Nearly optimal time-independent reversal of a spin chain

Aniruddha Bapat,Alexey V Gorshkov,Andrew M Childs,Eddie Schoute

doi:10.1103/physrevresearch.4.l012023

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.

Highlights

Quantum information transfer is a fundamental operation in quantum physics, and fast, accurate protocols for transferring quantum states across a physical system are likely to play a key role in the design of quantum computers [1,2]
We show that the execution time of our protocol is nearly optimal, comparable to the time-dependent protocol given in [28]. Through simulations, that these reversal protocols have reduced error scaling in system size to noise due to static disorder caused by imperfect fabrication when compared to a SWAP-based protocol
We give an explicit example of entanglement generated by state reversal and lower-bound the time using the capacity of a normalized two-qubit interaction in canonical form (2), even allowing for local operations and classical communication (LOCC)

Summary

INTRODUCTION

Quantum information transfer is a fundamental operation in quantum physics, and fast, accurate protocols for transferring quantum states across a physical system are likely to play a key role in the design of quantum computers [1,2]. By the signaling lower bound, we incur a time overhead linear in N to correct these phases and implement a reversal for a general state. These limitations were later removed by time-dependent protocols for state reversal [28–30]. We can compare to other time-independent Hamiltonian protocols that use nearest-neighbor interactions: [19] implements state transfer in time Nπ /4 and [25] implements state reversal in time Nπ /2 but introduces relative phases in the state as mentioned earlier. We give an explicit example of entanglement generated by state reversal and lower-bound the time using the capacity of a normalized two-qubit interaction in canonical form (2), even allowing for LOCC.

Proof and analysis of the protocol

Time lower bound

Discussion