That depends on what you mean by computational advances. If you mean advances in computer hardware, I wouldn't hold your breath on that helping much since these are generally exponentially scaling problems meaning that tiny incremental improvements in simulation fidelity or system size require doubling the computational resources.

Quantum computers, if large enough ones ever materialize could give us a revolution in computational many-body physics because they could actually circumvent this exponential scaling.

The most promising straightforward avenue though is actually just developing better algorithms that make more insightful, appropriate approximations to correctly capture the physics we care about. That may or may not be what you meant by computational advances.