Mitchell Institute for Fundamental Physics & Astronomy
College Station, Texas 77843
Ideas from quantum information theory have come to occupy increasingly important roles in theories of fundamental physics. Conversely, fundamental physics offers valuable tools for addressing problems in quantum information and computation. To exemplify the latter perspective, I will describe how ideas of geometric quantization and noncommutative geometry can be applied to the design of quantum error-correcting codes for infinite-dimensional (or continuous-variable) quantum systems. The symmetries of phase space suggest a unified set of principles for quantum error correction of both continuous-variable quantum information and discrete-variable quantum information based on finite-dimensional qubits. By understanding the foundations of quantum computation in the physical universe, it may be possible to better understand the universe itself.