The ambition of harnessing the quantum for computation is at odds with the fundamental phenomenon of decoherence. The purpose of quantum error correction (QEC) is to counteract thenatural tendency of a complex system to decohere. This cooperative process, which requires participation of multiple quantum and classical components, creates a special type of dissipation that removes the entropy caused by the errors faster than the rate at which these errors corrupt the stored quantum information. Previous experimental attempts to engineer such a process faced an excessive generation of errors that overwhelmed the error-correcting capability of the process itself. Whether it is practically possible to utilize QEC for extending quantum coherence thus remains an open question. We answer it by demonstrating a fully stabilized and error-corrected logical qubit whose quantum coherence is significantly longer than that of all the imperfect quantum components involved in the QEC process, beating the best of them with a coherence gain of G=2.27±0.07. We achieve this performance by combining innovations in several domains including the fabrication of superconducting quantum circuits and model-free reinforcement learning.
We introduce the cavity-embedded Cooper pair transistor (cCPT), a device which behaves as a highly nonlinear microwave cavity whose resonant frequency can be tuned both by charginga gate capacitor and by threading flux through a SQUID loop. We characterize this device and find excellent agreement between theory and experiment. A key difficulty in this characterization is the presence of frequency fluctuations comparable in scale to the cavity linewidth, which deform our measured resonance circles in accordance with recent theoretical predictions [B. L. Brock et al., Phys. Rev. Applied (to be published), arXiv:1906.11989]. By measuring the power spectral density of these frequency fluctuations at carefully chosen points in parameter space, we find that they are primarily a result of the 1/f charge and flux noise common in solid state devices. Notably, we also observe key signatures of frequency fluctuations induced by quantum fluctuations in the cavity field via the Kerr nonlinearity.
We present a model for measurements of the scattering matrix elements of tunable microwave cavities in the presence of resonant frequency fluctuations induced by fluctuations in thetuning parameter. We apply this model to the specific case of a two-sided cavity and find an analytic expression for the average scattering matrix elements. A key signature of this `fluctuating model‘ is a subtle deformation of the trajectories swept out by scattering matrix elements in the complex plane. We apply this model to experimental data and report a direct observation of this deformation in the data. Despite this signature, we show that the fluctuating and non-fluctuating models are qualitatively similar enough to be mistaken for one another, especially in the presence of measurement noise. However, if one applies the non-fluctuating model to data for which frequency fluctuations are significant then one will find damping rates that appear to depend on the tuning parameter, which is a common observation in tunable superconducting microwave cavities. We propose this model as both a potential explanation of and remedy to this apparent phenomenon.