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arXiv:1903.11419 · Quantum Information Processing

Robust and efficient transport of two-qubit entanglement via disordered spin chains

Rafael Vieira, Gustavo Rigolin

Published Mar 23, 2019• 11 citations
arXivHTMLPDF
DOI
10.1007/s11128-019-2254-1

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Quantum state transfer in the presence of static disorder and noise is one of the main challenges in building quantum computers. We compare the quantum state transfer properties for two classes of qubit chains under the influence of static disorder. In fully engineered chains all nearest-neighbor couplings are tuned in such a way that a single-qubit state can be transferred perfectly between the ends of the chain, while in chains with modified boundaries only the two couplings between the transmitting and receiving qubits and the remainder of the chain can be optimized. We study how the disorder in the couplings affects the state transfer fidelity depending on the disorder model and strength as well as the chain type and length. We show that the desired level of fidelity and transfer time are important factors in designing a chain. In particular we demonstrate that transfer efficiency comparable or better than that of the most robust engineered systems can also be reached in chains with modified boundaries without the demanding engineering of a large number of couplings.
Using a numerically exact technique we study spin transport and entanglement growth in the delocalized phase of a disordered spin chain with long-range interactions, decaying as a power law, ${r}^{\ensuremath{-}\ensuremath{\alpha}}$ with distance. For all considered $\ensuremath{\alpha}$'s and disorder strengths we find that the entanglement entropy grows sublinearly, and the underlying transport is subdiffusive. Since rare-blocking regions, which are central to the Griffiths theory of transport in disordered interacting systems, can be easily circumvented by long-range hops across the lattice, they cannot explain the mechanism of slow transport in long-range systems. Specifically, we show that for long-range systems the Griffiths theory predicts diffusive transport, which is inconsistent with our results.
We examine the transport of useful energy, i.e., extractable work as quantified by the ergotropy, along a spin chain with tunable exchange couplings between the sites. We focus on, and interpolate between, the two physically relevant limits of uniform interaction strengths and engineered couplings which achieve perfect state transfer (PST). By modeling the individual constituents as quantum batteries, we consider how the manner in which the extractable work appears in the initial state of the first site impacts the chain's ability to transport ergotropy to the final site. For non-PST couplings, we establish that there is a clear quantum advantage when the ergotropy is initially endowed in quantum coherences and demonstrate that this ergotropy is more efficiently transferred. For extractable work encoded in a population inverted state, we show that this considerably limits the length of chain over which any ergotropy can be faithfully transported. For PST couplings, we consider the robustness to disorder and again demonstrate a quantum advantage for coherently endowed ergotropy. Finally, we examine the work probability distribution associated with quenching on the interactions, which provides insight into the work cost in switching on the couplings. We show that PST couplings lead to smaller fluctuations in this work cost, indicating that they are more stable.