As our microprocessors make their steady march towards ever shrinking sizes, we move ever closer to the day when we can no longer live under the illusion that ours is a world ruled by the laws of classical mechanics. As this fateful day draws near, the techniques that have served us so well for decades will finally start to fall as phenomena arising from quantum mechanics such as "quantum tunneling" tear them to shreds. Our best hope to overcome this challenge is to stop running from the laws of quantum mechanics and instead to embrace them and the potential they offer for even greater power than classical computing. Unfortunately, to tap into this source of power by building a quantum computer is to launch an endless war against the armies of noise that nature unleashes against any who dare. The only hope that one has to get useful computation done in this maelstrom is to embed one's precious quantum information inside an error correcting code so that any damage can be identified and repaired; it is thus important that quality codes be available, and a great deal of research has devoted to this subject. Traditionally codes have been found through guesswork and theoretical analysis, but in this talk I shall present an alternative approach that instead uses systematic computational analysis; specifically I shall introduce CodeQuest, an algorithm that takes an input set of quantum (Pauli) measurements and produces as output the optimal quantum (subsystem) error correcting code that can be implemented using these measurements. I shall then demonstrate the utility of this algorithm by presenting the results of a systematic investigation of the quantum subsystem codes that can be implemented on lattices derived from the convex uniform tilings of the plane.
