Quantum computing with LDPC codes

量子计算机中的错误是不可避免的。控制存储在单个电子或光子中的量子比特（qubit）比控制传统计算机中的比特更具挑战性。直接使用物理量子比特通常只会产生非常短的寿命，因此在执行任何有意义的计算之前，信息就会丢失。幸运的是，我们可以使用量子纠错码来制作一个逻辑量子比特，这种方法使我们能够延长生命期，只要需要完成计算。虽然，我们延长寿命的时间越长，每个逻辑量子位需要的物理量子位就越多。每个逻辑量子位可能需要数百或数千个物理量子位。目前的量子硬件支持不到50个量子比特，因此成本很高。因此，从根本上重新思考我们如何设计量子计算机是一个紧迫的未来问题。传统信息技术系统中最有效的代码是低密度奇偶校验码，并用于所有Wi-Fi网络和移动通信网络。这个理论博士项目将探索不同的方式，这些高效的经典技术可以转换成高效的量子代码。

Errors in quantum computers are unavoidable. Controlling quantum bits (qubits)stored in individual electrons or photons is significantly more challenging thancontrolling bits in traditional computers. Direct use of physical qubits typicallyonly yields very short lifetimes such that information is lost before anymeaningful computation can be executed. Fortunately, we can use quantumerror correcting codes to make a logical qubit that is protected against errors.This approach allows us to extend the lifetime as long as is needed to completea computation. Although, the longer we extend the lifetime the more physicalqubits will be needed per logical qubit. Maybe hundreds or thousands of physicalqubits will be needed per logical qubit. Current quantum hardware supportsfewer than 50 qubits so this cost is substantial. Therefore, a fundamentalrethinking of how we design quantum computers is a pressing near-future issue.The most efficient codes in conventional information technology systems arecalled low-density parity check codes and are used in all Wi-Fi networks andmobile communication networks. This theoretical PhD project will explore thedifferent ways that these highly efficient classical techniques can be convertedinto highly efficient quantum codes.