Perfect state transfer on weighted graphs of the Johnson scheme
Perfect state transfer on weighted graphs of the Johnson scheme
复制标题
约翰逊方案加权图上的完美状态转移
DOI：
10.1007/s11005-020-01298-6
复制
发表时间：
2019
影响因子：
1.2
通讯作者：
Hanmeng Zhan
中科院分区：
文献类型：
--
作者：
L. Vinet;Hanmeng Zhan
我们刻画了约翰逊方案J（n，k）J（n，k）的实加权图上的量子完美态转移，该方案表示具有非最近邻耦合的自旋网络.给定J（n，k）={A_1，A_2，.，Ak J（n，k）= A1，A2，.，Ak和A（X）= w0A0 + wm + wmAmA（X）= w0A0 + wm + wmAmX在τ τ时刻有完全态转移当且仅当n = 2kn = 2k，m ≥ 2 ^n\log2（k）<$m ≥ 2 <$log2（k）<$m，且存在整数c1，c2，..., c_m c 1，c 2，.，cm使得（i）c_j cj是奇数当且仅当j是2的幂，以及（ii）对于r = 1，2，.，m r = 1，2，...，m，w_r = π τ ∑_j = r ^m c_j\left（（）. wr = π τ ∑ j = rmcj 2 jjk-rj-r。然后，我们刻画了J（n，k）J（n，k）的无权图上的完美状态转移。特别地，我们得到了一个简单的构造，它生成了J（n，k）J（n，k）在时间π/2 π/2处具有完美状态转移的所有图。
We characterize quantum perfect state transfer on real-weighted graphs of the Johnson scheme J (n, k) J (n, k), which represent spin networks with non-nearest neighbor couplings. Given J (n, k)={A_ 1, A_ 2, ..., A_ k\} J (n, k)= A 1, A 2,…, A k and A (X)= w_0A_0+ ⋯+ w_m A_m A (X)= w 0 A 0+⋯+ wm A m, we show that X has perfect state transfer at time τ τ if and only if n= 2k n= 2 k, m ≥ 2^ ⌊\log _2 (k) ⌋ m≥ 2⌊ log 2 (k)⌋, and there are integers c_ 1, c_ 2, ..., c_ m c 1, c 2,…, cm such that (i) c_j cj is odd if and only if j is a power of 2, and (ii) for r= 1, 2, ..., m r= 1, 2,…, m, w_r= π τ ∑ _ j= r^ m c_j\left ((). wr= π τ∑ j= rmcj 2 jjk-rj-r. We then characterize perfect state transfer on unweighted graphs of J (n, k) J (n, k). In particular, we obtain a simple construction that generates all graphs of J (n, k) J (n, k) with perfect state transfer at time π/2 π/2.