Soutenance d'Antoine Marquet

Over the past two decades, superconducting circuits have emerged as a promising platform for building a quantum computer. However, they remain limited by their coherence time which is still insufficient to demonstrate quantum advantage.

Quantum error correction (QEC) offers an approach to counter these errors. Its fundamental principle consists of introducing redundancy in order to define a so-called logical qubit. Thus, if an isolated physical qubit suffers an error, it can be detected and corrected without affecting the information stored within the logical qubit. One of the most intuitive approaches, and one that comes closest to conventional error correction, is to use an array of physical qubits to achieve the desired redundancy.

This thesis explores an alternative approach, based on encoding quantum information in superconducting cavities, where the redundancy is provided by the infinite dimension of the Hilbert space. Specifically, we use cat qubits for which the logical |0⟩ and |1⟩ states are coherent states |±α⟩ of a harmonic oscillator. These states are stabilized by leveraging dissipation to our advantage so that photon exchanges between the harmonic mode and its environment predominantly occur in pairs. In this way, "bit-flip" errors are exponentially suppressed as a function of the number of photons contained by the mode, at the modest cost of a linear increase in "phase-flip" errors. These errors could then be corrected by an additional layer of correction, such as a repetition code of cat qubits.

At the heart of this thesis work is the introduction of a self-parametric superconducting circuit that non-linearly couples a mode containing the cat qubit to a dissipative mode whose frequency is set to twice that of the cat mode. Unlike previous implementations, this passive coupling does not require a parametric pump and achieves a high two-photon dissipation rate κ2/2π of around 2 MHz. Bit-flip errors are then avoided for a characteristic period of up to 0.3 s, with a moderate impact on phase-flip errors. In addition, we demonstrate universal control of this qubit using the two-photon dissipation to implement X, Y, and Z logic gates of arbitrary θ angle.