Aharonov graduated from Hebrew University of Jerusalem with a BSc in Mathematics and Physics in 1994. She then graduated from Weizmann Institute of Science with an MSc in Physics. She received her doctorate for Computer Science in 1999 from the Hebrew University of Jerusalem, and her thesis was entitled "Noisy Quantum Computation." She also did her post-doctorate in the mathematics department of Princeton University, and in the computer science department of University of California Berkeley. She was a visiting scholar at the Institute for Advanced Study in 1998-99.
In 2005, Aharonov was profiled by the journal Nature as one of four "young theorists... who are making waves in their chosen fields.", and in the following year, she then received the Krill Prize for Excellence in Scientific Research. She was an invited speaker in International Congress of Mathematicians 2010, Hyderabad on the topic of "Mathematical Aspects of Computer Science."