What is the Qadiani (Ahmadiyyah) sect? Is it permissible for a Muslim to marry one of them?

In the answer to question no. 4060 we have explained that this group, which is known as Ahmadiyyah or Qadianiyyah, the followers of Mirza Ghulam Ahmad, are kaafirs. In that answer you will find a discussion of their kaafir beliefs and what the scholars have said about them.

Based on this, it is not permissible for a Muslim to marry one of them or to give his daughter in marriage to them, because they are kaafirs and apostates, and Allaah says (interpretation of the meaning): 

“And do not marry Al-Mushrikaat (idolatresses) till they believe (worship Allaah Alone). And indeed a slave woman who believes is better than a (free) Mushrikah (idolatress), even though she pleases you. And give not (your daughters) in marriage to Al‑Mushrikoon till they believe (in Allaah Alone) and verily, a believing slave is better than a (free) Mushrik (idolater), even though he pleases you. Those (Al-Mushrikoon) invite you to the Fire, but Allaah invites (you) to Paradise and forgiveness by His Leave, and makes His Ayaat (proofs, evidences, verses, lessons, signs, revelations, etc.) clear to mankind that they may remember”

[al-Baqarah 2:221]

al-Sa’di (may Allaah have mercy on him) said in his Tafseer (p. 99): 

i.e., do not marry mushrik women so long as they still believe in shirk, until they believe, for a believing woman, no matter how ugly she is, is better than a mushrik woman, no matter how beautiful she is. This is general in meaning and includes all mushrik women. The verse in Soorat al-Maa’idah is more specific and permits marriage to women of the people of the Book, as Allaah says: “(Lawful to you in marriage) are chaste women from the believers and chaste women from those who were given the Scripture (Jews and Christians) before your time” [al-Maa’idah 5:5]…  

Then Allaah mentions the wisdom behind the prohibition on the marriage of a Muslim man or woman to one whose beliefs differ from theirs, as He says: “Those (Al-Mushrikoon) invite you to the Fire” i.e., by their words, actions and circumstances, and the one who mixes with them faces danger from them. The danger is not in any worldly sense; rather the danger is eternal doom. End quote. 

If this friend of yours is in a haraam relationship, then you must explain to him that this relationship is haraam and that it is not permissible for a Muslim to be alone with a non-mahram woman, or to shake hands with her or correspond with her, and that he cannot end this relationship by getting married because it is haraam to marry apostate women. He should look for a wife who is religiously committed and can help him to protect his religious commitment and to obey his Lord, and whom he can trust with his children. 

And Allaah knows best.