Not since 1881, and anyhow secret doesn’t mean secret:

Secretum, the Vatican says, translates more accurately to “personal” than to “secret” and refers to the private letters and historical records of past popes. In fact, the archives haven’t been secret since 1881, when Pope Leo XIII opened them up to scholars.

There’s more more more about them in this intriguing* piece in the new all-Catholic news source Crux.

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* That is, quite interesting, not wrapped in or full of intrigue, of course.