One of the most profound mysteries in the fundamental physics which has puzzled scientists for almost a century is the nature of dark matter. It is hypothesized to makes up $25\%$ of the universe's energy density, however, a direct detection of the dark matter remains hypothetical so far. Due to the strict constraints placed by experimental null results on heavier particles (GeV) such as WIMPS, axions and hidden photons have emerged as a leading dark matter candidate. Both are sufficiently low-energy to behave as a coherent wave with macroscopic occupation number (unknown frequency or mass), and on rare occasion convert into a single photon via electro-magnetic interactions with normal matter. Current dark matter experiments operate a microwave cavity held at cryogenic temperature and use a linear amplifier operating near the standard quantum limit (SQL) to measure the signal power. While these amplifiers provide a big boost in the signal-to-noise ratio at sub GHz range, the noise power linearly increases and signal power plummets at higher frequency. In order to make the search tenable, quantum enhanced search combined with new cavity techniques are required to bring down the detector noise and improve the dark matter signal. In this thesis, I report the development of multiple complimentary techniques using superconducting qubits to speed up the dark matter search. First, we demonstrated a new quantum measurement technique of counting photons generated by the dark matter in a microwave cavity. By measuring only the field amplitude, the qubit is able to evade the SQL. With repeated quantum non-demolition (QND) measurements of the cavity photons and applying a hidden Markov model, we reduce the noise to $15.7$ dB below the quantum limit. Based on the measured background we set a new exclusion limit on hidden photon dark matter. Second, using a superconducting qubit to prepare the cavity in a Fock state and stimulate the emission of a photon from dark matter wave. By initializing the cavity in $\ket{n}=4$ Fock state, we demonstrate a $2.5\times$ ($4.0$ dB) improvement in the signal rate, taking into account the detection efficiency. Combining these two results in a $19.7$ dB improvement in signal-to-noise ratio over the conventional detection methods, speeding up the dark matter search by a factor of $10, 000$. The measured background sets a new exclusion limit on hidden photon search in a previously unexplored mass range. Lastly, we demonstrate a high quality factor photonic bandgap cavity which is compatible with large magnetic field. The measured quality factor is almost $50$ times higher than a conventional copper cavity with $Q=10^{4}$ at these frequencies and $50\%$ higher than the axion quality factor. A coherent integration of all these will greatly speed up the dark matter search in the future.