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首页> 外文期刊>Physical Review, A. Atomic, molecular, and optical physics >Optimal control-based efficient synthesis of building blocks of quantum algorithms: A perspective from network complexity towards time complexity
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Optimal control-based efficient synthesis of building blocks of quantum algorithms: A perspective from network complexity towards time complexity

机译：基于最优控制的量子算法构建块的有效综合：从网络复杂度到时间复杂度的视角

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摘要

In this paper, we demonstrate how optimal control methods can be used to speed up the implementation of modules of quantum algorithms or quantum simulations in networks of coupled qubits. The gain is most prominent in realistic cases, where the qubits are not all mutually coupled. Thus the shortest times obtained depend on the coupling topology as well as on the characteristic ratio of the time scales for local controls vs nonlocal (i.e., coupling) evolutions in the specific experimental setting. Relating these minimal times to the number of qubits gives the tightest known upper bounds to the actual time complexity of the quantum modules. As will be shown, time complexity is a more realistic measure of the experimental cost than the usual gate complexity. In the limit of fast local controls (as, e.g., in NMR), time-optimized realizations are shown for the quantum Fourier transform (QFT) and the multiply controlled NOT gate (Cn-1NOT) in various coupling topologies of n qubits. The speed-ups are substantial: in a chain of six qubits the quantum Fourier transform so far obtained by optimal control is more than eight times faster than the standard decomposition into controlled phase, Hadamard and SWAP gates, while the Cn-1NOT gate for a completely coupled network of six qubits is nearly seven times faster.
机译：在本文中，我们演示了如何使用最佳控制方法来加快耦合量子位网络中量子算法或量子模拟模块的实现。在现实情况下，量子位不是全部相互耦合的，增益是最显着的。因此，所获得的最短时间取决于耦合拓扑结构以及在特定实验环境中局部控制与非局部（即，耦合）进化的时间尺度的特征比。将这些最短时间与量子位数量相关联，可以为量子模块的实际时间复杂度提供最严格的已知上限。如将显示的，与通常的门复杂度相比，时间复杂度是对实验成本更现实的度量。在快速局部控制的极限（例如在NMR中）中，显示了n个量子比特的各种耦合拓扑中的量子傅立叶变换（QFT）和多重控制的非门（Cn-1NOT）的时间优化实现。加速是巨大的：到目前为止，在六个量子位的链中，通过最佳控制获得的量子傅里叶变换比标准分解成受控相，Hadamard和SWAP门的标准傅立叶变换快八倍以上，而Cn-1NOT门用于六个量子位完全耦合的网络快了将近七倍。

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