  The historical significance of the Stern-Gerlach experiment lies in its
provision of the initial evidence for space quantization. Over time, its
sequential form has evolved into an elegant paradigm that effectively
illustrates the fundamental principles of quantum theory. To date, the
practical implementation of the sequential Stern-Gerlach experiment has not
been fully achieved. In this study, we demonstrate the capability of
programmable quantum processors to simulate the sequential Stern-Gerlach
experiment. The specific parametric shallow quantum circuits, which are
suitable for the limitations of current noisy quantum hardware, are given to
replicate the functionality of Stern-Gerlach devices with the ability to
perform measurements in different directions. Surprisingly, it has been
demonstrated that Wigner's Stern-Gerlach interferometer can be readily
implemented in our sequential quantum circuit. With the utilization of the
identical circuits, it is also feasible to implement Wheeler's delayed-choice
experiment. We propose the utilization of cross-shaped programmable quantum
processors to showcase sequential experiments, and the simulation results
demonstrate a strong alignment with theoretical predictions. With the rapid
advancement of cloud-based quantum computing, such as BAQIS Quafu, it is our
belief that the proposed solution is well-suited for deployment on the cloud,
allowing for public accessibility. Our findings not only expand the potential
applications of quantum computers, but also contribute to a deeper
comprehension of the fundamental principles underlying quantum theory.
