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arXiv:1212.2565 · Journal of Physics A Mathematical and Theoretical

Noise-assisted quantum transport and computation

Diego de Falco, Dario Tamascelli

Published May 13, 2013• 23 citations
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Abstract

The transmission of an excitation along a spin chain can be hindered by the presence of small fixed imperfections that create trapping regions where the excitation may get caught (Anderson localization). A certain degree of noise, ensuing from the interaction with a thermal bath, allows us to overcome localization (noise-assisted transport). In this paper, we investigate the relation between the noise-assisted transport and (quantum) computation. In particular, we prove that noise does assist classical computation on a quantum computing device, but hinders the possibility of creating entanglement.

DOI
10.1088/1751-8113/46/22/225301

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The transmission of an excitation along a spin chain can be hindered by the presence of small fixed imperfections that create trapping regions where the excitation may get caught (Anderson localization). A certain degree of noise, ensuing from the interaction with a thermal bath, allows us to overcome localization (noise-assisted transport). In this paper, we investigate the relation between the noise-assisted transport and (quantum) computation. In particular, we prove that noise does assist classical computation on a quantum computing device, but hinders the possibility of creating entanglement.
In the current Noisy Intermediate-Scale Quantum era, noise is widely regarded as the primary obstacle to achieving fault-tolerant quantum computation. However, certain stages of the quantum computing pipeline can, in fact, benefit from this noise. In this work, we exploit the Eigenstate Thermalization Hypothesis to show that noise generically accelerates a fundamental task in quantum computing -- the preparation of Gibbs states. We demonstrate this behavior using classical and quantum simulations with Haar-random and phase-flip noise, respectively, on a spin-1/2 chain with a local Hamiltonian. Our non-integrable model sees ~3.5x faster thermalization in the presence of noise, while our integrable model, which would not otherwise thermalize, reaches a thermal state due to noise. Since certifying a local Gibbs state is relatively easy on a quantum computer, our approach provides a new practical solution to a key problem in quantum computing. More broadly, these results establish a new paradigm in which noise can be harnessed on quantum computers, enabling practical advantages before the years of fault-tolerance.
Transport phenomena are fundamental in physics. They allow for information and energy to be exchanged between individual constituents of communication systems, networks or even biological entities. Environmental noise will generally hinder the efficiency of the transport process. However, and contrary to intuition, there are situations in classical systems where thermal fluctuations are actually instrumental in assisting transport phenomena. Here we show that, even at zero temperature, transport of excitations across dissipative quantum networks can be enhanced by local dephasing noise. We explain the underlying physical mechanisms behind this phenomenon and propose possible experimental demonstrations in quantum optics. Our results suggest that the presence of entanglement does not play an essential role for energy transport and may even hinder it. We argue that Nature may be routinely exploiting dephasing noise and show that the transport of excitations in simplified models of light harvesting molecules does benefit from such noise assisted processes. These results point toward the possibility for designing optimized structures for transport, for example in artificial nanostructures, assisted by noise.
The study of noise assisted-transport in quantum systems is essential in a wide range of applications, from near-term NISQ devices to models for quantum biology. Here, we study a generalized XXZ model in the presence of stochastic collision noise, which allows describing environments beyond the standard Markovian formulation. Our analysis through the study of the local magnetization, the inverse participation ratio (IPR) or its generalization, and the inverse ergodicity ratio (IER) showed clear regimes, where the transport rate and coherence time could be controlled by the dissipation in a consistent manner. In addition, when considering various excitations, we characterized the interplay between collisions and system interactions, identifying regimes in which transport was counterintuitively enhanced when increasing the collision rate, even in the case of initially separated excitations. These results constitute an example of an essential building block for the understanding of quantum transport in structured noisy and warm-disordered environments.
The transport of excitations governs fundamental properties of matter. Particularly rich physics emerges in the interplay between disorder and environmental noise, even in small systems such as photosynthetic biomolecules. Counterintuitively, noise can enhance coherent quantum transport, which has been proposed as a mechanism behind the high transport efficiencies observed in photosynthetic complexes. This effect has been called ``environment-assisted quantum transport''. Here, we propose a quantum simulation of the excitation transport in an open quantum network, taking advantage of the high controllability of current trapped-ion experiments. Our scheme allows for the controlled study of various different aspects of the excitation transfer, ranging from the influence of static disorder and interaction range, over the effect of Markovian and non-Markovian dephasing, to the impact of a continuous insertion of excitations. Our paper discusses experimental error sources and realistic parameters, showing that it can be implemented in state-of-the-art ion-chain experiments.
Understanding the transport mechanisms and properties of complex networks is fundamental for the comprehension of a vast class of phenomena, from state transfer on a spin network to light-harvesting in photosynthetic complexes. It has been theoretically and experimentally demonstrated that noise can enhance transport when the system parameters are properly tuned, an effect known as noise-assisted transport (NAT). In this work we investigate the role of initial entanglement in the transfer efficiency of two walkers in a noisy network. By using the formalism of quantum walks, we define a range of small dephasing noise where initial site-entanglement provides transport enhancement and outperforms the NAT effect. Furthermore, we show two specific scenarios where entanglement-assisted transport can open faster channels for slow walkers and avoid a broken link in a communication line. These findings may be of potential interest for quantum technologies.