Quantum error-correction in light of new experimental advances

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The presence of noise is one the main bottlenecks in the development of quantum computers: qubits interact with their environment, which can destroy the information they contain. Quantum error-correction-the idea of encoding one logical qubit with several physical qubits in order to add redundancy-is a necessary step in the design of reliable large-scale quantum devices. Many quantum error-correcting codes have been proposed over the years, with distinctive features: the number of physical qubits required per logical qubit, the geometry of the underlying architecture (e.g. a 2D/3D grid of qubits), or the ability to work with more or less high-levels of noise. This last property can be quantified using the so-called noise threshold: the maximum level of noise required for the code to correct arbitrary errors. Code thresholds have traditionally been estimated using ideal noise models, where the two types of errors that can affect a qubit-bit-flips and phase-flips-occur with equal probability. However, recent progress in experimental quantum computing has shown that this model is often far from reality, or in other words, noise is biased. More recently, it has been shown that simple modifications of a quantum code can lead to large improvements of the noise threshold under biased noise.Over the course of this thesis, we will aim to bridge the gap between current error-correcting schemes and the experimental reality. We will look at the most promising error-correcting codes and research how they can be improved when considering not only biased noise, but any realistic noise model extracted from experiments. For that, we will need to consider the different components of an error-correcting protocol: the code itself, the decoder that produces the correction, and the techniques to implement quantum operations on a code. Overall, we will seek to make error-correction more amenable in the near-term, by adapting them to experimentally-feasible architectures and reducing the number of physical qubits required to implement them.