Processing and Distillation of Multi-Qubit Block Codes for Fault-Tolerant Quantum Computation

量子计算机利用量子力学效应来处理信息，可能很快就能比任何标准的经典计算机更有效地解决一些重要的计算问题。然而，量子计算机很难建造，因为它们对量子力学噪声或退相干非常敏感。该项目将通过使用新型量子纠错码来开发克服退相干的新方法。规避退相干的努力很重要，因为量子纠错可能会使具有实际设备的容错量子计算成为可能。该项目将研究如何提高量子纠错码的效率，以便实现纠错协议所需的物理资源更少。这将允许在更小、更合理大小的设备上进行大量的量子计算。该项目还将培训参与这项研究的量子信息科学基础课题的学生，这将有助于他们为进入学术界或高科技行业的职业生涯做准备。即使有容错设计，在短期内构建量子计算机也是一个挑战，因为容错需要大量的开销：完美的量子计算机所需的每个逻辑量子比特(Qubit)在受到代码保护后可能需要数千甚至数万个物理量子比特。该项目旨在大幅降低容错量子计算机所需的开销。不是单独编码每个逻辑量子比特，而是使用更有效的代码，在相同的码字中编码许多逻辑量子比特。使用这种多量子比特码进行计算需要新的技术，本项目将研究这些新技术：逻辑隐形传态，状态蒸馏，以及开发不同类型的码(如量子低密度奇偶校验码)，具有不同的性质。如果一切运行良好，开销可能会降低到每个逻辑量子比特几十个物理量子比特。这将允许合理大小的计算机进行非平凡的量子计算。

Quantum computers, which make use of quantum mechanical effects to process information, may soon be able to solve a number of important computational problems much more efficiently than any standard classical computer. However, quantum computers are difficult to build because they are very sensitive to quantum mechanical noise, or decoherence. This project will develop new ways to overcome decoherence by using novel types of quantum error-correcting codes. Efforts to circumvent decoherence are important because quantum error correction may enable fault-tolerant quantum computing with practical devices. This project will investigate ways to improve the efficiency of quantum error-correcting codes so that fewer physical resources are needed in order to implement error-correcting protocols. This would allow significant quantum computations to be done on smaller, more reasonably sized, devices. This project will also train students who participate in this research on fundamental topics in quantum information science, and this will help to prepare them for careers in academics or high technology industries.Even with fault-tolerant designs, constructing a quantum computer in the near term is a challenge because fault-tolerance requires a large amount of overhead: each logical quantum bit (qubit) needed by a perfect quantum computer could require thousands or even tens of thousands of physical qubits after being protected by codes. This project aims to dramatically reduce the overhead needed for fault-tolerant quantum computers. Instead of encoding each logical qubit separately, much more efficient codes are used that encode many logical qubits in the same codeword. Computing with such multi-qubit codes requires new techniques, which this project will study: logical teleportation, state distillation, and the development of different kinds of codes (such as quantum low-density parity-check codes), with different properties. If everything works well, the overhead could be reduced to as low as a few tens of physical qubits per logical qubit. This would allow nontrivial quantum computations by computers of a reasonable size.