Towards fault-tolerant quantum computing with minimal resources.

这个项目关注的是正在等待量子革命的高性能计算的未来。传统处理器时钟速度的进步已经放缓，几乎停滞不前，因此传统计算机的发展已经转向制造具有更多核心的机器，而不是更快的核心。在这些多核机器上，许多程序可以同时运行，并且在并行编程时可以实现巨大的加速。但许多计算任务不能并行化或处理需求呈指数级增长。量子计算是一种完全不同的范式，能够有效地处理这些非常困难的计算任务。该理论认为，通过对量子系统（如单个电子或光子）的精细控制，我们可以执行量子逻辑而不是二进制逻辑的算法。这些量子算法比经典算法需要更少的时钟周期，甚至更少！事实上，对量子系统的完美控制是不可能的。英国拥有一些最先进的量子计算实验室，牛津离子阱小组已经实现了99.9%完美的单个处理步骤。这可能会提高到99.99%，但是不可避免的离子和周围环境之间的相互作用使进一步的进展变得不太可能。虽然令人印象深刻，但这限制了我们在灾难性计算故障之前只有几百个基本步骤。该项目开发了重要的容错技术，尽管不可避免的实验限制，可以确保可靠的量子计算的任何长度。容错已经成为许多现代技术的基础；它允许轻微划伤的蓝光光盘播放电影，并通过太阳风与太阳系边缘的旅行者号宇宙飞船进行通信。这是有代价的。高端显卡是容错的，但为此需要12.5%的内存。容错量子计算本质上更具挑战性，需要处理更多的错误。目前估计超过99%的量子内存被用于提供容错功能。为有用的量子计算提供足够的内存将是一个巨大的工程挑战。这个项目的目的是找到一个软件解决方案。找到更好的容错方法，并将这些巨大的开销减少到更易于管理的数量。最近最大的进步是利用拓扑学的思想对信息进行编码。拓扑是一个全局特性。真实的地球和平面地球在日常生活中看起来都是平的，但在全球范围内却是不同的。量子信息同样可以存储在全局自由度中，而不会在局部补丁中留下任何证据。甜甜圈或环面拓扑一直是推动容错理论改进的引擎。在这些改进之前，容错的先决条件是如此严格，以至于实验无法满足它们。由于迫切需要减少容错开销，本项目再次从拓扑结构中寻找灵感。这一次，更奇怪和更奇特的拓扑结构将被用作模型，在此基础上以更低的资源成本构建容错量子计算机。该项目将开发这些拓扑容错计算机的数值模拟，以比较不同的方法并找到最具成本效益的方法。为了获得最佳性能，容错软件的拓扑结构必须反映在量子计算机的硬件设计中。在与实验学家的合作下，该项目将为第一代容错量子计算机提供现实的蓝图。

This project concerns the future of high-performance computing, which is waiting for a quantum revolution. Advances in conventional processor clock speed have slowed and almost plateaued, and so traditional computer development has shifted to building machines with more cores instead of faster cores. On these multicore machines, many programs can run simultaneously and huge speed-ups are possible when parallel programming. But many computational tasks can not be parallelized or have exponentially growing processing demands. Quantum computing is an entirely different paradigm capable of efficiently dealing with some of these very hard computational tasks. The theory is that through exquisite control of quantum systems, such as individual electrons or photons, we can can execute algorithms following a quantum rather than binary logic. These quantum algorithms need fewer clock cycles than classical counterparts, and even exponentially fewer! The reality is that perfect control of quantum systems is impossible. The UK is home to some of the most advanced quantum computing laboratories, and the Oxford Ion trap group has achieved single processing steps at 99.9% perfection. This might yet be improved to 99.99%, but then unavoidable interactions between Ions and their surrounding make further progress unlikely. Whilst impressive, this limits us to only a few hundred elementary steps before a catastrophic computational failure. This project develops important fault-tolerance techniques that can, despite inevitable experimental limitations, ensure reliable quantum computations of any length. Fault-tolerance already underpins many modern technologies; it allows lightly scratched Blu-ray discs to play movies, and communication through solar winds to the Voyager spacecraft at the edge of our solar system. This comes at some cost. High-end graphics cards are fault-tolerant but need 12.5% of their memory for this purpose. Fault-tolerant quantum computing is more challenging by nature and has to deal with more errors. Current estimates are upward of 99% of all quantum memory being used to provide fault-tolerance. Providing enough memory for a useful quantum computation would be a monumental engineering challenge. The aim of this project is find a software solution. To find better approaches to fault tolerance and reduce these monstrous overheads to a more manageable amount. The biggest recent advances have been to use ideas from topology to encode information. Topology is a global feature. The real Earth and a flat Earth would both look flat on an everyday level, but are globally distinct. Quantum information can similarly be stored in global degrees of freedom, without leaving any evidence in local patches. The donut, or torus, topology has been the engine driving improvements in fault-tolerance theory. Before these improvements, the prerequisites for fault-tolerance were so stringent that experiments could not meet them. With the pressing urgency of reducing fault-tolerance overheads, this project again looks to topology for inspiration. This time stranger and more exotic topologies will be used as models upon which to build fault-tolerant quantum computers at lower resource costs. This project will develop numerical simulations of these topologically fault-tolerant computers, to compare different approaches and find the most cost-effective method. For optimal performance, the topology of fault-tolerance software must be reflected in the hardware design of a quantum computers. In collaboration with experimentalists, the project will produce realistic blueprints for the first generation of fault-tolerant quantum computers.