Optimized Density Matrix Representations: Improving the Basis for Noise-Aware Quantum Circuit Design Tools

By exploiting quantum mechanical effects, quantum computers can tackle problems that are infeasible for classical computers. At the same time, these quantum mechanical properties make handling quantum states exponentially hard - imposing major challenges on design tools. In the past, methods such as tensor networks or decision diagrams have shown that they can often keep those resource requirements in check by exploiting redundancies within the description of quantum states. But developments thus far focused on pure quantum states which do not provide a physically complete picture and, e.g., ignore frequently occurring noise effects. Density matrix representations provide such a complete picture, but are substantially larger. At the same time, they come with characteristics that allow for a more compact representation. In this work, we unveil this untapped potential and use it to provide a decision diagram representation that is optimized for density matrix representations. By this, we are providing a basis for more efficient design tools such as quantum circuit simulation which explicitly takes noise/error effects into account.