  The quantum computer offers significant advantages in simulating physical
systems, particularly those with exponentially large state spaces, such as
quantum systems. Stochastic reaction-diffusion systems, characterized by their
stochastic nature, also exhibit exponential growth in the dimension of the
state space, posing challenges for simulation at a probability distribution
level. We explore the quantum simulation of stochastic reaction-diffusion
systems on a digital quantum computer, directly simulating the system at the
master equation level. Leveraging a spin representation of the system, we
employ Trotterization and probabilistic imaginary time evolution (PITE) to
simulate the probability distribution directly. We illustrate this approach
through four diverse examples, ranging from simple single-lattice site
generation-annihilation processes to a system featuring active-absorbing phase
transition.
