Publications

2023

1. Extrapolation of polaron properties to low phonon frequencies by Bayesian machine learning

   Pranav Kairon, John Sous, Mona Berciu, and 1 more author

   Nov 2023

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   Feasibility of accurate quantum calculations is often restricted by the dimensionality of the truncated Hilbert space required for the numerical computations. The present work demonstrates Bayesian machine learning (ML) models that use quantum properties in an effectively lower-dimensional Hilbert space to make predictions for the Hamiltonian parameters that require a larger basis set as applied to a classical problem in quantum statistical mechanics, the polaron problem. We consider two polaron models: the Su-Schrieffer-Heeger (SSH) model and the mixed SSH-Holstein model. We demonstrate ML models that can extrapolate polaron properties in the phonon frequency. We consider the sharp transition in the ground-state momentum of the SSH polaron and examine the evolution of this transition from the anti-adiabatic regime to the adiabatic regime. We also demonstrate Bayesian models that use the posterior distributions of highly approximate quantum calculations as the prior distribution for models of more accurate quantum results. This drastically reduces the number of fully converged quantum calculations required to map out the polaron dispersion relations for the full range of Hamiltonian parameters of interest.

   @article{kairon_roman_polaron_2023,
     title = {Extrapolation of polaron properties to low phonon frequencies by Bayesian machine learning},
     author = {Kairon, Pranav and Sous, John and Berciu, Mona and Krems, Roman},
     month = nov,
     year = {2023},
   }

2. Equivalence between exponential concentration in quantum kernels and Barren Plateaus in Variational Quantum Algorithms

   Pranav Kairon, Jonas Jäger, and Roman Krems

   Nov 2023

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   Machine learning algorithms based on parameterized quantum circuit are known to suffer from optimization problems such as Barren Plateaus where gradient of cost function vanishes, our goal is to optimize variational parameters of a quantum circuit which encodes our input data W (x, θ). We establish a compelling connection between the problem of Exponential Concentration(EC) in quantum kernels and Barren Plateaus (BP) in variational quantum algorithms. By leveraging analytical tools developed for BPs, we derive upper and lower bounds on the concentration of quantum resources in EC, identifying conditions under which EC occurs and providing methods to mitigate its impact on quantum kernel computations. Additionally, we investigate invariant kernels and demonstrate that they can be used to mitigate EC for quantum kernel-based algorithms.

   @article{kairon_roman_Jonas_2023,
     title = {Equivalence between exponential concentration in quantum kernels and Barren Plateaus in Variational Quantum Algorithms},
     author = {Kairon, Pranav and Jäger, Jonas and Krems, Roman},
     month = nov,
     year = {2023}
   }

2022

1. Coherence-based inequality for the discrimination of three-qubit GHZ and W class

   Pranav Kairon, Mukhtiyar Singh, and Satyabrata Adhikari

   Quantum Information Processing, May 2022

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   Quantum coherence and entanglement originate from the superposition principle. We derive a rigorous relation between the \\{l_1}\\-norm of coherence and concurrence, in that we show that the former is always greater than the latter. This result highlights the hierarchical relationship between coherence and concurrence, and proves coherence to be a fundamental and ubiquitous resource. We derive an analogous form of monogamy inequality, which is based on the partial coherence of the reduced two-qubit and reduced single qubit of the particular class of three-qubit state. Moreover, we provide coherence-based inequality for the classification of GHZ class and W class of three-qubit states. Finally, we provide theoretical discussion for the possible implementation of the scheme in an experiment.

   @article{kairon_coherence-based_2022,
     title = {Coherence-based inequality for the discrimination of three-qubit {GHZ} and {W} class},
     volume = {21},
     issn = {1573-1332},
     url = {https://doi.org/10.1007/s11128-022-03512-x},
     doi = {10.1007/s11128-022-03512-x},
     number = {5},
     journal = {Quantum Information Processing},
     author = {Kairon, Pranav and Singh, Mukhtiyar and Adhikari, Satyabrata},
     month = may,
     year = {2022},
     pages = {173},
     dimensions = {true},
   }

2021

1. COVID-19 Outbreak Prediction Using Quantum Neural Networks

   Pranav Kairon, and Siddhartha Bhattacharyya

   In Intelligence Enabled Research: DoSIER 2020, May 2021

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   Artificial intelligence has become an important tool in fight against COVID-19. Machine learning models for COVID-19 global pandemic predictions have shown a higher accuracy than the previously used statistical models used by epidemiologists. With the advent of quantum machine learning, we present a comparative analysis of continuous variable quantum neural networks (variational circuits) and quantum backpropagation multilayer perceptron (QBMLP). We analyze the convoluted and sporadic data of two affected countries, and hope that our study will help in effective modeling of outbreak while throwing a light on bright future of quantum machine learning.

   @incollection{kairon_covid-19_2021,
     address = {Singapore},
     title = {{COVID}-19 {Outbreak} {Prediction} {Using} {Quantum} {Neural} {Networks}},
     isbn = {978-981-15-9290-4},
     url = {https://doi.org/10.1007/978-981-15-9290-4_12},
     booktitle = {Intelligence {Enabled} {Research}: {DoSIER} 2020},
     publisher = {Springer Singapore},
     author = {Kairon, Pranav and Bhattacharyya, Siddhartha},
     editor = {Bhattacharyya, Siddhartha and Dutta, Paramartha and Datta, Kakali},
     year = {2021},
     doi = {10.1007/978-981-15-9290-4_12},
     pages = {113--123},
     dimensions = {true},
   }

2020

1. Noisy three-player dilemma game: robustness of the quantum advantage

   Pranav Kairon, Kishore Thapliyal, R. Srikanth, and 1 more author

   Quantum Information Processing, Aug 2020

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   Games involving quantum strategies often yield higher payoff. Here, we study a practical realization of the three-player dilemma game using the superconductivity-based quantum processors provided by IBM Q Experience. We analyze the persistence of the quantum advantage under corruption of the input states and how this depends on parameters of the payoff table. Specifically, experimental fidelity and error are observed not to be properly anti-correlated; i.e., there are instances where a class of experiments with higher fidelity yields a greater error in the payoff. Further, we find that the classical strategy will always outperform the quantum strategy if corruption is higher than 50%.

   @article{kairon_noisy_2020,
     title = {Noisy three-player dilemma game: robustness of the quantum advantage},
     volume = {19},
     issn = {1573-1332},
     url = {https://doi.org/10.1007/s11128-020-02830-2},
     doi = {10.1007/s11128-020-02830-2},
     number = {9},
     journal = {Quantum Information Processing},
     author = {Kairon, Pranav and Thapliyal, Kishore and Srikanth, R. and Pathak, Anirban},
     month = aug,
     year = {2020},
     pages = {327},
     dimensions = {true},
   }