How small/compact can a pump or other mechanism be, that would allow compressing gas (or liquid) to pressures of excess of 10GPa, continuously?
Throughput may be minuscule, of order of milligrams per hour; even lower is acceptable. Also, for "size of the device" let us count all the necessary infrastructure: if it requires energy of a nuclear power plant to operate, it's not compact. Let's say we have some 30 watt of energy "for free"; anything above that goes out of our "compactness budget".
Input gas is pressurized to "reasonable" levels - order of 30KPa; if more pressure is required, the container goes into "compactness budget" with at least 20kg of the gas inside.
There's abundant heat sinking capacity, but any extra heating goes out of our "budget". Operating (ambient) temperature - choose anything between 40K and 400K as you like. It should have operational lifetime of at least a year, preferably ~10 years.
(clarifying: "continuous" - we can assume a small "buffer" container on the output side, emitting the pressurized gas at rate that is the average of the intake speed, so short "discontinuity" like piston motion is fully acceptable - simply keep the "buffer" above 10GPa with losses of order of assumed average input (1mg/hour, or less if required, but fairly constant).)