Nearly optimal timeindependent reversal of a spin chain
Abstract
We propose a timeindependent Hamiltonian protocol for the reversal of qubit ordering in a chain of N spins. Our protocol has an easily implementable nearestneighbor, transversefield 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), 10.1103/PhysRevA.72.052301] 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 nearestneighbor 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 SWAPbased reversal. Finally, we extend our protocol to an infinite family of nearestneighbor, timeindependent Hamiltonian protocols for state reversal. This includes chains with nearly uniform coupling that may be especially feasible for experimental implementation.
 Publication:

Physical Review Research
 Pub Date:
 February 2022
 DOI:
 10.1103/PhysRevResearch.4.L012023
 arXiv:
 arXiv:2003.02843
 Bibcode:
 2022PhRvR...4a2023B
 Keywords:

 Quantum Physics;
 Physics  Atomic Physics
 EPrint:
 7 pages, 2 figures