At a secret location in the New Mexico desert, Dr. Sam Beckett is realizing his life's work: Project Quantum Leap. Based on his own String Theory, in which a lifetime, if visualized as a piece of string balled in your fist, can be traversed by leaping from one point to another that touches it, the project is the closest anyone has ever come to achieving time travel. Unfortunately it's very expensive, and with no measurable results, it's under threat of losing its funding. Desperate to prove its worth, Sam steps into the Accelerator Chamber prematurely and is swept into the past. Attempts are made to bring him back, but the Retrieval Program fails and Sam is stuck in 1956, where he has landed for the moment. While the rest of the team scrambles to figure out what went wrong and how to get Dr. Beckett back home, Al enters the Imaging Chamber where, locked onto Sam's neurons, he can appear in Sam's time and place as a hologram.
For his part, the leap has left Sam extremely discombobulated; he can't remember who he is, but he knows the reflection in the mirror is wrong. When he does regain his memory, it's in bits and pieces — a phenomenon Al compares to Swiss cheese because it's full of holes. Luckily Sam seems to remember crucial information when he needs it, such as his medical knowledge, which lends credence to the theory that he has more control over these leaps than he thinks. Nevertheless, no one can seem to figure out how to get Sam back to his present time, and it's only when he corrects some prior wrong that he leaps at all, so Al, artificial intelligence Ziggy, and the team scramble to figure out what Sam's mission is each time, hoping that one of these successful leaps will be enough to bring him home.