  Understanding complex quantum matter presents a central challenge in
condensed matter physics. The difficulty lies in the exponential scaling of the
Hilbert space with the system size, making solutions intractable for both
analytical and conventional numerical methods. As originally envisioned by
Richard Feynman, this class of problems can be tackled using controllable
quantum simulators. Despite many efforts, building an quantum emulator capable
of solving generic quantum problems remains an outstanding challenge, as this
involves controlling a large number of quantum elements. Here, employing a
multi-element superconducting quantum circuit and manipulating a single
microwave photon, we demonstrate that we can simulate the weak localization
phenomenon observed in mesoscopic systems. By engineering the control sequence
in our emulator circuit, we are also able to reproduce the well-known
temperature dependence of weak localization. Furthermore, we can use our
circuit to continuously tune the level of disorder, a parameter that is not
readily accessible in mesoscopic systems. By demonstrating a high level of
control and complexity, our experiment shows the potential for superconducting
quantum circuits to realize scalable quantum simulators.
