The Heisenberg representation of quantum operators provides a powerful technique for reasoning about quantum circuits, albeit those restricted to the common (non-universal) Clifford set H, S and CNOT. The Gottesman-Knill theorem showed that we can use this representation to efficiently simulate Clifford circuits. We show that Gottesman's semantics for quantum programs can be treated as a type system, allowing us to efficiently characterize a common subset of quantum programs. We also show that it can be extended beyond the Clifford set to partially characterize a broad range of programs. We apply these types to reason about separable states and the superdense coding algorithm.

中文翻译：

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量子程序的戈特斯曼类型

量子算子的海森堡表示提供了一种强大的技术来推理量子电路，尽管这些技术仅限于常见的（非通用）克利福德集 H、S 和 CNOT。Gottesman-Knill 定理表明我们可以使用这种表示来有效地模拟 Clifford 电路。我们表明，Gottesman 的量子程序语义可以被视为一个类型系统，使我们能够有效地表征量子程序的公共子集。我们还表明，它可以扩展到 Clifford 集之外，以部分表征广泛的程序。我们将这些类型应用于可分离状态和超密集编码算法的推理。