论文标题
与PBS-Calculus相干控制的量子计算的资源优化
Resource Optimisation of Coherently Controlled Quantum Computations with the PBS-calculus
论文作者
论文摘要
量子计算的相干控制可用于改善某些量子方案和算法。例如，可以通过允许连贯的控制而不是使用标准量子电路模型来严格降低某些给定统一转换的置换的复杂性。在本文中，我们解决了优化相干控制量子计算资源的问题。我们完善了PBS-Calculus，这是一种具有量子光学启发的相干控制的图形语言。为了获得更重要的语言，它操纵抽象门（可以解释为对甲骨文的查询），更重要的是，它可以通过允许不饱和极化光束拆分器来避免无用电线的表示。从技术上讲，语言形成了彩色道具。该语言配备了一种方程理论，我们表明是合理的，完整和最小的。 关于资源优化，我们引入了一个有效的过程，以最大程度地减少给定图的甲骨文查询数量。我们还考虑了最小化甲骨文查询数量和偏振梁拆分器的数量的问题。我们表明，这个优化问题通常是NP-HARD，但是引入了一种有效的启发式方法，当需要对每个Oracle的一个查询时，它最多可以产生最佳图。
Coherent control of quantum computations can be used to improve some quantum protocols and algorithms. For instance, the complexity of implementing the permutation of some given unitary transformations can be strictly decreased by allowing coherent control, rather than using the standard quantum circuit model. In this paper, we address the problem of optimising the resources of coherently controlled quantum computations. We refine the PBS-calculus, a graphical language for coherent control which is inspired by quantum optics. In order to obtain a more resource-sensitive language, it manipulates abstract gates -- that can be interpreted as queries to an oracle -- and more importantly, it avoids the representation of useless wires by allowing unsaturated polarising beam splitters. Technically the language forms a coloured prop. The language is equipped with an equational theory that we show to be sound, complete, and minimal. Regarding resource optimisation, we introduce an efficient procedure to minimise the number of oracle queries of a given diagram. We also consider the problem of minimising both the number of oracle queries and the number of polarising beam splitters. We show that this optimisation problem is NP-hard in general, but introduce an efficient heuristic that produces optimal diagrams when at most one query to each oracle is required.
