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Hilbert space dimension is a key resource for quantum information processing. A large Hilbert space is not only an essential requirement for quantum error correction, but it can also be advantageous for realizing gates and algorithms more efficiently. There has thus been considerable experimental effort in recent years to develop quantum computing platforms using qudits (d-dimensional quantum systems with d>2) as the fundamental unit of quantum information. Just as with qubits, quantum error correction of these qudits will be necessary in the long run, but to date error correction of logical qudits has not been demonstrated experimentally. Here we report the experimental realization of an error-corrected logical qutrit (d=3) and ququart (d=4) by employing the Gottesman-Kitaev-Preskill (GKP) bosonic code. Using a reinforcement learning agent, we optimize the GKP qutrit (ququart) as a ternary (quaternary) quantum memory and achieve beyond break-even error correction with a gain of 1.82 +/- 0.03 (1.87 +/- 0.03). This work represents a new way of leveraging the large Hilbert space of a harmonic oscillator for hardware-efficient quantum error correction.

Bosonic codes offer a hardware-efficient strategy for quantum error correction by redundantly encoding quantum information in the large Hilbert space of a harmonic oscillator. However, experimental realizations of these codes are often limited by ancilla errors propagating to the encoded logical qubit during syndrome measurements. The Kerr-cat qubit has been proposed as an ancilla for these codes due to its theoretically-exponential noise bias, which would enable fault-tolerant error syndrome measurements, but the coupling required to perform these syndrome measurements has not yet been demonstrated. In this work, we experimentally realize driven parametric coupling of a Kerr-cat qubit to a high-quality-factor microwave cavity and demonstrate a gate set enabling universal quantum control of the cavity. We measure the decoherence of the cavity in the presence of the Kerr-cat and discover excess dephasing due to heating of the Kerr-cat to excited states. By engineering frequency-selective dissipation to counteract this heating, we are able to eliminate this dephasing, thereby demonstrating a high on-off ratio of control. Our results pave the way toward using the Kerr-cat to fault-tolerantly measure error syndromes of bosonic codes.

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 the natural 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 $G = 2.27 \pm 0.07$. We achieve this performance by combining innovations in several domains including the fabrication of superconducting quantum circuits and model-free reinforcement learning.

A controlled evolution generated by nonlinear interactions is required to perform full manipulation of a quantum system, and such control is only coherent when the rate of nonlinearity is large compared to the rate of decoherence. As a result, engineered quantum systems typically rely on a bare nonlinearity much stronger than all decoherence rates, and this hierarchy is usually assumed to be necessary. In this work, we challenge this assumption by demonstrating the universal control of a quantum system where the relevant rate of bare nonlinear interaction is comparable to the fastest rate of decoherence. We do this by introducing a novel noise-resilient protocol for the universal quantum control of a nearly-harmonic oscillator that takes advantage of an in-situ enhanced nonlinearity instead of harnessing a bare nonlinearity. Our experiment consists of a high quality-factor microwave cavity with weak-dispersive coupling to a much lower quality superconducting qubit. By using strong drives to temporarily excite the oscillator, we realize an amplified three-wave-mixing interaction, achieving typical operation speeds over an order of magnitude faster than expected from the bare dispersive coupling. Our demonstrations include preparation of a single-photon state with $98\pm 1(\%)$ fidelity and preparation of squeezed vacuum with a squeezing level of $11.1$ dB, the largest intracavity squeezing reported in the microwave regime. Finally, we also demonstrate fast measurement-free preparation of logical states for the binomial and Gottesman-Kitaev-Preskill (GKP) quantum error-correcting codes.