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

量子计算机有着巨大的前景，它可以利用量子效应以一种全新的方式进行计算，解决世界上最快的传统计算机无法解决的问题。然而，量子效应是脆弱的。由于与周围世界的相互作用，量子系统很容易受到噪声和错误的影响，而这种噪声和错误往往会使量子计算机充其量也不会比传统的经典计算机更强大。虽然工程原型量子计算机在减少这种误差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小化其影响，但要在量子计算机上运行最有价值的大规模计算，噪声需要几乎完全消除。这可以使用量子纠错技术来实现，其中量子数据存储在纠错代码中。最主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，关于如何使用它来存储数据、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领先方法，大多数构建此类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，即使是相对适度的计算也需要非常大量的量子比特（量子位）。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来进行纠错。因此，在过去的25年里，自表面代码被发现以来，人们一直在不断地寻找更有效的代码，尽管如此，这些代码仍然具有表面代码的一些实际优点。这些代码的潜在候选者最近才被发现。它们属于被称为量子低密度奇偶校验码（或QLPDC码）的代码族。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移动网络中使用的纠错。这些量子类似物已经研究了近20年，但直到2022年才发现了一种量子密码，它在数据存储方面与最好的经典密码一样高效。这段代码，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，大幅减少量子比特的数量，从而加速大规模量子计算机的发展。然而，要实现这一承诺，还有很多工作要做。与表面代码的简单结构不同，这些新的高效代码非常复杂。因此，它们的好处能否在实际硬件中实现还远不清楚。此外，人们对使用这种代码进行计算的最佳方式知之甚少。该项目的目的是充分评估新型QLDPC码用于大规模量子计算的可行性。我们将通过设计详细的测量模型来检测错误，并发现在这些代码上实现量子门的新方法来实现这一点。该研究将通过软件设计来促进，软件设计将代码的复杂抽象描述转化为将在设备上实现的构建块（门和测量）的规范。我们将根据量子比特和门的数量来确定所需的资源，以实现我们的项目合作伙伴提供的一组基准计算，并使用这些资源来对基于这些新代码构建有用的量子计算机所需的资源与标准表面代码进行公平的实际比较。

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.