Emulation of spin dynamics using a superconducting phase qudit

In superconducting quantum circuits, the nonlinearity of the Josephson junction allows energy-level transitions to be addressed individually by their unique frequencies. Typically this is used to operate the system as an effective two-level system, a qubit. In a recent experiment, we extended our coherent control of a phase qubit to the first five energy levels, allowing us to operate the device as a qu{\it d}it with $d = 3$, $4$, or $5$. We use this system to emulate the dynamics of single spins with spin quantum number $s = 1/2$, $1$ and $3/2$. We show that the phase acquired by a spin under rotation around a closed path follows the theoretical prediction. In particular, we confirm the even (odd) parity of integer (half-integer) spins under $2\pi$ rotation.