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：量子比特与它们的环境相互作用，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编码一个逻辑量子比特以增加冗余的想法——是设计可靠的大规模量子器件的必要步骤。多年来已经提出了许多量子纠错码，具有独特的特征：每个逻辑量子比特所需的物理量子比特数量，底层架构的几何形状（例如量子比特的2D/3D网格），或者在或多或少高水平噪声下工作的能力。最后一个属性可以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水平。传统上，代码阈值是使用理想噪声模型来估计的，在理想噪声模型中，影响量子比特的两种错误——比特翻转和相位翻转——发生的概率是相等的。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，噪声是有偏见的。最近，研究表明，对量子码进行简单的修改可以大大提高偏置噪声下的噪声阈值。在本论文的过程中，我们将致力于弥合当前纠错方案与实验现实之间的差距。我们将研究最有前途的纠错码，并研究如何在考虑偏差噪声的同时，考虑从实验中提取的任何现实噪声模型，对它们进行改进。为此，我们需要考虑纠错协议的不同组成部分：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。总的来说，我们将寻求在短期内使纠错更容易实现，通过使它们适应实验可行的架构，并减少实现它们所需的物理量子位的数量。

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.