  Simulating long-range interacting systems is a challenging task due to its
computational complexity that the computational effort for each local update is
of order $\cal{O}$$(N)$, where $N$ is the size of system. Recently, a
technique, called hereby the clock factorized quantum Monte Carlo method, was
developed on the basis of the so-called factorized Metropolis filter [Phys.
Rev. E 99 010105 (2019)]. In this work, we first explain step by step how the
clock factorized quantum Monte Carlo method is implemented to reduce the
computational overhead from $\cal{O}$$(N)$ to $\cal{O}$(1). In particular, the
core ingredients, including the concepts of bound probabilities and bound
rejection events, the tree-like data structure, and the fast algorithms for
sampling an extensive set of discrete and small probabilities, are elaborated.
Next, we show how the clock factorized quantum Monte Carlo method can be
flexibly implemented in various update strategies, like the Metropolis and
worm-type algorithms, and can be generalized to simulate quantum systems.
Finally, we demonstrate the high efficiency of the clock factorized quantum
Monte Carlo algorithms in the examples of the quantum Ising model and the
Bose-Hubbard model with long-range interactions and/or long-range hopping
amplitudes. We expect that the clock factorized quantum Monte Carlo algorithms
would find broad applications in statistical and condensed-matter physics.
