The development of performant integrated detectors, which are sensitive to quantum fluctuations of coherent light, are strongly desired to realize a scalable and determinist photonic quantum processor based on continuous variables states of light. Here, we investigate the performance of hot electron bolometers (HEBs) fabricated on top of a silicon-on-insulator (SOI) photonic circuit showing responsivities up to 8600 V/W and a record noise equivalent temperature of 1.1 dB above the quantum limit. Thanks to a detailed analysis of the noise sources of the waveguide integrated HEB, we estimate 14.8 dBV clearance between the shot noise and electrical noise with just 1.1µW of local oscillator power. The full technology compatibility with superconducting nanowire single photon detectors (SNSPDs) opens the possibility of nonclassical state engineering and state tomography performed within the same platform, enabling a new class of optical quantum processors.