arXiv subjects

Elizabeth C. Behrman

Publications and source records attributed to Elizabeth C. Behrman.

6 recordsLinked to original sources

arXiv2025

A quantum GAN for entanglement detection and image classification

Machine learning can be used as a systematic method to non-algorithmically program quantum computers. Quantum machine learning enables us to perform computations without breaking down an algorithm into its gate building blocks, eliminating that difficult step and potentially reducing unnecessary complexity. In addition, the machine learning approach is robust to both noise and to decoherence, which is ideal for running on inherently noisy NISQ devices which are limited in the number of qubits available for error correction. Here we apply our prior work in quantum machine learning technique, to create a QGAN, a quantum analog to the classical Stylenet GANs developed by Kerras for image generation and classification. A quantum system is used as a generator and a separate quantum system is used as a discriminator. The generator Hamiltonian quantum parameters are augmented by quantum style parameters which play the role of the style parameters used by Kerras. Both generator parameters are trained in a GAN MinMax problem along with quantum parameters of the discriminator Hamiltonian. We choose a problem to demonstrate the QGAN that has purely quantum information. The task is to generate and discriminate quantum product states. Real product states are generated to be detected and separated from fake quantum product states generated by the quantum generator. The problem of detecting quantum product states is chosen to demonstrate the QGAN because is well known as purely quantum mechanical, has no classical analog and is an open problem for quantum product states of more than 2 qubits. With proper encoding of image pixels into quantum states as density matrices, the method demonstrated here is applicable to GAN image generation and detection that can be hosted on and take advantage of the nature of quantum computers.

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arXiv2022

Programming Quantum Hardware via Levenberg Marquardt Machine Learning

Significant challenges remain with the development of macroscopic quantum computing, hardware problems of noise, decoherence, and scaling, software problems of error correction, and, most important, algorithm construction. Finding truly quantum algorithms is quite difficult, and many quantum algorithms, like Shor prime factoring or phase estimation, require extremely long circuit depth for any practical application, necessitating error correction. Machine learning can be used as a systematic method to nonalgorithmically program quantum computers. Quantum machine learning enables us to perform computations without breaking down an algorithm into its gate building blocks, eliminating that difficult step and potentially reducing unnecessary complexity. In addition, we have shown that our machine learning approach is robust to both noise and to decoherence, which is ideal for running on inherently noisy NISQ devices which are limited in the number of qubits available for error correction. We demonstrated this using a fundamentally non classical calculation, experimentally estimating the entanglement of an unknown quantum state. Results from this have been successfully ported to the IBM hardware and trained using a powerful hybrid reinforcement learning technique which is a modified Levenberg Marquardt LM method. The LM method is ideally suited to quantum machine learning as it only requires knowledge of the final measured output of the quantum computation, not intermediate quantum states which are generally not accessible. Since it processes all the learning data simultaneously, it also requires significantly fewer hits on the quantum hardware. Machine learning is demonstrated with results from simulations and runs on the IBM Qiskit hardware interface.

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arXiv2021

Quantum circuit representation of Bayesian networks

Probabilistic graphical models such as Bayesian networks are widely used to model stochastic systems to perform various types of analysis such as probabilistic prediction, risk analysis, and system health monitoring, which can become computationally expensive in large-scale systems. While demonstrations of true quantum supremacy remain rare, quantum computing applications managing to exploit the advantages of amplitude amplification have shown significant computational benefits when compared against their classical counterparts. We develop a systematic method for designing a quantum circuit to represent a generic discrete Bayesian network with nodes that may have two or more states, where nodes with more than two states are mapped to multiple qubits. The marginal probabilities associated with root nodes (nodes without any parent nodes) are represented using rotation gates, and the conditional probability tables associated with non-root nodes are represented using controlled rotation gates. The controlled rotation gates with more than one control qubit are represented using ancilla qubits. The proposed approach is demonstrated for three examples: a 4-node oil company stock prediction, a 10-node network for liquidity risk assessment, and a 9-node naive Bayes classifier for bankruptcy prediction. The circuits were designed and simulated using Qiskit, a quantum computing platform that enables simulations and also has the capability to run on real quantum hardware. The results were validated against those obtained from classical Bayesian network implementations.

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arXiv2020

A Quantum Annealing Approach for Dynamic Multi-Depot Capacitated Vehicle Routing Problem

Quantum annealing (QA) is a quantum computing algorithm that works on the principle of Adiabatic Quantum Computation (AQC), and it has shown significant computational advantages in solving combinatorial optimization problems such as vehicle routing problems (VRP) when compared to classical algorithms. This paper presents a QA approach for solving a variant VRP known as multi-depot capacitated vehicle routing problem (MDCVRP). This is an NP-hard optimization problem with real-world applications in the fields of transportation, logistics, and supply chain management. We consider heterogeneous depots and vehicles with different capacities. Given a set of heterogeneous depots, the number of vehicles in each depot, heterogeneous depot/vehicle capacities, and a set of spatially distributed customer locations, the MDCVRP attempts to identify routes of various vehicles satisfying the capacity constraints such as that all the customers are served. We model MDCVRP as a quadratic unconstrained binary optimization (QUBO) problem, which minimizes the overall distance traveled by all the vehicles across all depots given the capacity constraints. Furthermore, we formulate a QUBO model for dynamic version of MDCVRP known as D-MDCVRP, which involves dynamic rerouting of vehicles to real-time customer requests. We discuss the problem complexity and a solution approach to solving MDCVRP and D-MDCVRP on quantum annealing hardware from D-Wave.

math.OC↗

arXiv2020

Experimental evaluation of quantum Bayesian networks on IBM QX hardware

Bayesian Networks (BN) are probabilistic graphical models that are widely used for uncertainty modeling, stochastic prediction and probabilistic inference. A Quantum Bayesian Network (QBN) is a quantum version of the Bayesian network that utilizes the principles of quantum mechanical systems to improve the computational performance of various analyses. In this paper, we experimentally evaluate the performance of QBN on various IBM QX hardware against Qiskit simulator and classical analysis. We consider a 4-node BN for stock prediction for our experimental evaluation. We construct a quantum circuit to represent the 4-node BN using Qiskit, and run the circuit on nine IBM quantum devices: Yorktown, Vigo, Ourense, Essex, Burlington, London, Rome, Athens and Melbourne. We will also compare the performance of each device across the four levels of optimization performed by the IBM Transpiler when mapping a given quantum circuit to a given device. We use the root mean square percentage error as the metric for performance comparison of various hardware.

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arXiv2019

Quantum Learning with Noise and Decoherence: A Robust Quantum Neural Network

Noise and decoherence are two major obstacles to the implementation of large-scale quantum computing. Because of the no-cloning theorem, which says we cannot make an exact copy of an arbitrary quantum state, simple redundancy will not work in a quantum context, and unwanted interactions with the environment can destroy coherence and thus the quantum nature of the computation. Because of the parallel and distributed nature of classical neural networks, they have long been successfully used to deal with incomplete or damaged data. In this work, we show that our model of a quantum neural network (QNN) is similarly robust to noise, and that, in addition, it is robust to decoherence. Moreover, robustness to noise and decoherence is not only maintained but improved as the size of the system is increased. Noise and decoherence may even be of advantage in training, as it helps correct for overfitting. We demonstrate the robustness using entanglement as a means for pattern storage in a qubit array. Our results provide evidence that machine learning approaches can obviate otherwise recalcitrant problems in quantum computing.

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