Nearly optimal time-independent reversal of a spin chain

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, nonuniform 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. We give numerical evidence that the fast reversal protocols are more robust to noise than a SWAP-based reversal. 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.

Automated summary

The study introduces a time-independent Hamiltonian protocol for the reversal of qubit ordering in a chain of spins, achieving faster state reversal than a naive approach using SWAP gates. By proving lower bounds on state reversal using entanglement capacity results, the protocol demonstrates advantages in implementing state reversal and offers extensions to other types of Hamiltonian protocols.