He earned a certificate of advanced study in mathematics and a master of philosophy degree from Cambridge University in 1983 and 1984, while on a Marshall Scholarship.

[2] Lloyd was awarded a doctorate by Rockefeller University in 1988 (advisor Heinz Pagels) after submitting a thesis on Black Holes, Demons, and the Loss of Coherence: How Complex Systems Get Information, and What They Do With It.

From 1988 to 1991, Lloyd was a postdoctoral fellow in the High Energy Physics Department at the California Institute of Technology, where he worked with Murray Gell-Mann on applications of information to quantum-mechanical systems.

From 1991 to 1994, he was a postdoctoral fellow at Los Alamos National Laboratory, where he worked at the Center for Nonlinear Systems on quantum computation.

[3] However, Lloyd shows that there are limits to rapid exponential growth in a finite universe, and that it is very unlikely that Moore's Law will be maintained indefinitely.

[16] During July 2019, reports surfaced that MIT and other institutions had accepted funding from convicted sex offender Jeffrey Epstein.