Propagation of errors and quantum advantage in analogue quantum simulation

With progress towards quantum advantage for problems designed to test quantum hardware, there is increasing focus on when we will observe a practical quantum advantage for relevant problems with applications in science or industry. Simulating quantum many-body dynamics is a particularly promising example, both because analogue quantum simulation is implemented in ongoing experiments, and because these problems are challenging for classical calculations. The classical complexity (especially in quantum quench dynamics) is linked directly to the build up of entanglement, and scrambling of quantum information in these systems.

For some quantum simulation platforms, we can build microscopic models of the underlying processes, including noise and decoherence. This gives us a theoretical handle on how errors propagate, and allows us to analyse in which regimes the outcome of an analogue simulation will be reliable. We have recently analysed the requirements for quantitatively reliable quantum simulation beyond the capabilities of existing classical methods for analogue quantum simulators with neutral atoms in optical lattices and trapped ions [1]. Considering the primary sources of error in analogue devices and how they propagate after a quench in studies of the Hubbard or long-range transverse field Ising model, we identified the level of error expected in quantities we extract from experiments, as well as the hardware requirements to reach the same level of accuracy with future fault-tolerant digital quantum simulation. As an outlook I will briefly discuss whether we can overcome decoherence limits to the useful size scale of quantum simulators, using long-range interactions and linking to the fast scrambling of quantum information.

[1] S Flannigan, N Pearson, G H Low, A Buyskikh, I Bloch, P Zoller, M Troyer, and A J Daley, Quantum Science and Technology 7, 045025 (2022)