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arXiv:2001.05472 · Advanced Quantum Technologies

Machine Learning Transfer Efficiencies for Noisy Quantum Walks

Alexey A. Melnikov, Leonid Evgenevich Fedichkin, Ray‐Kuang Lee, Alexander Alodjants

Published Feb 13, 2020• 21 citations
arXivHTMLPDF

Abstract

Abstract Quantum effects are known to provide an advantage in particle transfer across networks. In order to achieve this advantage, requirements on both a graph type and a quantum system coherence must be found. Here, it is shown that the process of finding these requirements can be automated by learning from simulated examples. The automation is done by using a convolutional neural network of a particular type that learns to understand with which network and under which coherence requirements quantum advantage is possible. The machine learning approach is applied to study noisy quantum walks on cycle graphs of different sizes. It is found that it is possible to predict the existence of quantum advantage for the entire decoherence parameter range, even for graphs outside of the training set. The results are of importance for demonstration of advantage in quantum experiments and pave the way toward automating scientific research and discoveries.

DOI
10.1002/qute.201900115

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Abstract Quantum effects are known to provide an advantage in particle transfer across networks. In order to achieve this advantage, requirements on both a graph type and a quantum system coherence must be found. Here, it is shown that the process of finding these requirements can be automated by learning from simulated examples. The automation is done by using a convolutional neural network of a particular type that learns to understand with which network and under which coherence requirements quantum advantage is possible. The machine learning approach is applied to study noisy quantum walks on cycle graphs of different sizes. It is found that it is possible to predict the existence of quantum advantage for the entire decoherence parameter range, even for graphs outside of the training set. The results are of importance for demonstration of advantage in quantum experiments and pave the way toward automating scientific research and discoveries.
Abstract Quantum walks are at the heart of modern quantum technologies. They allow to deal with quantum transport phenomena and are an advanced tool for constructing novel quantum algorithms. Quantum walks on graphs are fundamentally different from classical random walks analogs, in particular, they walk faster than classical ones on certain graphs, enabling in these cases quantum algorithmic applications and quantum-enhanced energy transfer. However, little is known about the possible advantages on arbitrary graphs not having explicit symmetries. For these graphs one would need to perform simulations of classical and quantum walk dynamics to check if the speedup occurs, which could take a long computational time. Here we present a new approach for the solution of the quantum speedup problem, which is based on a machine learning algorithm that predicts the quantum advantage by just ‘looking’ at a graph. The convolutional neural network, which we designed specifically to learn from graphs, observes simulated examples and learns complex features of graphs that lead to a quantum advantage, allowing to identify graphs that exhibit quantum advantage without performing any quantum walk or random walk simulations. The performance of our approach is evaluated for line and random graphs, where classification was always better than random guess even for the most challenging cases. Our findings pave the way to an automated elaboration of novel large-scale quantum circuits utilizing quantum walk based algorithms, and to simulating high-efficiency energy transfer in biophotonics and material science.
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Abstract Despite the complexity of quantum systems in the real world, models with just a few effective many-body states often suffice to describe their quantum dynamics, provided decoherence is accounted for. We show that a machine learning algorithm is able to construct such models, given a straightforward set of quantum dynamics measurements. The effective Hilbert space can be a black box, with variations of the coupling to just one accessible output state being sufficient to generate the required training data. We demonstrate through simulations of a Markovian open quantum system that a neural network can automatically detect the number N of effective states and the most relevant Hamiltonian terms and state-dephasing processes and rates. For systems with N ⩽ 5 we find typical mean relative errors of predictions in the 10 % range. With more advanced networks and larger training sets, it is conceivable that a future single software can provide the automated first stop solution to model building for an unknown device or system, complementing and validating the conventional approach based on physical insight into the system.
Particle transport in quantum systems, which can be modeled by quantum walks on graphs, demonstrates a faster propagation advantage over the corresponding transport in classical systems. As known from several graph examples, achieving further advantages is possible by adding directional control in quantum walks. One way to introduce directional bias is via time-reversal symmetry breaking that can be achieved with chiral quantum walks, where complex phases are added to the edge weights. However, it is not known for which complex phases values and on which graphs quantum transport can be enhanced. Therefore, the classification of graph properties remains an open problem. Here we tackle this graph classification problem with a graph convolutional neural network trained on a set of simulated examples. We find that chiral quantum-walk dynamics leads to almost always faster transport on hypercubes compared to nonchiral dynamics. We connect our paper to physical implementations of quantum walks in superconducting qubits and optical waveguides. Our results open the possibility and flexibility of experimental implementations in demonstrating quantum-walk advantage.
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We study hitting times of quantum walks on graphs from a machine learning perspective. Given a graph it is difficult to decide if quantum walks give an advantage relative to classical random walks. It was shown that machine learning can help to detect quantum advantage even though quantum walk and random walk dynamics on the graph has never been simulated. Here we describe the procedure by which training data is generated for the machine learning approach, and discuss possible future improvements.