Since quantum computers can solve important problems faster than classical computers, many resources have gone into the development of this technology in recent decades. Despite the tremendous progress that has already been made toward the development of quantum computers, they are still an emerging technology, which restricts access and reliability. Thus, research on quantum algorithms still heavily relies on quantum circuit simulators that run on classical hardware. However, simulating the execution of a quantum computer on conventional hardware is exponentially difficult, which is also the reason why quantum computing is an interesting technology in the first place. Particularly complex is noise-aware simulation of quantum computers, i.e., the consideration of noise effects that are common in today’s quantum hardware during quantum circuit simulation. In this work, we investigate the use of decision diagrams for this task. To this end, we present two distinct approaches for noise-aware quantum circuit simulation, investigate how they can be realized using decision diagrams, and implement decision diagram-based solutions for each of the presented noise-aware simulation schemes. In an extensive evaluation, we unveil potential for further improvements and also demonstrate substantial speed-ups compared to the current state of the art.

IEEE Transactions on Computer-Aided Design of Integrated Circuits and SystemsJun 13, 202223 citations

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

Thomas Grurl, Jürgen Fuß, Robert Wille

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.

IEEE International Symposium on Multiple-Valued Logic (ISMVL)May 1, 20231 citation