The Q/U Imaging ExperimenT (QUIET) is designed to measure polarization in the cosmic microwave background, targeting the imprint of inflationary gravitational waves at large angular scales(~1°). Between 2008 October and 2010 December, two independent receiver arrays were deployed sequentially on a 1.4 m side-fed Dragonian telescope. The polarimeters that form the focal planes use a compact design based on high electron mobility transistors (HEMTs) that provides simultaneous measurements of the Stokes parameters Q, U, and I in a single module. The 17-element Q-band polarimeter array, with a central frequency of 43.1 GHz, has the best sensitivity (69 μKs1/2) and the lowest instrumental systematic errors ever achieved in this band, contributing to the tensor-to-scalar ratio at r < 0.1. The 84-element W-band polarimeter array has a sensitivity of 87 μKs1/2 at a central frequency of 94.5 GHz. It has the lowest systematic errors to date, contributing at r < 0.01. The two arrays together cover multipoles in the range ℓ ~ 25-975. These are the largest HEMT-based arrays deployed to date. This article describes the design, calibration, performance, and sources of systematic error of the instrument.