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成果转化为现实世界的性能至关重要。寻找健壮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，在量子硬件可用的短期内，电路长度减半可能意味着计算任务的成功和失败之间的差异。从长远来看，这些技术使容错计算成为可能，这需要对庞大、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比特子电路，其中电路长度的减少，即使只是一个恒定系数，也表现为计算性能的指数级改进。虽然单量子比特电路的优化算法已经广为人知，但目前的努力主要集中在解决两量子比特电路的优化编译问题上。这一重要里程碑的实现将进一步应用于更大的电路，这依赖于具有跨学科专业知识的收敛努力，吸引本科生和研究生参与研究和教育计划，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：给定表示计算算法操作的某个酉矩阵和一组通用量子门，找到一个门序列，该序列要么等价于酉阵(称为精确综合)，要么在期望的精度内近似酉阵(称为非精确综合法)。最有效的编译器是通过最小化给定的成本度量优化的电路综合算法，例如门计数，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两个量子比特电路的最优或至少接近最优的算法。据估计，门计数可以减少大约1~10个常数倍。两种情况下的算法都有各自的取值范围，并且是互补的。它们可以同时探索，也可以独立完成。此外，这些算法可以作为构建更大量子比特数电路的综合技术的基础。这一奖项反映了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。

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.