AI 中文总结
ReOC是支持量子控制递归结构的编译框架，可将高级递归预言机规范转为可逆量子程序，通过递归感知非计算策略降低开销，且经证明编译正确。
AI 中文摘要
量子预言机是许多量子算法的核心组件，其规范可能包含依赖运行时量子数据的递归控制流。然而，现有的可逆编译框架对这类量子控制的递归结构支持有限。本文提出ReOC，一个能将带量子控制流的高级递归预言机规范转换为可逆量子程序的编译框架。该框架包含RQIMP——用于指定递归预言机的高级命令式源语言，以及将该语言的程序编译为现有带量子控制流的高级量子递归语言RQC++的方法，从而避免了直接用RQC++编写量子预言机的繁琐且易出错的过程。为在动态量子控制下管理静态存储，ReOC采用索引静态寄存器规范来隔离递归层间的活跃变量，在控制量子存储使用的同时实现安全的寄存器复用。此外，为解决递归场景下朴素非计算导致的指数时间膨胀问题，ReOC采用递归感知非计算策略：递归调用产生的临时变量通过延迟策略清理以控制时间开销，而非递归语句产生的临时变量则立即清理以减少空间使用。对于线性递归，该策略产生的开销与递归深度呈线性关系，参数为每层寄存器占用量和基本操作成本。最后，本文提供从RQIMP到RQC++的编译正确性数学证明，确立了语义保留和临时量子变量的正确非计算。
英文摘要
Quantum oracles are essential to many quantum algorithms, and their specifications may involve recursive control flow that depends on runtime quantum data. However, existing reversible compilation frameworks provide limited support for such quantum-controlled recursive structures. We present ReOC, a compilation framework that transforms high-level recursive oracle specifications with quantum control flow into reversible quantum programs. The framework comprises RQIMP, a high-level imperative source language for specifying recursive oracles, and a method of compiling programs in that language into RQC++, an existing high-level quantum recursive language with quantum control flow. In this way, we avoid the tedious and error-prone process of directly writing quantum oracles in RQC++. To manage static storage under dynamic quantum control, ReOC uses an indexed static-register discipline to isolate live variables across recursion layers, enabling safe register reuse while controlling quantum storage usage. Furthermore, to address the exponential time blow-up caused by naive uncomputation in recursive settings, ReOC employs a recursion-aware uncomputation strategy: temporary variables from recursive calls are cleaned using deferred strategies to control time overhead, while those from non-recursive statements are cleaned eagerly to reduce space usage. For linear recursion, this strategy yields overhead linear in recursion depth, parameterized by the per-layer register footprint and primitive-operation costs. Finally, we provide a mathematical proof of compilation correctness from RQIMP to RQC++, establishing semantic preservation and correct uncomputation of temporary quantum variables.
Comments168 pages, including appendices
