FET: Small: Improving Quantum Computing and Classical Communication using Discrete Sets of Unitary Matrices

量子计算机有望比任何经典计算机更有能力解决某些问题，这些设备正在走出实验室，变得普遍可编程。 量子比特的不同物理实现具有相当不同的优点和缺点，在设计量子计算机时必须考虑这些特性。 这个项目使用捕获离子量子比特的错误特性来调整算法设计和硬件实现这种物理架构。该研究计划结合了抽象数学，量子物理学和信号处理;它是高度跨学科的。 在工程物理和信号处理接口的研究经验将为学生提供在学术界或工业界建立这些学科之间的桥梁所需的技能。 在GitHub上发布的代码将鼓励不同的研究社区使用。该项目将设计新的算法，优化作用于编码量子位的逻辑运算符的实现，并使用捕获离子量子位的错误特性来选择适合该架构的实现。 第一阶段将开发用于操纵泡利算子的工具，包括稳定器组（带符号），Clifford算子和由环上的对称矩阵表示的对角门。 开发的软件将与常用的量子电路优化软件兼容。第二阶段将实施有效的算法来合成支持横向小角度旋转的稳定器代码。该奖项反映了NSF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 computers promise to be more capable than any classical computer at solving certain problems and these devices are moving out of the lab and becoming generally programmable. The different physical implementations of qubits have quite different strengths and weaknesses, and it is essential to consider these characteristics when designing a quantum computer. This project uses the error characteristics of trapped-ion qubits to align algorithm design and hardware implementation for this physical architecture. The research program combines abstract mathematics, quantum physics, and signal processing; it is highly interdisciplinary. Research experience at the interface of engineering physics and signal processing will provide students with the skills needed to build bridges between these disciplines in either academia or industry. Code released on GitHub will encourage use by different research communities.This project will design new algorithms that optimize the realization of logical operators acting on encoded qubits, and that use the error characteristics of trapped-ion qubits to choose appropriate realizations for this architecture. Phase 1 will develop tools for manipulating Pauli operators, including stabilizer groups (with signs), Clifford operators, and diagonal gates represented by symmetric matrices over rings. The software that is developed will be compatible with commonly used software for quantum circuit optimization. Phase 2 will implement efficient algorithms to synthesize stabilizer codes that support transversal small-angle rotations.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.