Codes, Circuits, and Networks for Modular Quantum Computation

量子纠错(QEC)是大规模量子计算所需的关键技术之一，虽然几种已知的量子算法表明量子计算机可能远远优于普通计算机，但到目前为止QEC还没有得到充分的证明。拟议的研究计划广泛关注量子纠错，涉及相干保护，这是量子计算和量子密码学的关键使能技术。在量子计算中实现可伸缩性是一项复杂的任务，其解决方案可能需要使用不同性质的量子设备用于存储、逻辑和单元之间的通信的模块化方法。为了优化量子纠错码的容错性能，有可能利用这种异质硬件的优点的量子码将被构造并在电路层面上进行分析。它包括代表单节点和多节点量子计算机体系结构的证候测量电路和网络的并行优化，以及相关统计力学模型中的相变分析。这一资金周期的新内容是对不同硬件的关注，特别是将量子比特、量子比特、谐波振荡器和用于通过隐形传态进行纠缠交换的光通信通道相结合的混合基代码的理论。将构建新的码和码族；将分析并利用Clifford测量电路中的错误传播和相关关系来构建近最佳译码方案；将根据相关的统计-机械模型来分析成功译码的概率。构建这种映射到量子计算机实际架构的模型，编码为网络，将允许优化节点大小和可伸缩性所需的节点之间的连接。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Quantum error correction (QEC) is one of the key technologies needed for large-scale quantum computation, and while several known quantum algorithms demonstrate that quantum computers may be far superior to ordinary computers, QEC has not been fully demonstrated thus far. The proposed research program is broadly focused on QEC and concerns coherence protection, the key enabling technology for quantum computation and quantum cryptography. Achieving scalability in quantum computation is a complex task, whose solution may require a modular approach with quantum devices of different nature used for storage, logic, and communication between the units. Quantum codes with the potential to utilize the benefits of such a heterogeneous hardware will be constructed and analyzed at the circuit level to optimize their fault-tolerant performance.In more technical terms, the proposed research targets theory of quantum error-correcting codes operating in a fault-tolerant regime. It includes concurrent optimization of syndrome measurement circuits and networks representing architecture of single- and multi-node quantum computers, and analysis of phase transitions in related statistical-mechanical models. New in this funding cycle is the focus on heterogeneous hardware, in particular, theory of mixed-base codes combining qubits, qudits, harmonic oscillators, and optical communication channels for entanglement exchange via teleportation. New codes and code families will be constructed; error propagation and associated correlations in Clifford measurement circuits will be analyzed and used to construct near-optimal decoding schemes; and the successful decoding probability will be analyzed in terms of associated statistical-mechanical models. Construction of such models mapped to the actual architecture of a quantum computer, encoded as a network, will allow the optimization of the node size and the connectivity between the nodes required for scalability.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.