论文标题
通过简单的成对交互实施量子粉丝操作
Implementing the quantum fanout operation with simple pairwise interactions
论文作者
论文摘要
已经表明，即使对于$ n $，根据哈密顿量的$ n $ Qubits的发展，这是粒子之间成对交互的总和，可用于精确实现$（n+1）$ - 使用特定的常数deptth电路[arxiv：arxiv：part-ph/0309163]。但是，假定该论文中考虑的哈密顿量的耦合系数被认为是相等的。在本文中，我们概括了这些结果并表明，对于所有$ n $，包括奇数$ n $，一个人都可以实现$（n+1）$ - Qubit Parity门，因此，使用类似的汉密尔顿（Hamiltonian）等同于$（n+1）$ - Qubit fanout Gate，但使用类似的汉密尔顿（Hamiltonian），但具有不平等的couplings，我们可以通过couplate couplate couplate coupleant coupleant coupleant and coupleant and coupleant and couplet and couplet。 我们还调查了满足逆平方定律的成对耦合，并给出了在遵守该法律的两个和三个维度的相同量子位的空间安排的必要和足够的标准。我们使用我们的标准为四个量子位的平面安排（与目标值一起）足以实施$ 5 $ qubit的粉丝。
It has been shown that, for even $n$, evolving $n$ qubits according to a Hamiltonian that is the sum of pairwise interactions between the particles, can be used to exactly implement an $(n+1)$-qubit fanout gate using a particular constant-depth circuit [arXiv:quant-ph/0309163]. However, the coupling coefficients in the Hamiltonian considered in that paper are assumed to be all equal. In this paper, we generalize these results and show that for all $n$, including odd $n$, one can exactly implement an $(n+1)$-qubit parity gate and hence, equivalently in constant depth an $(n+1)$-qubit fanout gate, using a similar Hamiltonian but with unequal couplings, and we give an exact characterization of which couplings are adequate to implement fanout via the same circuit. We also investigate pairwise couplings that satisfy an inverse square law, giving necessary and sufficient criteria for implementing fanout given spatial arrangements of identical qubits in two and three dimensions subject to this law. We use our criteria to give planar arrangements of four qubits that (together with a target qubit) are adequate to implement $5$-qubit fanout.
