具有延迟轨迹的图形语言：描绘有限存储的量子计算
Graphical Language with Delayed Trace: Picturing Quantum Computing with Finite Memory
摘要：
图形语言，如量子线路或ZX演算，已经成功地设计用于表示作用于有限数量量子位的（无记忆）量子计算。与此同时，延迟跟踪已被用作一种图形化的方式来表示流上的有限内存计算，在经典的设置中（carpet数据类型）。我们合并这两种方法，并描述了一个一般的建设，扩展任何图形语言，配备了丢弃的概念，有限内存计算的图形语言。为了处理像ZX演算的情况下，这是完整的后选择的量子力学，我们扩展了延迟跟踪形式主义超越因果关系的情况下，完善的因果关系流Transformers的概念。我们设计了一个基于状态态射序列的流语义，并在一定的假设下，证明了它的普适性和完备性。最后，我们调查的链接，我们的框架与以前的工作carbohydrate数据类型，信号流图，和量子信道与内存。
英文摘要：
Graphical languages, like quantum circuits or ZX-calculus, have been successfully designed to represent (memoryless) quantum computations acting on a finite number of qubits. Meanwhile, delayed traces have been used as a graphical way to represent finite-memory computations on streams, in a classical setting (cartesian data types). We merge those two approaches and describe a general construction that extends any graphical language, equipped with a notion of discarding, to a graphical language of finite memory computations. In order to handle cases like the ZX-calculus, which is complete for post-selected quantum mechanics, we extend the delayed trace formalism beyond the causal case, refining the notion of causality for stream transformers. We design a stream semantics based on stateful morphism sequences and, under some assumptions, show universality and completeness results. Finally, we investigate the links of our framework with previous works on cartesian data types, signal flow graphs, and quantum channels with memories.
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