  We propose cyclic quantum refrigeration in solid-state, employing a gas of
magnetic field vortices in a type-II superconductor -- also known as fluxons --
as the cooling agent. Refrigeration cycles are realized by envisioning a
racetrack geometry consisting of both adiabatic and isothermal arms, etched
into a type-II superconductor. The guided propagation of fluxons in the
racetrack is achieved by applying an external electrical current, in a Corbino
geometry, through the sample. A gradient of magnetic field is set across the
racetrack allowing one to adiabatically cool down and heat up the fluxons,
which subsequently exchange heat with the cold, and hot reservoirs,
respectively. We characterize the steady state of refrigeration cycles
thermodynamically for both $s-$wave and $d-$wave pairing symmetries, and
present their figures of merit such as the cooling power delivered, and the
coefficient of performance. Our cooling principle can offer significant cooling
for on-chip micro-refrigeration purposes, by locally cooling below the base
temperatures achievable in a conventional dilution refrigerator. We estimate
$10\mathrm{nW}/\mathrm{mm}^2$ of cooling power per unit area under typical
operating conditions. Integrating the fluxon fridge to quantum circuits can
enhance their coherence time by locally suppressing thermal fluctuations, and
improve the efficiency of single photon detectors and charge sensors.
