The word Persian reminded me of history, while the present day countries in the area are called Iran, Afganistan, etc. I did not know about any modern Persian calendar.

Persian calendar
The modern Persian calendar uses quite complicated leap year rules, defining a 2820-year cycle with 683 leap years, which results a in mean length of a year of 365 683/2820 = 365,2422 days. Considering the length of the tropical year as being constant, the remaining error would amount to a day in more than 2 million years.

The 2820-year cycle is divided into 21 subcycles of 128 years each, and a 132-year subcycle at the end of each 2820-year cycle. A 128-year subcycle consists of a 29-year sub-subcycle, followed by 3 sub-subcycles of 33 years each. Finally, the 132-year subcycle consists of one sub-subcycle of 29 years, followed by two 33-year sub-subcycles and a final sub-subcycle of 37 years.
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The 1st paragraph stands, is relevant to any calendar, including Persian, and I repeat it:

We know the solar year more accurately than anybody else in history. The calendar year in a particular time zone must start and end at midnight, i.e., the calendar year must have an integer number of days. We can always skip a (century) leap year if the calendar falls out of the step with the solar year by more than, say, 0.5 of a day. This flexibility allows the calendar to be in step with the Sun ± 0.5 day and you cannot do better than that.

Compare this to the complicated and rigid pattern of leap years in the Persian calendar. Moreover, making calendar for more than a few millenia is quite unjustified, certainly with the present experimental data (which is better than any other experimental data in history). We even know how the Earth rotation is slowing down - about 5.33 sec/millenium at present:

Scientific article:
One of the latest (1990) experimetal formula for the length of tropical year is

t = 365.242189669781 - 6.161870·10-6·T - 6.44·10-10·T2.

where T is the time reckoned from the year 2000 and measured in Julian centuries of 365.25 ephemeris days. The formula valid over about 8000 years centered at the present. A comparison of the Gregorian calendar with a perfect solar calendar suggests that the former will be adequate at least during the nearest one to two thousand years. Due to high uncertainty in the Earth rotation it is premature at present to suggest any reform that would reach further than a few thousand years into the future.