  Quantum computers promise significant speedups in solving problems
intractable for conventional computers but, despite recent progress, remain
limited in scaling and availability. Therefore, quantum software and hardware
development heavily rely on simulation that runs on conventional computers.
Most such approaches perform strong simulation in that they explicitly compute
amplitudes of quantum states. However, such information is not directly
observable from a physical quantum computer because quantum measurements
produce random samples from probability distributions defined by those
amplitudes. In this work, we focus on weak simulation that aims to produce
outputs which are statistically indistinguishable from those of error-free
quantum computers. We develop algorithms for weak simulation based on quantum
state representation in terms of decision diagrams. We compare them to using
state-vector arrays and binary search on prefix sums to perform sampling.
Empirical validation shows, for the first time, that this enables mimicking of
physical quantum computers of significant scale.
