"],
     )
     tm.assert_series_equal(result, expected)
+
+
+@pytest.mark.parametrize(
+    "pa_type", tm.DATETIME_PYARROW_DTYPES + tm.TIMEDELTA_PYARROW_DTYPES
+)
+def test_quantile_temporal(pa_type):
+    # GH52678
+    data = [1, 2, 3]
+    ser = pd.Series(data, dtype=ArrowDtype(pa_type))
+    result = ser.quantile(0.1)
+    expected = ser[0]
+    assert result == expected