
Over the past years there has been rapid development in
hardware for quantum computing across a range of platforms. In
parallel to these developments, highly controlled quantum systems
ranging from ultra-cold atoms to superconducting qubits are being
applied as "analogue quantum simulators" to study problems of
interest in many-body physics. However, the big question is when
and how they might answers to questions that we cannot address
with simulation on classical computers.
I will give an introduction to the overarching question of what is
difficult to compute regarding many-body systems, and how we might
approach these questions using digital quantum computers, or
analogue quantum simulators. I will discuss under which conditions
the answers we get out of each platform are quantitatively
reliable, and where we might expect to obtain a practical quantum
advantage for simulation of quantum systems in the early
fault-tolerant era of quantum computing.