  Quantum computers promise to solve important problems faster than
conventional computers. However, unleashing this power has been challenging. In
particular, design automation runs into (1) the probabilistic nature of quantum
computation and (2) exponential requirements for computational resources on
non-quantum hardware. In quantum circuit simulation, Decision Diagrams (DDs)
have previously shown to reduce the required memory in many important cases by
exploiting redundancies in the quantum state. In this paper, we show that this
reduction can be amplified by exploiting the probabilistic nature of quantum
computers to achieve even more compact representations. Specifically, we
propose two new DD-based simulation strategies that approximate the quantum
states to attain more compact representations, while, at the same time,
allowing the user to control the resulting degradation in accuracy. We also
analytically prove the effect of multiple approximations on the attained
accuracy and empirically show that the resulting simulation scheme enables
speed-ups up to several orders of magnitudes.
