Nearly optimal time-independent reversal of a spin chain
Aniruddha Bapat, Eddie Schoute, Alexey Vyacheslavovich Gorshkov, Andrew M. Childs · Physical Review Research · 2022
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 timeindependent, 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.