We have developed a PW (0.5 ps/500 J) laser system to demonstrate fast heating of imploded core plasmas using a hollow cone shell target. Significant enhancement of thermal neutron yield has been realized with PW-laser heating, confirming that the high heating efficiency is maintained as the short-pulse laser power is substantially increased to a value nearly equivalent to the ignition condition. It appears that the efficient heating is realized by the guiding of the PW laser pulse energy within the hollow cone and by self-organized relativistic electron transport. Based on the experimental results, we are developing a 10 kJ-PW laser system to study the fast heating physics of high-density plasmas at an ignition-equivalent temperature.