4 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 N =51 25 N =51 15 25 15 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 N =51 25 N =51 15 25 15  0  0.1  0.2  0.3  0  0.1  0.2  0.3 0 0.1 0.2 0.3 0.4 0.5 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.5 0.6 0.7 0.8 0.9 1 N =51 25 N =51 15 25 15  0  0.1  0.2  0.3  0.5  0.6  0.7  0.8  0.9  1  0  0.1  0.2  0.3 h h J h h h J J J F F h Fidelity > 0.8 > 0.66 > 0.5 > 0.95 > 0.95 > 0.8 > 0.66 > 0.5 > 0.95 > 0.8 (b) (c) (a) (a) (b) (c) > 0.5 > 0.66 FIG. 2: Averaged (over 1000 realizations) fidelity 〈 F 〉 in noisy spin chains for (a) sequential swap , (b) spin-coupling, and (c) adiabatic protocols. Top panel shows the dependence of 〈 F 〉 on the diagonal disorder σ$_{h}$ with σ J = 0 (upper plots), and on the off-diagonal disorder σ J with σ$_{h}$ = 0 (lower plots), for the chains of lengths N = 15 , 25 , 51. Bottom panel shows 〈 F 〉 versus both σ$_{h}$ with σ J in spin chains with N = 25. that for the spin-coupling scheme, related analysis has been performed in [21]. spin chains of length N = 25. In the noiseless chain we have perfect transfer | A$_{N}$ ( t$_{out}$ ) | 2 = 1, while in the pres- ence of diagonal and off-diagonal disorder characterized by standard deviations σ$_{h}$ = σ$_{J}$ = 0 . 15 J$_{max}$ , the aver- aged transfer probabilities are reduced to 〈| A$_{N}$ ( t$_{out}$ ) | $^{2}$〉 ≃ 0 . 2, 0 . 42 and 0 . 96 for the cases of (a), (b) and (c), re- spectively. Thus, among the three transfer protocols, the sequential swap scheme is the most susceptible to noise, especially to the off-diagonal disorder which leads to de- viations of the subsequent pulse areas from the required value of π ; in this particular example, the off-diagonal disorder alone is responsible for at least 70% reduction of the transfer probability. The spin-coupling scheme is somewhat more robust with respect to noise, with both diagonal and off-diagonal disorder comparably contribut- ing to the reduction of the transfer probability by about 20% and 40%, respectively. Finally, the adiabatic trans- fer scheme is very tolerant to noise, as far as the transfer probability is concerned, but is quite slow; in fact it can tolerate even more disorder at the expense of slowing it further down (equivalent to increasing C ). The physical origin of disorder may be two-fold: (i) fabrication imperfections of the particular system realiz- ing the spin chain, and (ii) noise of the external controls, which is assumed to vary slowly enough on the time-scale of state transfer t$_{out}$ , as is typically the case in most experimental situations pertaining to coupled quantum dots [22], superconducting qubits [23] or atoms [24]. We shall distinguish diagonal and off-diagonal disorder. The diagonal disorder corresponds to random on-site energies, or equivalently the local magnetic fields h$_{j}$ , normally dis- tributed around 〈 h$_{j}$ 〉 = 0 with variance σ 2 h (without loss of generality, we assume that the energies of the first and the last sites of the chain are exempt from disor- der, h$_{1}$ = h$_{N}$ = 0, since otherwise the state | ψ 〉 would dephase even before and after the transfer). The off- diagonal disorder introduces randomness in the inter-site coupling strengths J$_{j}$ → J$_{j}$ (1 + δJ$_{j}$ ) where δJ$_{j}$ are nor- mally distributed around 〈 δJ$_{j}$ 〉 = 0 with variance σ 2 $_{J}$. Consistently with the above description, we will treat the disorder as static during each realization of the nu- merical experiment for the particular protocol, but com- pletely uncorrelated between different realizations. The results presented below are obtained by averaging over many (typically 1000) independent realizations. The probability of excitation transfer alone is not enough to fully characterize the state transfer, since, e.g., | A$_{N}$ ( t$_{out}$ ) | 2 = 1 but completely random phase φ amounts to classical information transfer only, and the resulting fidelity for quantum state transfer is merely F = 0 . 66. We will therefore quantify the performance of the sys- tem subject to varying level of noise using fidelity 〈 F 〉 Figure 1 compares the single excitation transfer for the three protocols (a), (b) and (c) in ideal and disordered