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.

Quantum computers promise to efficiently solve important problems classical computers never will. However, in order to capitalize on these prospects, a fully automated quantum software stack needs to be developed. This involves a multitude of complex tasks from the classical simulation of quantum circuits, over their compilation to specific devices, to the verification of the circuits to be executed as well as the obtained results. All of these tasks are highly non-trivial and necessitate efficient data structures to tackle the inherent complexity. Starting from rather straight-forward arrays over decision diagrams (inspired by the design automation community) to tensor networks and the ZX-calculus, various complementary approaches have been proposed. This work provides a look "under the hood" of today's tools and showcases how these means are utilized in them, e.g., for simulation, compilation, and verification of quantum circuits.

Recent years have seen unprecedented advance in the design and control of quantum computers. Nonetheless, their applicability is still restricted and access remains expensive. Therefore, a substantial amount of quantum algorithms research still relies on simulating quantum circuits on classical hardware. However, due to the sheer complexity of simulating real quantum computers, many simulators unrealistically simplify the problem and instead simulate perfect quantum hardware, i.e., they do not consider errors caused by the fragile nature of quantum systems. Stochastic quantum simulation provides a conceptually suitable solution to this problem: physically motivated errors are applied in a probabilistic fashion throughout the simulation. In this work, we propose to use decision diagrams, as well as concurrent executions, to substantially reduce resource-requirements-which are still daunting—for stochastic quantum circuit simulation. Backed up by rigorous theory, empirical studies show that this approach allows for a substantially faster and much more scalable simulation for certain quantum circuits.

By using quantum mechanical effects, quantum computers promise significant speedups in solving problems intractable for conventional computers. However, despite recent progress they remain limited in scaling and availability---making quantum software and hardware development heavily reliant on quantum simulators running on conventional hardware. However, most of those simulators mimic perfect quantum computers and, hence, ignore the fragile nature of quantum mechanical effects which frequently yield to decoherence errors in real quantum devices. Considering those errors during the simulation is complex, but necessary in order to tailor quantum algorithms for specific devices. Thus far, most state-of-the-art simulators considering decoherence errors rely on (exponentially) large array representations. As an alternative, simulators based on decision diagrams have been shown very promising for simulation of quantum circuits in general, but have not supported decoherence errors yet. In this work, we are closing this gap. We investigate how the consideration of decoherence errors affects the simulation performance of approaches based on decision diagrams and propose advanced solutions to mitigate negative effects. Experiments confirm that this yields improvements of several orders of magnitudes compared to a naive consideration of errors.