Noise-Aware Quantum Circuit Simulation with Decision Diagrams

Richard Feynman was the first to propose the use of a quantum computer to efficiently simulate quantum systems, a task that is exponentially hard on classical computers. Since then, many more applications for quantum computers have been found, and first quantum computers are already commercially available. With the interest in quantum computing, the need for quantum circuit simulators, i.e., tools that simulate the execution of a quantum circuit on classical hardware, has also risen.
However, the task of quantum circuit simulation is exponentially hard on classical machines. Worse still, today’s quantum computers are prone to noise effects (i.e., errors), that obscure their calculations. Considering those noise effects during quantum circuit simulation makes the problem even more complex, but is necessary to understand how algorithms behave when executed on real hardware.
This thesis proposes to tackle the complexity of noise-aware quantum circuit simulation using decision diagrams. While decision diagrams have already been successfully used for other design tasks, their potential for noise-aware quantum circuit simulation has been largely unexplored. This is changed in this thesis.
To this end, the current state-of-the-art of decision diagram-based quantum circuit simulation is reviewed and dedicated extensions for handling errors are proposed. Then, two complementary decision diagram-based noise-aware quantum circuit simulation approaches are presented and implemented in an optimized fashion. Subsequent evaluations against industry-grade simulators demonstrate the viability of the proposed solutions with substantial speed-ups for many applications. Finally, the necessity of noise-aware quantum circuit simulation is demonstrated on one use-case: quantum error correction.