  It is shown here that Brillouin amplification can be used to produce
picosecond pulses of petawatt power. Brillouin amplification is far more
resilient to fluctuations in the laser and plasma parameters than Raman
amplification, making it an attractive alternative to Raman amplification.
Through analytic theory and multi-dimensional computer simulations, a novel,
well-defined parameter regime has been found, distinct from that of Raman
amplification, where pump-to-probe compression ratios of up to 100 and peak
laser fluences over 1 kJ/cm$^2$ with 30\% efficiency have been achieved. High
pulse quality has been maintained through control of parasitic instabilities.
