Quantum computers are fundamentally different from classical computers because the physics of quantum information is also the physics of possibility. Classical computer memories are constrained to exist at any given time as a simple list of zeros and ones. In contrast, in a single quantum memory many such combinations—even all possible lists of zeros and ones—can all exist simultaneously. During a quantum algorithm, this symphony of possibilities split and merge, eventually coalescing around a single solution. The complexity of these large quantum states made of multiple possibilities make a complete description of quantum search or factoring a daunting task.