Unlocking the potential of Quantum LDPC Codes for low-overhead fault-tolerance

释放量子 LDPC 码在低开销容错方面的潜力

• 批准号: EP/Y004620/1
• 负责人: Daniel Edward Browne
• 金额: $ 48.78万
• 依托单位: University College London
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2023
• 资助国家: 英国
• 起止时间: 2023 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FY004620%2F1
• 关键词: Unlocking; potential; Quantum; LDPC; Codes

Quantum computers have huge promise to solve problems which lie beyond the capabilities of even the world's fastest conventional computer using quantum effects to compute in a fundamentally new way. However, quantum effects are fragile. Quantum systems are vulnerable to noise and error due to interactions with the world around them, and this noise and error tends to render a quantum computer no more powerful, at best, than a conventional classical computer.While progress in engineering prototype quantum computers to reduce this error is impressive, and clever algorithmic tricks are being developed to help minimise its effects, to run the most valuable large-scale computations on a quantum computer, the noise needs to be removed almost entirely.This can be done using the techniques of quantum error correction, where quantum data is stored in an error correcting code. The leading quantum error correcting code is called the surface code - a particularly simple code with a repeated regular structure which can be realised on a two-dimensional surface. The surface code is now very well studied, and the full details of how it can be used to store data, correct errors and implement logical gates are well studied. It is the leading approach to large scale quantum computation and most industrial roadmaps for building such a device are based on it.However, the surface code has a key disadvantage. It is a highly inefficient way of storing information, and very large numbers of quantum bits (qubits) are required to use it for even a relatively modest computation. For every quantum bit used for computation, thousands or more are needed for the error correction.There has thus been an ongoing search, over the last 25 years since the surface code was discovered, to find more efficient codes, which nevertheless share some of the practical advantages of the surface code. Potential candidates for such codes have very recently been discovered. They are in a family of codes known as Quantum Low-Density Parity Check codes (or QLPDC codes). Classical LDPC codes are widely used due to their efficient encoding and useful properties, for example in the error correction used in 5G mobile networks. The quantum analogues of these have been studied for nearly 20 years, but only in 2022 was a quantum code discovered which is as efficient in data storage as the best classical codes.This code, and codes like it, promise to revolutionise the path to large-scale fault tolerant quantum computation, dramatically reducing the number of quantum bits, and therefore hastening the development of large-scale quantum computers.To realise this promise, however, much work needs to be done. Unlike the simple structure of the surface code, these new highly efficient codes are very complicated. It is therefore far from clear whether their benefits can be realised in practical hardware. Furthermore, little is known about the best way to use such codes for computation. This aim of this project is to fully assess the feasibility of novel QLDPC codes for large-scale quantum computation.We shall do this by designing detailed models of the measurements which detect errors, and discover new ways to realise quantum gates on these codes. The research will be facilitated by the design of software which will translate the complicated abstract descriptions of the codes into a specification of the building blocks (gates and measurements) which will be realised on the device. We will determine the resources required, in terms of number of qubits and gates, to achieve a set of benchmark computations provided by our project partners, and use these to enable to a fair practical comparison between the resources required to construct a useful quantum computer based on these novel codes compared to the standard surface code.

量子计算机有巨大的潜力来解决问题，即使是世界上最快的传统计算机也无法使用量子效应以一种全新的方式进行计算。然而，量子效应是脆弱的。由于量子系统与周围世界的相互作用，量子系统容易受到噪声和错误的影响，这种噪声和错误往往使量子计算机的功能充其量不会比传统的经典计算机更强大。尽管量子计算机原型工程在减少这种错误方面的进展令人印象深刻，并且正在开发聪明的算法技巧来帮助最大限度地减少其影响，为了在量子计算机上运行最有价值的大规模计算，需要几乎完全消除噪声。这可以使用量子纠错技术来完成，其中量子数据存储在纠错码中。最重要的量子纠错码被称为表面码-一种特别简单的代码，具有重复的规则结构，可以在二维表面上实现。表面代码现在已经得到了很好的研究，它如何被用来存储数据，纠正错误和实现逻辑门的全部细节也得到了很好的研究。它是大规模量子计算的主要方法，大多数构建这种设备的工业路线图都是基于它的。然而，表面代码有一个关键的缺点。这是一种非常低效的存储信息的方式，即使是相对温和的计算也需要非常大量的量子比特（qubit）。对于用于计算的每个量子比特，需要数千个或更多的量子比特用于纠错。因此，自从表面码被发现以来，在过去的25年里，人们一直在寻找更有效的码，尽管这些码具有表面码的一些实际优点。最近发现了这种代码的潜在候选者。它们属于被称为量子低密度奇偶校验码（或QLPDC码）的码族。经典LDPC码由于其高效的编码和有用的特性而被广泛使用，例如在5G移动的网络中使用的纠错中。这些量子类似物已经被研究了近20年，但直到2022年才发现一种量子代码，它在数据存储方面与最好的经典代码一样有效。这种代码以及类似的代码有望彻底改变大规模容错量子计算的道路，大大减少量子比特的数量，因此加速了大规模量子计算机的发展。然而，要实现这一承诺，还需要做很多工作。与表面码的简单结构不同，这些新的高效码非常复杂。因此，它们的好处是否能在实际硬件中实现还远未可知。此外，很少有人知道使用这种代码进行计算的最佳方式。本项目的目的是全面评估新型QLDPC码用于大规模量子计算的可行性。我们将通过设计检测错误的测量的详细模型来实现这一点，并发现在这些码上实现量子门的新方法。研究将通过软件的设计来促进，该软件将代码的复杂抽象描述转换为将在设备上实现的构建块（门和测量）的规范。我们将根据量子位和门的数量确定所需的资源，以实现我们的项目合作伙伴提供的一组基准计算，并使用这些资源来实现基于这些新代码与标准表面代码构建有用的量子计算机所需的资源之间的公平实际比较。