The energy resolution of a single photon counting Microwave Kinetic Inductance Detector (MKID) can be degraded by noise coming from the primary low temperature amplifier in the detectors readout system. Until recently, quantum limited amplifiers have been incompatible with these detectors due to dynamic range, power, and bandwidth constraints. However, we show that a kinetic inductance based traveling wave parametric amplifier can be used for this application and reaches the quantum limit. The total system noise for this readout scheme was equal to ~2.1 in units of quanta. For incident photons in the 800 to 1300 nm range, the amplifier increased the average resolving power of the detector from ~6.7 to 9.3 at which point the resolution becomes limited by noise on the pulse height of the signal. Noise measurements suggest that a resolving power of up to 25 is possible if redesigned detectors can remove this additional noise source.
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