Beyond classical computation with a noisy intermediate-scale quantum processor
We begin by studying how computational complexity grows and quantum information scrambling takes place under quantum circuits such as those used in the quantum supremacy experiment in 2019. We demonstrate that the complexity of quantum circuits is directly revealed through measurements of out-of-time-order correlators (OTOCs), which capture the spatial-temporal spread of local perturbations. We visualize the dispersion of the scrambling wavefront as it changes from diffusive to ballistic propagation, resulting from changing the entangling gates. After probing the origin of complexity, next we investigate how to control dynamics with computational accuracy beyond the current state of-the-art classical methods. We provide a blueprint for an accurate quantum matter simulator and demonstrate it by probing fundamental electronic properties of a one-dimensional wire. We demonstrate nearly complete mitigation of decoherence errors and arrive at an accuracy in measuring energy eigenvalues of this wire with an error of ~0.01 radians, whereas typical energy scales are of order 1 radian. Finally, by turning into the study of topologically ordered states, we show how our platform can be used to study problems commonly investigated in condensed matter settings. We prepare the ground state of the celebrated Kitaev toric code Hamiltonian using an efficient quantum circuit. We measure a topological entanglement entropy near the expected value of ln2, and simulate anyon interferometry to extract the braiding statistics of the emergent excitations. Time permitting, I share investigation of key aspects of the surface code, including logical state injection and the decay of the non-local order parameter.