Abstract
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 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 argue that this problem is 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.
Highlights
Quantum sampling problems present the most promising near-term way to demonstrate “quantum supremacy” [1,2], where quantum hardware solves a problem that no classical supercomputer is capable of completing in a reasonable amount of time
We first describe our simulation methods and parameters in detail, plot results for entanglement negativity, a collection of different statistical measures of the output distribution, and the expected fidelity loss from various sources including approximations made in simulation and error processes in the quantum hardware itself
We presented a simple modification to a leading quantum sampling problem– weak but resonant coupling to lossy cavities– and showed that it leads to dramatic changes in the quantum dynamics
Summary
Quantum sampling problems present the most promising near-term way to demonstrate “quantum supremacy” [1,2], where quantum hardware solves a problem that no classical supercomputer is capable of completing in a reasonable amount of time. We simulate the dynamics of our protocol using experimentally realistic target parameters, and compute a series of key benchmark quantities to demonstrate classical hardness These include volume entanglement, signatures of quantum chaos in the form of distance from a Porter-Thomas distribution, number fluctuations, inverse participation ratio, and heavy output generation. Extrapolating from these results, we provide estimates for expected classical simulation difficulty at larger system sizes, and show that, under the assumption that direct Hamiltonian time evolution is the most efficient simulation method, the system should become impossible to accurately simulate with near-term classical hardware for chains or grids of between 25 and 30 qubit-cavity pairs, depending on protocol details
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