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上级普通计算机，但迄今为止QEC尚未得到充分证明。拟议的研究计划主要集中在QEC和相干性保护，这是量子计算和量子密码学的关键使能技术。实现量子计算的可扩展性是一项复杂的任务，其解决方案可能需要模块化方法，其中不同性质的量子设备用于单元之间的存储，逻辑和通信。量子码有可能利用这种异构硬件的好处，将在电路级构建和分析，以优化其容错性能。在更多的技术术语中，拟议的研究目标是量子纠错码在容错机制中运行的理论。它包括并发优化的综合征测量电路和网络代表单节点和多节点量子计算机的架构，并在相关的物理力学模型的相变分析。这个资金周期的新重点是异构硬件，特别是混合基码理论，它结合了量子比特、量子点、谐振子和光通信信道，通过隐形传态进行纠缠交换。新的代码和代码的家庭将被构造;错误传播和相关的Clifford测量电路将被分析和用于构建近最佳的解码方案;和成功的解码概率将被分析在相关的物理力学模型。 构建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扩展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.