  The intensive pursuit for quantum advantage in terms of computational
complexity has further led to a modernized crucial question: {\it When and how
will quantum computers outperform classical computers?} The next milestone is
undoubtedly the realization of quantum acceleration in practical problems. Here
we provide a clear evidence and arguments that the primary target is likely to
be condensed matter physics. Our primary contributions are summarized as
follows: 1) Proposal of systematic error/runtime analysis on state-of-the-art
classical algorithm based on tensor networks; 2) Dedicated and high-resolution
analysis on quantum resource performed at the level of executable logical
instructions; 3) Clarification of quantum-classical crosspoint for ground-state
simulation to be within runtime of hours using only a few hundreds of thousand
physical qubits for 2d Heisenberg and 2d Fermi-Hubbard models, assuming that
logical qubits are encoded via the surface code with the physical error rate of
$p=10^{-3}$. To our knowledge, we argue that condensed matter problems offer
the earliest platform for demonstration of practical quantum advantage that is
order-of-magnitude more feasible than ever known candidates, in terms of both
qubit counts and total runtime.
