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，虽然一些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QEC迄今尚未得到充分证明。提出的研究计划广泛关注量子计算和量子加密的关键使能技术相干保护。在量子计算中实现可扩展性是一项复杂的任务，其解决方案可能需要采用模块化方法，使用不同性质的量子器件用于存储、逻辑和单元之间的通信。量子码具有利用这种异构硬件优势的潜力，将在电路级构建和分析，以优化其容错性能。在更专业的术语中，提出的研究目标是在容错制度下运行的量子纠错码理论。它包括表征单节点和多节点量子计算机体系结构的综合征测量电路和网络的并发优化，以及相关统计力学模型中的相变分析。这个资金周期的新亮点是关注异构硬件，特别是结合量子比特、量子比特、谐波振荡器和通过隐形传态进行纠缠交换的光通信信道的混合基码理论。新的代码和代码族将被构建；将分析Clifford测量电路中的误差传播和相关关系，并用于构建接近最优的解码方案；并根据相关的统计力学模型对解码成功概率进行分析。这种模型的构建映射到量子计算机的实际架构，编码为网络，将允许优化节点大小和可扩展性所需的节点之间的连接。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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.