This is a shameful act carried out by Taliban shattering our already bleak image in the world. First of all it is the duty of the Government to implement Sharia. They have no right to sentence a person to death (in this case the punishment of lashes) they are not the government.
Now if they carried out this act in the name of sharia then they should have fulfilled the requirements. As they say that the accused two (the girl and his father-in-law) accepted they committed zina or adultery then where were the 4 witnesses as required per Islamic laws and where was the Qazi? You, me or anyone cannot give a judgement on any case, there is a proper systematic channel in Sharia Qanoon.
But many people here and on many TV stations are calling this a barbaric act. This is denying the teachings of Allah and Prophet Muhammad (P.B.U.H). I will quote some verses from the Quran.
1. (This is) a Surah (chapter of the Qur'an) which We have sent down and which We have enjoined, (ordained its legal laws) and in it We have revealed manifest Ayat (proofs, evidences, verses, lessons, signs, revelations lawful and unlawful things, and set boundries of Islamic Religion), that you may remember.
2. The woman and the man guilty of illegal sexual intercourse, flog each of them with a hundred stripes. Let not pity withhold you in their case, in a punishment prescribed by Allah, if you believe in Allah and the Last Day. And let a party of the believers witness their punishment. (This punishment is for unmarried persons guilty of the above crime but if married persons commit it, the punishment is to stone them to death, according to Allah's Law).
3. The adulterer marries not but an adulteress or a Mushrikah and the adulteress none marries her except an adulterer or a Muskrik [and that means that the man who agrees to marry (have a sexual relation with) a Mushrikah (female polytheist, pagan or idolatress) or a prostitute, then surely he is either an adulterer, or a Mushrik (polytheist, pagan or idolater, etc.) And the woman who agrees to marry (have a sexual relation with) a Mushrik (polytheist, pagan or idolater) or an adulterer, then she is either a prostitute or a Mushrikah (female polytheist, pagan, or idolatress, etc.)]. Such a thing is forbidden to the believers (of Islamic Monotheism).
4. And those who accuse chaste women, and produce not four witnesses, flog them with eighty stripes, and reject their testimony forever, they indeed are the Fasiqun (liars, rebellious, disobedient to Allah).
5. Except those who repent thereafter and do righteous deeds, (for such) verily, Allah is Oft-Forgiving, Most Merciful.