Quantum algorithms promise quadratic or exponential speedups for applications in cryptography, chemistry and material sciences. The topologies of today's quantum computers offer limited connectivity, leading to significant overheads for implementing such quantum algorithms. One-dimensional topology displacements that remedy these limits have been recently demonstrated for architectures based on Rydberg atoms, and they are possible in principle in photonic and ion trap architectures. We present the first optimal quantum circuit-to-architecture mapping algorithm that exploits such one-dimensional topology displacements. We benchmark our method on quantum circuits with up to 15 qubits and investigate the improvements compared with conventional mapping based on inserting swap gates into the quantum circuits. Depending on underlying technology parameters, our approach can decrease the quantum circuit depth by up to 58% and increase the fidelity by up to 29%. We also study runtime and fidelity requirements on one-dimensional displacements and swap gates to derive conditions under which one-dimensional topology displacements provide benefits.

中文翻译：

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基于里德堡原子的近期量子体系结构的最优映射

量子算法有望在密码学、化学和材料科学领域的应用中实现二次或指数加速。当今量子计算机的拓扑结构提供有限的连接性，导致实现此类量子算法的开销很大。最近已经在基于里德堡原子的架构中证明了弥补这些限制的一维拓扑位移，并且它们在光子和离子阱架构中原则上是可能的。我们提出了第一个利用这种一维拓扑位移的最优量子电路到架构映射算法。我们在多达 15 个量子位的量子电路上对我们的方法进行了基准测试，并研究了与基于将交换门插入量子电路的传统映射相比的改进。根据底层技术参数，我们的方法可以将量子电路深度降低多达 58%，并将保真度提高多达 29%。我们还研究了一维位移和交换门的运行时间和保真度要求，以推导出一维拓扑位移提供好处的条件。