There have been various philosophical conjectures along these lines since antiquity but there was at least 1 serious theory in the modern sense that predates the books listed here....(but this book is pretty interesting too)
"In 1967 Zuse also suggested that the universe itself is running on a grid of computers (digital physics); in 1969 he published the book Rechnender Raum (translated into English as Calculating Space). This idea has attracted a lot of attention, since there is no physical evidence against Zuse's thesis. Edward Fredkin (1980s), Juergen Schmidhuber (1990s), Stephen Wolfram (A New Kind of Science) and others have expanded on it."
There's also work by Burkhard Heim about possible implementation.
In my view, this makes a lot of sense. Reality is a system of percentages of probabilities, and so is science, because that is what nature is. A quantum computer universe basically allows for various percentages of probabilities.
Or you can see it as potentialities.