Discovering dark matter is one of the great challenges in contemporary physics. Successive generations of experiments -- each more impressive and sophisticated than the last -- have all failed to uncover dark matter's most basic properties. We have abundant evidence suggesting that dark matter exists, but we do not know the identity of the particle(s) that make up dark matter (let alone their mass, lifetime, spin, or coupling to other particles). In spite of decades of fruitless searching, the experimental physics community has not given up on identifying dark matter, since the payoff of a successful detection would be enormous. Characterizing dark matter would provide the first-ever opportunity to study a particle outside the Standard Model, and probing the structure of the Milky Way's dark matter halo would open up an entirely new avenue to study astrophysics and cosmology. These exciting prospects have motivated ever larger and more costly detectors, which acquire years' worth of data in order to accumulate sufficient statistics. Because of the intensive effort that has already been dedicated to finding dark matter, it is challenging to make progress without an expensive and large-scale experiment. This thesis describes a small part of the ongoing effort to make dark matter searches more tractable by adopting the techniques of quantum information science. Quantum information science has developed by leaps and bounds over the past decade, driven largely by the desire to build a quantum computer that exceeds the performance of any realistic classical computer. Although an unequivocal demonstration of such a "quantum speedup" remains elusive, the quantum information community has made impressive progress in preparing, manipulating, and detecting quantum states of light and matter. Leveraging such non-classical states in a dark matter detector allows it to greatly exceed the sensitivity of an equivalent, purely classical detector. A quantum speedup (in sensing, rather than computing) would dramatically reduce the size and cost of a useful dark matter detector. However, quantum states are fragile and difficult to manipulate, so substantial effort is needed to fully realize any non-classical advantage. This thesis is divided into two parts. In the first part, I design, build, and characterize the DM Radio Pathfinder, a modestly-scaled dark matter detector. I use the Pathfinder to set the best laboratory limits on a particular dark matter candidate particle, the hidden photon. Although the detector uses many techniques relevant to quantum information science, including cryogenics and sensitive superconducting circuits, it is a classical experiment which does not achieve any quantum speedup. In the second part of the thesis, I propose the RQU, a superconducting circuit that could plausibly achieve a quantum speedup in a dark matter experiment similar to the Pathfinder. I design and fabricate prototype RQUs and characterize their properties in several experiments. Finally, I propose a realistic path towards using RQUs to achieve a quantum speedup in a real dark matter detector.