  We introduce the task of shadow process simulation, where the goal is to
reproduce the expectation values of arbitrary quantum observables at the output
of a target physical process. When the sender and receiver share classical
random bits, we show that the performance of shadow process simulation exceeds
that of conventional process simulation protocols in a variety of scenarios
including communication, noise simulation, and data compression. Remarkably,
shadow simulation provides increased accuracy without any increase in the
sampling cost. Overall, shadow simulation provides a unified framework for a
variety of quantum protocols, including probabilistic error cancellation and
circuit knitting in quantum computing.
