S. Hearth: Benchmarking Quantum Hardware with Conservation Laws

The remarkable advances made towards control over individual quantum degrees of freedom have made quantum computation appear closer than ever. Competition between quantum hardware platforms and simulation protocols has accelerated, and each year comes with new claims of quantum supremacy over classical simulation. Although these claims may apply to niche, toy problems; there does not appear to be a fundamental barrier preventing quantum computation from tackling physics problems with wider interest and applicability. In order to quantify and characterize the progress of these devices, we need to improve our benchmarking protocols and codesign them with the hardware limitations in mind. Here, I describe a number of benchmarks and protocols for analyzing the states and capabilities of modern quantum hardware. In particular, I first focus on hardware with intrinsic U(1) conservation laws, then shift focus to systems which develop emergent charge-conserving theories. I present analytical results on the scrambling time for circuits with such constraints, protocols for extracting classical information from these systems, and finally results comparing classical simulation to quantum annealing on the D-Wave 2000Q.