Entanglement and complexity of interacting transmon qubits subject to asymmetric noise*

The simulation complexity of predicting the time evolution of delocalized many-body quantum systems has attracted much recent interest, and simulations of such systems in real quantum hardware are promising routes to demonstrating a quantum advantage over classical machines. In these proposals, random noise is an obstacle that must be overcome for a faithful simulation, and a single error event can be enough to drive the system to a classically trivial state. We argue that this need not always be the case, and consider a modification to a leading quantum sampling problem-- time evolution in an interacting Bose-Hubbard chain of transmon qubits [Neill et al, Science 360, 195 (2018)] -- where each site in the chain has a driven coupling to a lossy resonator and particle number is no longer conserved. The resulting quantum dynamics are complex and highly nontrivial. We show that this problem is likely to be harder to simulate than the isolated chain, and that it can achieve volume-law entanglement even in the strong noise limit (likely persisting up to system sizes beyond the scope of classical simulation). Further, we show that the metrics which suggest classical intractability for the isolated chain point to similar conclusions in the noisy case. These results suggest that quantum sampling problems including nontrivial noise could be good candidates for demonstrating a quantum advantage in near-term hardware.