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arXiv · 2003.02843

Nearly optimal time-independent reversal of a spin chain

Aniruddha Bapat·Eddie Schoute·Alexey V. Gorshkov·Andrew M. Childs
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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 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.

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Aniruddha Bapat, Eddie Schoute, Alexey V. Gorshkov, Andrew M. Childs. 2020-03-05. Nearly optimal time-independent reversal of a spin chain. https://doi.org/10.1103/physrevresearch.4.l012023

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