  Coherent coupling between distant qubits is needed for any scalable quantum
computing scheme. In quantum dot systems, one proposal for long-distance
coupling is to coherently transfer electron spins across a chip in a moving
potential. Here, we use simulations to study challenges for spin shuttling in
Si/SiGe heterostructures caused by the valley degree of freedom. We show that
for devices with valley splitting dominated by alloy disorder, one can expect
to encounter pockets of low valley splitting, given a long-enough shuttling
path. At such locations, inter-valley tunneling leads to dephasing of the spin
wavefunction, substantially reducing the shuttling fidelity. We show how to
mitigate this problem by modifying the heterostructure composition, or by
varying the vertical electric field, the shuttling velocity, the shape and size
of the dot, or the shuttling path. We further show that combinations of these
strategies can reduce the shuttling infidelity by several orders of magnitude,
putting shuttling fidelities sufficient for error correction within reach.
