The advent of complex optimization problems such as drug synthesis, economic forecasting and cryptography has led to a need for increased computational speeds. Quantum computing offers exponentially faster computation than is capable by current state of the art computers. However, the information they process is extremely susceptible to noise and they require cryogenic environments to function. This necessitates that any electronics required to interface with them must be low noise, to preserve the information of these computers, and low power, to enable them to operate within a cryogenic environment. Voltage controlled oscillators (VCO) are of particular importance as they generate radio-frequency pulses that manipulate the operations of quantum computers. This thesis proposes a noise-matching topology for VCOs that utilizes impedance networks to limit phase noise at the oscillation frequency. Theoretical equations based on small-signal circuit models and impulse sensitivity functions were derived to demonstrate the feasibility and to guide the design procedure. The circuit parameters were then determined using numerical calculations in MATLAB and the optimization tool in Cadence. Two sets of VCOs were fabricated in GlobalFoundries 22nm technology to verify the findings. Tests were conducted in a cryostat at 295K, 200K, 70K and 20K. An 8GHz VCO was built which achieved -134.6dBc/Hz of phase noise at 10MHz offset at 20K while consuming 0.373mW. A 5.5-9GHz tunable VCO was also demonstrated which achieved a best phase noise of -136.2dBc/Hz at 10MHz offset at 20K with 0.678mW of power. Overall, this thesis demonstrates a first step towards building a low noise and low power VCO suitable for quantum computing with the noise matching topology and less than 1mW of power consumption.