Stanford
“Dictionary between quantum codes and phases”
For many interesting problems, from quantum simulations to prime factoring, quantum computation promises powerful computational speedups relative to conventional classical computation. However, quantum information is fragile, requiring extensive error correction to remedy corruption of the quantum bits involved in computations. Error correction involves encoding information in a nonlocal manner into “quantum codes” that should be resilient to any unwanted local noise.
Intuition for these codes can come from the study of phases of matter. These phases go beyond the usual “liquid, solid, gas;” we sometimes have in mind magnetic phases involving the macroscopic cooperation of many miniscule magnets, or more usually topological phases distinguished by sensitivity to global properties of the space they inhabit.
We flesh out connections between codes and phases to use intuition in one to generate breakthroughs in the other, with the particular aim of solving a long-standing open problem in topological phases.