EAGER: QIA: Optimal Synthesis Algorithms for Few-Qubit Fault-Tolerance

开发快速高效的量子编译工具对于将量子计算能力的理论收益转化为现实世界的性能至关重要。寻找稳健的技术将量子算法编译成最短的标准通用量子门序列，对量子计算的近期和长期都有深远的影响。在目前或不久的将来可用的量子硬件的短期内，电路长度的一半可能意味着计算任务的成功与失败之间的差异。从长远来看，这些技术使容错计算成为可能，这需要对庞大而复杂的电路进行优化。实现这一目标的最可行的方法是将一个大电路分解成几个量子位的子电路，在这种情况下，电路长度的减少即使只是一个常数因素，也会表现为计算性能的指数级提高。虽然单量子位电路的最佳算法已经被很好地理解，但目前的努力主要集中在解决双量子位电路的最佳编译问题。实现这一重要的里程碑，导致进一步应用于更大的电路依赖于跨学科专业知识的融合努力，吸引本科生和研究生水平的研究和教育计划，以及工业合作者的参与。这里要解决的一般量子编译问题如下：给定一个表示计算算法操作的酉矩阵和一组通用量子门，找到一个与酉矩阵等效的门序列（称为精确合成）或在所需精度范围内近似于酉矩阵（称为不精确合成）。最有效的编译器是通过最小化给定成本指标（如门数）来优化的电路合成算法，特别是对于难以以容错方式实现的门。利用基于数论和矩阵分解的技术，可以实现精确和不精确合成的双量子位电路的最优或至少接近最优算法。据估计，栅极计数可以减少一个常数因子，范围约为1~10。两种情况下的算法都具有独立的值，并且彼此互补。它们可以同时探索，也可以独立完成。此外，这些算法可以成为构建更大量子位数电路合成技术的基础。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。

Developing fast and efficient quantum compiling tools is critical to translate theoretical gains in quantum computation power to real world performance. Finding robust techniques to compile a quantum algorithm into the shortest sequence of standard universal quantum gates has profound impact to quantum computation in both near and long term. In the near term with the quantum hardware available currently or in the near future, halving the circuit lengths can mean the difference between success and failure of a computation task. In the long term, these techniques make fault-tolerant computing possible, which requires optimization of vast, complex circuits. The most viable approach to achieve this goal is to break up a large circuit into few-qubit subcircuits where reduction of the circuit length even merely by a constant factor manifests as an exponential improvement in computation performance. While optimal algorithms for single-qubit circuits have been well-understood, current efforts focus on solving the optimal compiling problem of two-qubit circuits. Achievement of this important milestone leading to further applications to larger circuits relies on a convergent effort with cross-disciplinary expertise, engaging students at both undergraduate and graduate levels in research and education programs, and participation of industrial collaborators.The general quantum compiling problem being addressed here is as follows: given some unitary matrix representing the operation of a computation algorithm and a universal set of quantum gates, find a sequence of gates that either is equivalent to the unitary matrix (called exact synthesis) or approximates the unitary matrix within a desired precision (called inexact synthesis). The most efficient compiler is a circuit synthesis algorithm optimized by minimization of a given cost-metrics, such as the gate-count, especially for the gates that are difficulty to implement in a fault-tolerance manner. Optimal or at least nearly-optimal algorithms of two-qubit circuits for exact and inexact synthesis are achievable utilizing techniques based on number theory and matrix decomposition. It is estimated that the gate-count can be reduced by a constant-factor ranging roughly 1~10. Algorithms for either case have stand along values and are complementary to each other. They can be explored simultaneously and completed independently. Furthermore, these algorithms can be the basis to build synthesis techniques for even larger qubit-number circuits.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.