Propagation of errors and quantitative quantum simulation with quantum advantage

Abstract The rapid development in hardware for quantum computing and simulation has led to much interest problems where these devices can exceed the capabilities of existing classical computers known methods. Approaching this that go beyond testing performance a device is an important step, many-body quench dynamics one most promising candidates early practical advantage. We analyse requirements quantitatively reliable methods analogue simulators with neutral atoms optical lattices trapped ions. Considering primary sources error how they propagate after studies Hubbard or long-range transverse field Ising model, we identify level expected quantities extract from experiments. conclude models are directly implementable regimes advantage attained current experiments simulators. also reach same accuracy future fault-tolerant digital simulation. Verification techniques already available test assumptions make here, demonstrating will be next step.