Although the Big Bang theory has been well tested based on many observations, there are critical problems that remain unanswered. The leading hypothesis to resolve these problems is cosmological inflation, or the theory that our universe went through a period of accelerated expansion at a very early stage before ordinary (i.e. decelerating) expansion started. The inflation theory predicts that primordial gravitational waves were created during the inflationary era. Measuring the polarization of cosmic microwave background (CMB) radiation is thought to be the best probe to detect the primordial gravitational waves. Since the expected signal is very faint, state-of-the-art low-temperature detector arrays with superconducting sensors are indispensible for future measurements. In this article, first, we describe the scientific goals of the CMB polarization measurements. This is followed by an explanation of the current status and future plans in Japan, including a discussion of experimental requirements for very-low-temperature detectors and cryogenics.