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Abstract
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.
Citation
Bapat, A., Schoute, E., Gorshkov, A. V., & Childs, A. M. (2022). “Nearly optimal time-independent reversal of a spin chain”. Physical Review Research, 4(1), L012023.
@article{bapat2022nearly,
title={Nearly optimal time-independent reversal of a spin chain},
author={Bapat, Aniruddha and Schoute, Eddie and Gorshkov, Alexey V and Childs, Andrew M},
journal={Physical Review Research},
volume={4},
number={1},
pages={L012023},
year={2022},
publisher={APS}
}