The Quran

الزّانِيَةُ وَالزّاني فَاجلِدوا كُلَّ واحِدٍ مِنهُما مِائَةَ جَلدَةٍ ۖ وَلا تَأخُذكُم بِهِما رَأفَةٌ في دينِ اللَّهِ إِن كُنتُم تُؤمِنونَ بِاللَّهِ وَاليَومِ الآخِرِ ۖ وَليَشهَد عَذابَهُما طائِفَةٌ مِنَ المُؤمِنينَ

(Saheeh International)

The [unmarried] woman or [unmarried] man found guilty of sexual intercourse¹ – lash each one of them with a hundred lashes,² and do not be taken by pity for them in the religion [i.e., law] of Allāh,³ if you should believe in Allāh and the Last Day. And let a group of the believers witness their punishment.

Either by voluntary confession of the offender or the testimony of four male witnesses to having actually seen the act take place. Otherwise, there can be no conviction.
The ruling in this verse is applicable to unmarried fornicators. Execution by stoning is confirmed in the sunnah for convicted adulterers.
i.e., Do not let sympathy for a guilty person move you to alter anything ordained by Allāh, for in His law is protection of society as a whole.