Engineering topics

Dixit, Vivek

Publications and source records attributed to Dixit, Vivek.

3 records

DOE OSTI2022

Training a Quantum Annealing Based Restricted Boltzmann Machine on Cybersecurity Data

A restricted Boltzmann machine (RBM) is a generative model that could be used in effectively balancing a cybersecurity dataset because the synthetic data a RBM generates follows the probability distribution of the training data. RBM training can be performed using contrastive divergence (CD) and quantum annealing (QA). QA-based RBM training is fundamentally different from CD and requires samples from a quantum computer. We present a real-world application that uses a quantum computer. Specifically, we train a RBM using QA for cybersecurity applications. The D-Wave 2000Q has been used to implement QA. RBMs are trained on the ISCX data, which is a benchmark dataset for cybersecurity. For comparison, RBMs are also trained using CD. CD is a commonly used method for RBM training. Our analysis of the ISCX data shows that the dataset is imbalanced. We present two different schemes to balance the training dataset before feeding it to a classifier. The first scheme is based on the undersampling of benign instances. The imbalanced training dataset is divided into five sub-datasets that are trained separately. A majority voting is then performed to get the result. Our results show the majority vote increases the classification accuracy up from 90.24% to 95.68%, in the case of CD. For the case of QA, the classification accuracy increases from 74.14% to 80.04%. In the second scheme, a RBM is used to generate synthetic data to balance the training dataset. We show that both QA and CD-trained RBM can be used to generate useful synthetic data. Balanced training data is used to evaluate several classifiers. Among the classifiers investigated, K-Nearest Neighbor (KNN) and Neural Network (NN) perform better than other classifiers. They both show an accuracy of 93%. Our results show a proof-of-concept that a QA-based RBM can be trained on a 64-bit binary dataset. The illustrative example suggests the possibility to migrate many practical classification problems to QA-based techniques. Further, we show that synthetic data generated from a RBM can be used to balance the original dataset.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Prime factorization using quantum variational imaginary time evolution

The road to computing on quantum devices has been accelerated by the promises that come from using Shor’s algorithm to reduce the complexity of prime factorization. However, this promise hast not yet been realized due to noisy qubits and lack of robust error correction schemes. Here we explore a promising, alternative method for prime factorization that uses well-established techniques from variational imaginary time evolution. We create a Hamiltonian whose ground state encodes the solution to the problem and use variational techniques to evolve a state iteratively towards these prime factors. We show that the number of circuits evaluated in each iteration scales as \(O(n^{5}d)\) , where n is the bit-length of the number to be factorized and d is the depth of the circuit. We use a single layer of entangling gates to factorize 36 numbers represented using 7, 8, and 9-qubit Hamiltonians. We also verify the method’s performance by implementing it on the IBMQ Lima hardware to factorize 55, 65, 77 and 91 which are greater than the largest number (21) to have been factorized on IBMQ hardware.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Training Restricted Boltzmann Machines With a D-Wave Quantum Annealer

Restricted Boltzmann Machine (RBM) is an energy-based, undirected graphical model. It is commonly used for unsupervised and supervised machine learning. Typically, RBM is trained using contrastive divergence (CD). However, training with CD is slow and does not estimate the exact gradient of the log-likelihood cost function. In this work, the model expectation of gradient learning for RBM has been calculated using a quantum annealer (D-Wave 2000Q), where obtaining samples is faster than Markov chain Monte Carlo (MCMC) used in CD. Training and classification results of RBM trained using quantum annealing are compared with the CD-based method. The performance of the two approaches is compared with respect to the classification accuracies, image reconstruction, and log-likelihood results. The classification accuracy results indicate comparable performances of the two methods. Image reconstruction and log-likelihood results show improved performance of the CD-based method. It is shown that the samples obtained from quantum annealer can be used to train an RBM on a 64-bit “bars and stripes” dataset with classification performance similar to an RBM trained with CD. Though training based on CD showed improved learning performance, training using a quantum annealer could be useful as it eliminates computationally expensive MCMC steps of CD.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗