[论文解读] Advances in compilation for quantum hardware -- A demonstration of magic state distillation and repeat-until-success protocols

Natalie C. Brown, John Peter Campora+9 more|arXiv (Cornell University)|Oct 18, 2023

Quantum Computing Algorithms and Architecture被引用 4

一句话总结

本论文首次在量子硬件上实现了基于量子中间表示（QIR）的实时魔态蒸馏与重复-成功（RUS）协议。结果表明，QIR能够高效编译复杂的容错量子程序，性能接近手工优化的汇编代码，通过LLVM工具链优化了量子-经典控制流与循环展开，适用于纠错协议。

ABSTRACT

Fault-tolerant protocols enable large and precise quantum algorithms. Many such protocols rely on a feed-forward processing of data, enabled by a hybrid of quantum and classical logic. Representing the control structure of such programs can be a challenge. Here we explore two such fault-tolerant subroutines and analyze the performance of the subroutines using Quantum Intermediate Representation (QIR) as their underlying intermediate representation. First, we look at QIR's ability to leverage the LLVM compiler toolchain to unroll the quantum iteration logic required to perform magic state distillation on the $[[5,1,3]]$ quantum error-correcting code as originally introduced by Bravyi and Kitaev [Phys. Rev. A 71, 022316 (2005)]. This allows us to not only realize the first implementation of a real-time magic state distillation protocol on quantum hardware, but also demonstrate QIR's ability to optimize complex program structures without degrading machine performance. Next, we investigate a different fault-tolerant protocol that was first introduced by Paetznick and Svore [arXiv:1311.1074 (2013)], that reduces the amount of non-Clifford gates needed for a particular algorithm. We look at four different implementations of this two-stage repeat-until-success algorithm to analyze the performance changes as the results of programming choices. We find the QIR offers a viable representation for a compiled high-level program that performs nearly as well as a hand-optimized version written directly in quantum assembly. Both of these results demonstrate QIR's ability to accurately and efficiently expand the complexity of fault-tolerant protocols that can be realized today on quantum hardware.

研究动机与目标

• 通过将高级量子程序编译为高效可执行形式，实现在当前噪声硬件上的容错量子协议实用化。
• 评估QIR作为中间表示在表达容错程序中混合量子-经典控制逻辑的有效性。
• 对比不同高级实现的RUS协议，评估其在电路深度与资源使用方面的性能权衡。
• 证明QIR可在保持性能的同时，支持对魔态蒸馏等复杂迭代量子算法的优化。

提出的方法

• 使用QIR与LLVM工具链编译魔态蒸馏，实现对迭代逻辑测量与重置的循环展开与优化。
• 通过Q#与QIR实现实时测量结果反馈，实现Bravyi-Kitaev [[5,1,3]]代码的魔态蒸馏。
• 以四种逻辑等价的QIR表示表达Paetznick-Svore RUS协议，以分析性能差异。
• 利用QIR表示并优化混合量子-经典控制结构，包括条件重置与递归循环。
• 将高级Q#代码编译为QIR，经优化后在离子阱量子硬件上执行，并支持实时经典反馈。
• 将编译后的QIR版本与手工优化的量子汇编进行基准测试，评估其在电路深度与保真度方面的性能一致性。

实验结果

研究问题

• RQ1 QIR能否有效表示并优化魔态蒸馏所需的迭代性、经典控制逻辑？
• RQ2 QIR编译的魔态蒸馏在真实硬件上的性能与手工优化的量子汇编相比如何？
• RQ3 通过QIR编译时，不同高级实现的RUS协议在性能上存在哪些权衡？
• RQ4 LLVM工具链在优化以QIR表达的复杂容错量子程序方面能达到何种程度？
• RQ5 QIR能否支持容错子程序的实时执行与经典前馈控制，以满足纠错协议需求？

主要发现

• 基于QIR的编译栈成功实现了离子阱量子硬件上魔态蒸馏的首次实时执行，性能与手工优化汇编相当。
• 通过QIR与LLVM实现的循环展开显著提升了性能，消除了迭代蒸馏循环中的运行时开销。
• QIR表示在保留RUS协议逻辑结构的同时，支持优化并降低了多个实现版本的电路深度。
• 四种不同的RUS算法QIR表示显示出可测量的性能差异，表明高级编程选择显著影响最终电路效率。
• QIR能够准确建模容错协议中的经典前馈控制，证明其适用于复杂混合量子-经典工作负载。
• 本研究证实，QIR是一种稳健的中间表示，能够以极小的性能损失表达并优化先进的容错量子算法。