BUG: Load data frame pickled under pandas 1.0.5 using pandas 1.1.0
- [x] I have checked that this issue has not already been reported.

- [x] I have confirmed this bug exists on the latest version of pandas.

- [ ] (optional) I have confirmed this bug exists on the master branch of pandas.

---

**Note**: Please read [this guide](https://matthewrocklin.com/blog/work/2018/02/28/minimal-bug-reports) detailing how to provide the necessary information for us to reproduce your bug.

#### Code Sample, a copy-pastable example

```python
'''
Have pandas 1.0.5 installed.
'''


#%% import libs;
import numpy as np
import pandas as pd
import time
import datetime
import pickle

#%% do;
df0 = pd.DataFrame(
                    {
                        'sdtr3mm':      [datetime.datetime.now()],
                        'count1':       [1]
                    }
                 )
df0['month_year'] = df0['sdtr3mm'].dt.to_period('M')
df0['year'] = df0['sdtr3mm'].dt.to_period('Y')
with open("Z:/test.data", "wb") as filehandle:
    pickle.dump(df0, filehandle)

'''
Update to pandas           : 1.1.0
'''


with open("Z:/test.data", "rb") as filehandle:
    df1 = pickle.load(filehandle)
```
[test.zip](https://github.com/pandas-dev/pandas/files/5067895/test.zip) (zipped data frame, pickled under pandas 1.0.5)



#### Problem description

I pickled a dataframe, containing a datetime variable, an integer, a pandas-month-year, panda-year variable, under pandas 1.0.5 to my disk.
After the update to pandas 1.1.0, I can no longer load it, receiving an "TypeError: Expected tuple, got dict",
with:
```
Traceback (most recent call last):

  File "<ipython-input-5-fa4170ff1942>", line 2, in <module>
    df1 = pickle.load(filehandle)

  File "stringsource", line 17, in pandas._libs.tslibs.period.PeriodMixin.__setstate_cython__
```



Creating a data frame as above under pandas 1.1.0 and trying to load it in under pandas 1.0.5 does not work either.

*** Update:
Also does not work using pd.read_pickle either.

I am sorry if this is the wrong place and/or the wrong way to post my issue.

#### Expected Output

Load in the data frame created as in the code above.


#### Output of ``pd.show_versions()``

<details>

[paste the output of ``pd.show_versions()`` here leaving a blank line after the details tag]

INSTALLED VERSIONS
------------------
commit           : None
python           : 3.7.7.final.0
python-bits      : 64
OS               : Windows
OS-release       : 10
machine          : AMD64
processor        : Intel64 Family 6 Model 94 Stepping 3, GenuineIntel
byteorder        : little
LC_ALL           : None
LANG             : en
LOCALE           : None.None

pandas           : 1.0.5
numpy            : 1.19.1
pytz             : 2020.1
dateutil         : 2.8.1
pip              : 20.2.1
setuptools       : 49.2.1.post20200807
Cython           : None
pytest           : None
hypothesis       : None
sphinx           : 3.2.0
blosc            : None
feather          : None
xlsxwriter       : None
lxml.etree       : None
html5lib         : None
pymysql          : None
psycopg2         : None
jinja2           : 2.11.2
IPython          : 7.17.0
pandas_datareader: None
bs4              : None
bottleneck       : None
fastparquet      : None
gcsfs            : None
lxml.etree       : None
matplotlib       : 3.2.2
numexpr          : None
odfpy            : None
openpyxl         : 3.0.4
pandas_gbq       : None
pyarrow          : None
pytables         : None
pytest           : None
pyxlsb           : None
s3fs             : None
scipy            : 1.5.0
sqlalchemy       : None
tables           : None
tabulate         : None
xarray           : None
xlrd             : 1.2.0
xlwt             : 1.3.0
xlsxwriter       : None
numba            : None


</details>

