Quantum error-correction in light of new experimental advances

噪声的存在是量子计算机发展的主要瓶颈之一：量子比特与其环境相互作用，这可能会破坏它们所包含的信息。量子纠错--用几个物理量子比特对一个逻辑量子比特进行编码，以增加冗余--是设计可靠的大规模量子设备的必要步骤。多年来，已经提出了许多量子纠错码，它们具有独特的特征：每个逻辑量子比特所需的物理量子比特的数量，底层体系结构的几何形状(例如，2D/3D量子比特网格)，或者或多或少与高水平噪声一起工作的能力。最后一个属性可以使用所谓的噪声阈值来量化：代码纠正任意错误所需的最大噪声级别。代码阈值传统上是使用理想的噪声模型来估计的，在这种模型中，可能影响量子比特的两种类型的错误-比特翻转和相位翻转-以相等的概率发生。然而，实验量子计算的最新进展表明，这种模型往往与现实相去甚远，换句话说，噪声是有偏差的。最近，有研究表明，在有偏噪声的情况下，对量子编码进行简单的修改可以大大提高噪声阈值。在本论文的过程中，我们将致力于弥合现有纠错方案与实验现实之间的差距。我们将查看最有希望的纠错码，并研究当不仅考虑有偏噪声，而且考虑从实验中提取的任何现实噪声模型时，如何改进它们。为此，我们需要考虑纠错协议的不同组件：代码本身、产生纠错的解码器，以及在代码上实现量子操作的技术。总体而言，我们将寻求使纠错在短期内更加顺从，通过使它们适应实验上可行的体系结构，并减少实现它们所需的物理量子比特的数量。

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.