A quantum resonator was a device that allowed people to glimpse into what might have been, in other words, hypothetical worlds. It was not common to societies like 1851 England, as the Eleventh Doctor likened finding a quantum resonator in that time period to finding an atomic bomb in the Library of Alexandria. One was created by Charles Fairfax, after an "angel" presented the plans through his wife.
The "angel" was actually the Hypothetical Gentleman, who planned to escape his hypothetical world through the machine to Earth, and make himself a reality. To power such a device required massive amounts of artron energy to power it, or, as the Doctor put it, "a battery the size of the universe." A TARDIS could be used to power one. Amy Pond destroyed such a device. (COMIC: Hypothetical Gentleman)