Two implementations with targeting final distance *L* = 11*L*_{0} and fidelity *F*_{final} = 0.976, by using the CTSL scheme. Each storage qubit is represented by ∗. All of the relevant entangled states are shown. The order to produce these entangled states is from bottom to top; states on the same row can be produced simultaneously. The two kinds of entangled states are: purified entangled states (type A, solid black line) and unpurified entangled states (type B, dashed blue line). On the left side of each purified entangled state, there is a label “A*k*,” where the number *k* indicates that this purified entangled state is obtained from *k* steps of entanglement pumping. (*a*) The unoptimized (*Left*) implementation has three pumping steps after each entanglement connection, with average time of ≈11 sec to produce the pair wanted. (*b*) The optimized (*Right*) implementation is from optimization over pair-generation time, connection position, and the number of pumping steps. The optimized choice of connection position does not necessarily break the long pair into two almost identical shorter pairs; for example, the entangled state to which the black arrow points in the ninth row is obtained by connecting two very different shorter pairs in the row below. In addition, the possibility of multilevel pumping is also taken into account during the dynamic programming. As pointed out by the red arrows, the pair of storage qubits in the third row pumps the pair in the second row, and the latter pumps the pair in the first row. The average time is ≈1.5 sec for the optimized implementation, about 8 times faster than the unoptimized one.

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