KeyError(f"None of [{key}] are in the [{axis_name}]")
### System information
- **OS Platform and Distribution (e.g., Linux Ubuntu 16.04)**:
- **Modin version** (`modin.__version__`): 0.7.2
- **Python version**: 3.7
- **Code we can use to reproduce**:
```
import pandas as pd
import modin.pandas as mpd

df = pd.DataFrame({'idx': [1,4,5], 'A': [4,5,6], 'B':['a','b','c']})
df = df.set_index("idx")
# write out parquet with index using pandas
df.to_parquet("./data/tmp.parquet")
# read the same parquet using modin.pandas
mdf = mpd.read_parquet("./data/tmp.parquet")
```
returns 
>"None of [Index(['idx'], dtype='object')] are in the [columns]"
<!--
You can obtain the Modin version with

python -c "import modin; print(modin.__version__)"
-->

### Describe the problem
<!-- Describe the problem clearly here. -->
Parquet files that are written using Pandas, throws this error when read using modin's `read_parquet()`

### Source code / logs
<!-- Include any logs or source code that would be helpful to diagnose the problem. If including tracebacks, please include the full traceback. Large logs and files should be attached. Try to provide a reproducible test case that is the bare minimum necessary to generate the problem. -->

> KeyError: "None of [Index(['idx'], dtype='object')] are in the [columns]"
diff --git a/modin/backends/pandas/parsers.py b/modin/backends/pandas/parsers.py
index caf6ca4b2..d59716ec4 100644
--- a/modin/backends/pandas/parsers.py
+++ b/modin/backends/pandas/parsers.py
@@ -141,18 +141,21 @@ class PandasJSONParser(PandasParser):
 class PandasParquetParser(PandasParser):
     @staticmethod
     def parse(fname, **kwargs):
-        import pyarrow.parquet as pq
-
         num_splits = kwargs.pop("num_splits", None)
         columns = kwargs.get("columns", None)
         if num_splits is None:
             return pandas.read_parquet(fname, **kwargs)
         kwargs["use_pandas_metadata"] = True
-        df = pq.read_table(fname, **kwargs).to_pandas()
+        df = pandas.read_parquet(fname, **kwargs)
+        if isinstance(df.index, pandas.RangeIndex):
+            idx = len(df.index)
+        else:
+            idx = df.index
+        columns = [c for c in columns if c not in df.index.names and c in df.columns]
         if columns is not None:
             df = df[columns]
         # Append the length of the index here to build it externally
-        return _split_result_for_readers(0, num_splits, df) + [len(df.index), df.dtypes]
+        return _split_result_for_readers(0, num_splits, df) + [idx, df.dtypes]
 
 
 class PandasHDFParser(PandasParser):  # pragma: no cover
diff --git a/modin/engines/base/io/column_stores/column_store_reader.py b/modin/engines/base/io/column_stores/column_store_reader.py
index 4cac35243..905dd0f12 100644
--- a/modin/engines/base/io/column_stores/column_store_reader.py
+++ b/modin/engines/base/io/column_stores/column_store_reader.py
@@ -60,7 +60,11 @@ class ColumnStoreReader(FileReader):
         from modin.pandas import DEFAULT_NPARTITIONS
 
         index_len = cls.materialize(partition_ids[-2][0])
-        index = pandas.RangeIndex(index_len)
+        if isinstance(index_len, int):
+            index = pandas.RangeIndex(index_len)
+        else:
+            index = index_len
+            index_len = len(index)
         index_chunksize = compute_chunksize(
             pandas.DataFrame(index=index), DEFAULT_NPARTITIONS, axis=0
         )
diff --git a/modin/engines/base/io/column_stores/parquet_reader.py b/modin/engines/base/io/column_stores/parquet_reader.py
index 8599833fe..f55863273 100644
--- a/modin/engines/base/io/column_stores/parquet_reader.py
+++ b/modin/engines/base/io/column_stores/parquet_reader.py
@@ -66,7 +66,18 @@ class ParquetReader(ColumnStoreReader):
                 pd = ParquetDataset(path)
                 column_names = pd.schema.names
             else:
-                pf = ParquetFile(path)
-                column_names = pf.metadata.schema.names
+                meta = ParquetFile(path).metadata
+                column_names = meta.schema.names
+                # This is how we convert the metadata from pyarrow to a python
+                # dictionary, from which we then get the index columns.
+                # We use these to filter out from the columns in the metadata since
+                # the pyarrow storage has no concept of row labels/index.
+                # This ensures that our metadata lines up with the partitions without
+                # extra communication steps once we `have done all the remote
+                # computation.
+                index_columns = eval(
+                    meta.metadata[b"pandas"].replace(b"null", b"None")
+                ).get("index_columns", [])
+                column_names = [c for c in column_names if c not in index_columns]
             columns = [name for name in column_names if not PQ_INDEX_REGEX.match(name)]
         return cls.build_query_compiler(path, columns, **kwargs)
diff --git a/modin/pandas/test/test_io.py b/modin/pandas/test/test_io.py
index c1c219442..a52daf125 100644
--- a/modin/pandas/test/test_io.py
+++ b/modin/pandas/test/test_io.py
@@ -428,6 +428,24 @@ def test_from_parquet_partitioned_columns_with_columns(make_parquet_file):
     df_equals(modin_df, pandas_df)
 
 
+def test_from_parquet_pandas_index():
+    # Ensure modin can read parquet files written by pandas with a non-RangeIndex object
+    pandas_df = pandas.DataFrame(
+        {
+            "idx": np.random.randint(0, 100_000, size=2000),
+            "A": np.random.randint(0, 100_000, size=2000),
+            "B": ["a", "b"] * 1000,
+            "C": ["c"] * 2000,
+        }
+    )
+    pandas_df.set_index("idx").to_parquet("tmp.parquet")
+    # read the same parquet using modin.pandas
+    df_equals(pd.read_parquet("tmp.parquet"), pandas.read_parquet("tmp.parquet"))
+
+    pandas_df.set_index(["idx", "A"]).to_parquet("tmp.parquet")
+    df_equals(pd.read_parquet("tmp.parquet"), pandas.read_parquet("tmp.parquet"))
+
+
 def test_from_parquet_hdfs():
     path = "modin/pandas/test/data/hdfs.parquet"
     pandas_df = pandas.read_parquet(path)
['modin/engines/base/io/column_stores/column_store_reader.py', 'modin/engines/base/io/column_stores/parquet_reader.py', 'modin/backends/pandas/parsers.py', 'modin/pandas/test/test_io.py']