Local Dimension Invariant Qudit Stabilizer Codes

Abstract

Protection of quantum information from noise is a massive challenge. One avenue people have begun to explore is reducing the number of particles needing to be protected from noise and instead use systems with more states, so called qudit quantum computers. These systems will require codes which utilize the full computational space. Many prior qudit codes are very restrictive on relations between parameters. In this paper we show that codes for these systems can be derived from already known codes, often relaxing the constraints somewhat, a result which could prove to be very useful for fault-tolerant qudit quantum computers.