  Magnetic fields break time-reversal symmetry, which is leveraged in many
settings to enable the nonreciprocal behavior of light. This is the core
physics of circulators and other elements used in a variety of microwave and
optical settings. Commercial circulators in the microwave domain typically use
ferromagnetic materials and wave interference, requiring large devices and
large fields. However, quantum information devices for sensing and computation
require small sizes, lower fields, and better on-chip integration. Equivalences
to ferromagnetic order -- such as the XY model -- can be realized at much lower
magnetic fields by using arrays of superconducting islands connected by
Josephson junctions. Here we show that the quantum-coherent motion of a single
vortex in such an array suffices to induce nonreciprocal behavior, enabling a
small-scale, moderate-bandwidth, and low insertion loss circulator at very low
magnetic fields and at microwave frequencies relevant for experiments with
qubits.
