  The numerical sign problem is a major obstacle to the quantitative
understanding of many important physical systems with first-principles
calculations. Typical examples for such systems include finite-density QCD,
strongly-correlated electron systems and frustrated spin systems, as well as
the real-time dynamics of quantum systems. In this talk, we argue that the
"tempered Lefschetz thimble method" (TLTM) [M. Fukuma and N. Umeda,
arXiv:1703.00861] and its extension, the "worldvolume tempered Lefschetz
thimble method" (WV-TLTM) [M. Fukuma and N. Matsumoto, arXiv:2012.08468], may
be a reliable and versatile solution to the sign problem. We demonstrate the
effectiveness of the algorithm by exemplifying a successful application of
WV-TLTM to the Stephanov model, which is an important toy model of
finite-density QCD. We also discuss the computational scaling of WV-TLTM.
