SHF: Small: Fault-Tolerant Quantum Computation in Multi-Qubit Block Codes

量子计算机利用量子力学的特殊性质-叠加、纠缠和干涉--来进行新型的信息处理。大规模量子计算机可以解决标准经典计算机无法解决的某些难题。由于退相干-量子噪声-扰乱了所需的量子效应，建造量子计算机是具有挑战性的。解决方案是容错量子计算：量子信息被编码在量子纠错码中，并免受噪声的影响。理论表明，如果消相干率不是太高，这将是可行的，但大多数结构需要令人望而生畏的开销来进行计算。所需的量子比特(量子比特)和基本运算(量子门)的数量乘以一个非常大的因子。这项研究将通过在多量子比特存储块中对计算的量子比特进行编码来最小化所需的开销，这些多量子比特存储块获得比以前研究的大多数代码更高的速率。还将使用不同的量子代码构建少量额外的处理器块。这些不同的代码可以有效地完成不同类型的量子门，所以通过选择正确的代码组合，任何量子计算都可以进行：这样的量子计算机被称为通用量子计算机。量子比特通过量子隐形传态在码块之间传输，并始终受到退相干的保护。该项目在容错方面也采取了一些不同的策略。这项研究不会研究允许任意大小的量子计算的条件，而是询问在固定的代码选择和给定的消相干水平下，可以进行多大的量子计算。由于实际上只能完成一定大小的计算，这是最紧迫的实际问题。这个项目将支持南加州大学的两名博士生，并将是南加州大学量子信息科学与技术中心(CQIST)的一个活跃的研究方向。CQIST和PI支持洛杉矶地区和其他地方的教育和推广，还组织和赞助关于量子信息科学的国际会议。

Quantum computers use the peculiar properties of quantum mechanics---superposition, entanglement, and interference---to do new kinds of information processing. Large scale quantum computers could solve certain difficult problems that are beyond the ability of standard classical computers. Building quantum computers is challenging due to decoherence---quantum noise---which disrupts the needed quantum effects. The solution is fault-tolerant quantum computation: quantum information is encoded in quantum error-correcting codes, and shielded from the effects of noise. Theory shows that this will work if the decoherence rate is not too high, but most constructions require a daunting amount of overhead to do computation. The number of quantum bits (qubits) and basic operations (quantum gates) needed are multiplied by a very large factor.This research will minimize the overhead required by encoding the qubits of the computation in multi-qubit storage blocks that achieve higher rates than most codes that have been studied before. A small number of additional processor blocks will also be constructed, using a different quantum code. These different codes allow different types of quantum gates to be done efficiently, so by choosing the right combination of codes, any quantum computation can be done: such a quantum computer is called universal. Qubits are transferred between the code blocks by quantum teleportation, and are protected from decoherence at all times.This project also takes a somewhat different tack on fault tolerance. Rather than study conditions that allow quantum computations of arbitrarily large size, this research will ask, for a fixed choice of codes and a given level of decoherence, how large a quantum computation can be done. Since in reality only computations up to a certain size can actually be done, this is the most immediately practical question.This project will support two Ph.D. students at USC, and will be an active strand of research at USC's Center for Quantum Information Science and Technology (CQIST). CQIST, and the PI, support education and outreach in the Los Angeles area and elsewhere, and also organize and sponsor international conferences on quantum information science.