  A strongly coupled spin chain can mediate long-distance effective couplings
or entanglement between remote qubits, and can be used as a quantum data bus.
We study how the fidelity of a spin-1/2 Heisenberg chain as a spin bus is
affected by static random exchange couplings and magnetic fields. We find that,
while non-uniform exchange couplings preserve the isotropy of the qubit
effective couplings, they cause the energy levels, the eigenstates, and the
magnitude of the couplings to vary locally. On the other hand, random local
magnetic fields lead to an avoided level crossing for the bus ground state
manifold, and cause the effective qubit couplings to be anisotropic.
Interestingly, the total magnetic moment of the ground state of an odd-size bus
may not be parallel to the average magnetic field. Its alignment depends on
both the direction of the average field and the field distribution, in contrast
with the ground state of a single spin which always aligns with the applied
magnetic field to minimize the Zeeman energy. Lastly, we calculate
sensitivities of the spin bus to such local variations, which are potentially
useful for evaluating decoherence when dynamical fluctuations in the exchange
coupling or magnetic field are considered.
