  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 detector's 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.
