of Eq. (3) averaged over many independent realizations of protocols (a), (b) and (c). Figure 2 summarizes the results of our numerical simulations for the chains of lengths N = 15, 25 and 51. Unsurprisingly, the longer the chain the lower the fidelity of the state transfer. We find that, for the same values of diagonal σ$_{h}$ and/or off- diagonal σ$_{J}$ disorder, the sequential swap scheme yields lower fidelity than the spin-coupling scheme. Moreover, both schemes are somewhat more susceptible to the off- diagonal disorder. The behavior of the fidelity for the adi- abatic transfer scheme is, however, profoundly different: it is very robust with respect to the off-diagonal disorder σ$_{J}$ , but much more sensitive to the diagonal disorder σ$_{h}$ : already for σ$_{h}$ > ∼ 0 . 1 the fidelity 〈 F 〉 ≃ 0 . 66 (but then decreases slowly with increasing σ$_{h}$ ). This is despite the fact that the transfer probability 〈| A$_{N}$ ( t$_{out}$ ) | $^{2}$〉 remains above 0 . 9 up to σ$_{h,J}$ < ∼ 0 . 28, i.e., the excitation transfer is very efficient up to large values of both diagonal and off-diagonal disorder. The adiabatic transfer protocol is so sensitive to diagonal disorder because it is slow: during the long transfer time t$_{out}$ even little noise in the on-site energies σ$_{h}$ accumulates to large random phase φ spread over σ$_{φ}$ ∼ σ$_{h}$t$_{out}$ . 

We have critically examined the state and excitation transfer in disordered spin chains using the sequential 

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## IV. CONCLUSIONS 

swap , spin-coupling and adiabatic transfer protocols. We have found that, depending on the character of disor- der, namely the diagonal disorder corresponding to ran- dom on-site energies (or magnetic filed) or off-diagonal disorder leading to variations in inter-site couplings, ei- ther the fast spin-coupling protocol or the slow adiabatic transfer protocol is more suitable for high-fidelity trans- fer of quantum states between the two ends of the spin chain. 

Reliable quantum channels, based on, e.g., spin chains, are indispensable for achieving scalable and efficient quantum information processing in solid-state systems with fixed qubit positions and finite-range inter-qubit in- teractions. Our results therefore have important impli- cations for attaining scalability in such systems. 

This work was supported by the EC Marie Curie Research-Training Network EMALI (MRTN-CT-2006- 035369). 

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## Acknowledgments 

