论文标题
量子路由的优势和局限性
Advantages and limitations of quantum routing
论文作者
论文摘要
交换门是用于移动量子硬件信息的无处不在的工具，但是可以将其视为经典操作，因为它不纠缠产品状态。真正的量子操作可以胜过将Qubits在体系结构中置于架构的任务，我们称之为路由。我们考虑在两个模型中考虑量子路由：（1）允许任意的两数分位数，或（2）允许具有标准相互作用的汉密尔顿人。我们根据代表体系结构交互约束的图的光谱属性来降低量子深度或量子路由的时间，并为所有简单连接的$ n $ vertex图提供了广义上限。特别是，我们提供了超多种经典 - 量词路由分离的条件，该路由分离排除了较小的光谱间隙和界图的图。最后，我们提供了基于门的和哈密顿路由模型之间二次分离的示例，如果我们还允许快速的本地交互，则具有恒定数量的每个量子局部数量的局部Ancillas和$ω（n）$加速。
The Swap gate is a ubiquitous tool for moving information on quantum hardware, yet it can be considered a classical operation because it does not entangle product states. Genuinely quantum operations could outperform Swap for the task of permuting qubits within an architecture, which we call routing. We consider quantum routing in two models: (1) allowing arbitrary two-qubit unitaries, or (2) allowing Hamiltonians with norm-bounded interactions. We lower bound the circuit depth or time of quantum routing in terms of spectral properties of graphs representing the architecture interaction constraints, and give a generalized upper bound for all simple connected $n$-vertex graphs. In particular, we give conditions for a superpolynomial classical-quantum routing separation, which exclude graphs with a small spectral gap and graphs of bounded degree. Finally, we provide examples of a quadratic separation between gate-based and Hamiltonian routing models with a constant number of local ancillas per qubit and of an $Ω(n)$ speedup if we also allow fast local interactions.
