  We propose a time-independent Hamiltonian protocol for the reversal of qubit
ordering in a chain of $N$ spins. Our protocol has an easily implementable
nearest-neighbor, transverse-field Ising model Hamiltonian with
time-independent, non-uniform couplings. Under appropriate normalization, we
implement this state reversal three times faster than a naive approach using
SWAP gates, in time comparable to a protocol of Raussendorf [Phys. Rev. A 72,
052301 (2005)] that requires dynamical control. We also prove lower bounds on
state reversal by using results on the entanglement capacity of Hamiltonians
and show that we are within a factor $1.502(1+1/N)$ of the shortest time
possible. Our lower bound holds for all nearest-neighbor qubit protocols with
arbitrary finite ancilla spaces and local operations and classical
communication. Finally, we extend our protocol to an infinite family of
nearest-neighbor, time-independent Hamiltonian protocols for state reversal.
This includes chains with nearly uniform coupling that may be especially
feasible for experimental implementation.
