Quantum Machine Learning Classifier and Neural Network Transfer Learning

Abstract

This chapter explores quantum machine learning (QML) and neural network transfer learning. It begins by describing the potential of QML. The discussion then shifts to transfer learning, leveraging pre-trained neural models across diverse domains. A demonstration of advancements in both fields forms the core of the chapter, showcasing how QML classifiers can be used with classical neural networks for enhanced performance. To improve the accuracy of COVID-19 screening, ensemble method and sliding window mechanism measurements have been employed using computer vision on frequency domain spectrograms of audio files. Parallel with this, the accuracy of these measurements could be improved by quantum machine transfer learning. The chapter describes a case study where a hybrid approach demonstrated significant improvements in data processing accuracy, offering an understanding of practical applications. In conclusion, the authors present ideas on how the combination of QML and transfer learning could unfold new horizons in various fields with complex, large-scale datasets. The chapter concludes with predictions about the trajectory of these technologies, emphasizing their role in shaping the future of transfer learning. This combination of current research and visionary thinking inspires further exploration at the intersection of quantum computing machine learning and neural network transfer learning.

1. Introduction

1.1 Transfer learning in the context of quantum machine learning

Quantum machine learning transfer learning, or transfer learning in the context of quantum machine learning, is a concept that blends the principles of transfer learning with the unique capabilities of quantum computing. To define it, let us first break down its two main components:

1.1.1 Transfer learning in classical machine learning

Transfer learning is a technique where a data model developed for one task is reused as the starting point for a model on a second task. It is particularly useful in scenarios where the second task has limited data available for training. In essence, transfer learning allows for the leveraging of pre-trained models to achieve quicker and more efficient learning in a new, but related, problem. Transfer learning is an idea that is taken from how the human mind works. In the human mind, previous experience is used to handle training on a new task that must be learned to assist it into learning the new task more quickly. An example is learning a new foreign language. If one language has already been learned, then the new language training is guided by that previous experience, to speed up the process, as described in “A computer science perspective on models of the mind” by Brooks et al. [1].

1.1.2 Quantum machine learning

This involves using quantum algorithms to either improve classical machine learning methods or develop new machine learning models that operate on quantum data as described in “Quantum deep learning neural networks”, by Kamruzzaman et al. [2] and “Quantum machine learning: A review and case studies” by Zeguendry et al. [3].

1.2 Combining these concepts

Quantum machine learning transfer learning can be understood as follows:

1.2.1 Leveraging pre-trained quantum models

It involves reusing a model, which has been trained on a quantum computer for one task, for a different but related task. This is particularly beneficial given the computational expense of training models on quantum computers.

1.2.2 Hybrid approach

It might also involve using quantum algorithms to enhance classical machine learning models that have been pre-trained on classical data. This could mean, for instance, fine-tuning a classical neural network using a quantum-enhanced optimization algorithm. Hybrid approaches are currently the most popular form of quantum machine transfer learning. This approach is used for the illustration in this chapter.

1.2.3 Cross-domain applications

Transfer learning in the quantum domain can be especially powerful for tasks where classical data needs to be augmented with quantum data or vice versa. For example, a quantum machine learning model initially trained on quantum simulation data might be adapted for a more specialized task in quantum chemistry with minimal retraining.

1.2.4 Efficiency and scalability

Quantum transfer learning aims to reduce the computational resources needed to train quantum models from scratch, which is especially crucial given the current limitations of quantum hardware.

1.3 The rest of this chapter is about

The rest of this chapter illustrates the terms described above in the Introduction with a survey of the research that serves as an example of each of the concepts, a practical example of using quantum machine learning transfer learning in a hybrid with classical neural networks, and a conclusion.

2. Illustrations and examples

2.1 Example of transfer learning in classical machine learning

An example of transfer learning in classical machine learning is given in “Using a Novel Transfer Learning Method for Designing Thin Film Solar Cells with Enhanced Quantum Efficiencies” [4] which observes that machine learning can learn from the human brain, which applies transfer learning to take what it learns from previous experience and applying it to a new task to reduce training time. An example of this is a human computer programmer learning a new programming language, where they do not start from the beginning, but rather by using the programming language(s) that are already known, and applying that knowledge to the new language, reducing learning time. The transfer learning in this case is applied to finding a more optimized design to “thin film multilayer solar cells” by using a surrogate model. A surrogate model (also called metamodel) is an approximation to a black box model that searches for optimal points. When design specifications change, the surrogate model must also change. However, using transfer learning, the new surrogate model can be refitted more efficiently, resulting in a model that learned and optimized the new function with 2–3 times the accuracy and using only half as many training data points as the original. Transfer learning is best when it uses the model developed on one data set on another similar data set as in this research paper. In this case, the model developed was from another similar set of materials as in the thin film multilayer structure.

2.2 Examples of quantum machine learning

Several examples of quantum machine learning (QML) are given in “Quantum Machine Learning: A Review and Case Studies” by Amine et al. [3] providing a comprehensive overview of the intersection of quantum computing and machine learning, particularly focusing on quantum machine learning (QML). It explores fundamental quantum theory, quantum algorithms, and their applications in machine learning, aiming to make this complex field understandable to computer scientists who have no physics background. The need for understanding quantum physics in order to understand quantum computing is a significant conceptual challenge for computer scientists who mistakenly believe that it is required. However, it is not necessary to study quantum physics in order to understand quantum computing. An understanding of the basics of linear algebra is all that is necessary.

The article begins with an introduction to machine learning and its reliance on linear algebra for processing data as matrices. It highlights the potential of quantum computing to improve machine learning by handling large matrices more efficiently using quantum bits (qubits). It reviews key quantum computing concepts such as quantum bits, superposition, entanglement, quantum measurement, and the structure of quantum circuits.

The authors discuss various quantum algorithms, including Grover’s and Shor’s algorithms, and their implications for machine learning. Grover’s algorithm promises quadratic speedup of computations. Shor’s algorithm promises to break the RSA encryption algorithm and therefore unleash plaintext in worldwide systems that rely on RSA encryption to secure their key information, especially the world’s financial systems and military systems. They also explore quantum variants of popular machine learning algorithms like quantum neural networks (QNN), quantum support vector machines (QSVM), and quantum principal component analysis (QPCA).

The article presents case studies comparing the performance of QML algorithms with their classical counterparts. These include implementing quanvolutional neural networks (QNNs) to recognize handwritten digits and comparing them with classical convolutional neural networks (CNNs), implementing quantum support vector machines (QSVM) on a breast cancer dataset and comparing it to classical support vector machine (SVM), and implementing the variational quantum classifier (VQC) on the Iris dataset to compare accuracies with classical classifiers.

In conclusion, the paper discusses challenges in quantum computing, such as the need for quantum random access memory (QRAM) for efficiently handling classical data, and suggests future research directions in QML.

Overall, this paper provides a detailed insight into how quantum computing can revolutionize machine learning by enabling faster processing and handling of complex data.

2.3 Example of leveraging pre-trained quantum models

An example of leveraging pre-trained quantum models with transfer learning is given in “Hybrid Model of Quantum Transfer Learning to Classify Face Images with a COVID-19 Mask” by Soto-Paredes and Sulla-Torres [5], which presented a study on classifying face images of individuals wearing COVID-19 masks. The authors aimed to categorize images into three classes: (1) correctly worn mask, (2) incorrectly worn mask, and (3) no mask. They utilized a hybrid model combining Quantum Transfer Learning with the classical ResNet-18 model.

Key points from the article include:

Context and motivation: given the widespread impact of COVID-19 and the essential role of masks in controlling its spread, the study focuses on using technology to monitor mask usage effectively.

Data set: the study gathered 660 images of people across genders and ages 18–86. These images were then categorized into the three classes for mask usage.

Methodology: the classical transfer learning model used was ResNet-18, augmented with a quantum approach using the Pennylane quantum simulator. Various layers and templates were employed in the quantum model, including Basic Entangling Layers and Strongly Entangling Layers.

Results: the model achieved a high accuracy of 99.05% in classifying correctly worn masks. Different variations of the model were compared, demonstrating that Stochastic Gradient Descent with Nesterov Momentum was the most effective optimization method.

Comparison with other studies: the study compared its approach and results with other related works in the field, highlighting the novelty and effectiveness of their hybrid model.

Conclusions and future work: the article concluded that the hybrid model is a promising tool for detecting correct mask usage. It also suggests exploring other quantum templates and improving hyper-parameters in future research.

This research is significant in the context of public health and safety during the COVID-19 pandemic, offering a technological solution to monitor and encourage proper mask usage. The use of a hybrid classical-quantum approach also demonstrates the potential of quantum computing in enhancing traditional machine learning methods.

2.4 An additional example of leveraging pre-trained quantum models

The paper “Transfer learning in hybrid classical-quantum neural networks” by ***Mari et al. [6] explores the application of transfer learning in the context of hybrid neural networks that incorporate both classical and quantum elements. The paper is particularly relevant in the current era of intermediate-scale quantum technology and focuses on how a pre-trained classical network can be augmented with a final variational quantum circuit. This hybrid approach allows for efficient processing of high-dimensional data, such as images, using state-of-the-art classical networks, followed by embedding a select set of features into a quantum processor for further processing. This paper is so important that it is posted on Pennylane, the artificial intelligence machine learning simulator website, as a tutorial in quantum transfer learning.

Key points of the paper include:

Introduction to transfer learning: the concept of transfer learning, common in artificial intelligence, is introduced. This concept involves transferring knowledge acquired in one context to a different area. The paper aims to investigate the potential of transfer learning in quantum machine learning, focusing on hybrid models where quantum variational circuits and classical neural networks are jointly trained.

Hybrid classical-quantum networks: the study reviews basic concepts of hybrid networks and introduces dressed quantum circuits. These circuits consist of a variational quantum circuit augmented with classical layers for pre-processing and post-processing input and output data, respectively. The addition of the classical layers is known as “dressing”.

Transfer learning variants: the study identifies four variants of transfer learning in hybrid systems: classical-to-classical (CC), classical-to-quantum (CQ), quantum-to-classical (QC), and quantum-to-quantum (QQ). Each variant offers unique opportunities for leveraging the strengths of both classical and quantum computing.

Implementation and examples: the study presents several proof-of-concept examples demonstrating practical implementations of quantum transfer learning for tasks like image recognition and quantum state classification. These examples use the PennyLane software library for simulations and test a high-resolution image classifier on real quantum computers provided by IBM and Rigetti. To gain access to the IBM real quantum computers, one needs only to go to the IBM website and log-in for free academic access to the older machines. To gain access to the Rigetti real quantum computers, one can use Amazon Web Services (AWS) and pay for each “shot”.

Results and analysis: the study reports the successful application of transfer learning in hybrid systems, with specific emphasis on the classical-to-quantum (CQ) approach due to its relevance to current quantum technology. The CQ approach is used to classify high-resolution images using real quantum processors.

Conclusion: the authors conclude that transfer learning is a promising approach in the context of near-term quantum devices. They note the potential benefits of combining the power of quantum computers with the well-established methods of classical machine learning, especially for tasks like image processing.

This research is significant as it explores the intersection of quantum computing and machine learning, demonstrating the feasibility and potential advantages of applying transfer learning techniques in hybrid classical-quantum settings. The results indicate that such hybrid approaches could be valuable in efficiently processing complex data using the combined strengths of classical and quantum computation.

2.5 Hybrid approach illustration

The article “Screening for COVID-19 via Acoustics using Artificial Intelligence” by Bakhitov et al. [5] presented a novel approach for COVID-19 screening by analyzing audio files using deep learning techniques. This research did not include quantum computing or transfer learning, however, in subsequent research done for this chapter, the authors have extended the work to include both.

The original hybrid approach started with crowdsourced audio files of individuals exhibiting COVID-19 symptoms and compared them to those of healthy subjects. The methodology involved processing these audio samples into log-power spectrograms (image format) using the librosa Python library, which were then analyzed by Convolutional Neural Networks (CNNs) to identify patterns indicative of the virus.

The study utilized a dataset from the Coswara project found at Ref. [6], which contained audio samples from 1433 healthy individuals and 681 positive COVID-19 cases. Each dataset entity contained nine files recorded by one individual such as breathing heavy, counting fast, vowel sounds, etc. The researchers trained their model on 70% of this data, validated it on 20%, and tested it on the remaining 10%, achieving promising initial results with an 85% Area Under the (Receiver Operating Characteristics (ROC)) Curve (AUC).

This original research emphasized the importance of a hybrid approach that combined audio preprocessing, image transformation, and advanced deep learning (specifically CNNs) to address the challenge of rapid and accessible COVID-19 screening. The significant aspect of this approach was its potential to reduce the costs and logistical challenges associated with traditional testing methods while also minimizing the risk of false negatives. The article also highlighted the high incidence of false negatives in current COVID-19 tests and suggested that this AI-driven method could offer a more reliable alternative for preliminary screening.

Future directions at that time for this work included improving the model through more advanced techniques such as exploring the use of quantum computing and transfer learning. The team aimed to process the entire Coswara dataset with the improved model and test their approach on additional COVID-19 audio datasets as they became available. They did not become available.

The way that this research was improved and extended for this chapter was to add quantum transfer learning. An illustration of the addition of quantum computing to the neural network to create a hybrid network is to take the classical neural network done for the original research such as that seen in Figure 1, and replace it with a hybrid classical-quantum neural network, such as that seen in Figure 2. The difference between the two figures is that the final fully connected (fc) layer of the neural network in Figure 2 has been cut out and replaced by a quantum circuit layer, simulated in this instance by the use of the Pennylane quantum computing simulation software platform found at Ref. [7] in Python. The effect of this was that the first neural network from Figure 1 became a feature extractor for the second, hybrid neural network from Figure 2. The way this is done is to freeze the pre-trained layers from the first neural network that is used for the transfer learning, before adding the quantum circuit layers for the hybrid. The authors placed the data model in the data scientist sharing platform Hugging Face at Ref. [8] and the code on GitHub at Ref. [9]. Similar to the approach in Ref. [4] with the transfer learning done with the materials of solar cells, the authors picked a similar dataset to use for the transfer learning of the model, picking a different subset of the Coswara data, that had not been used for training the original model. Transfer learning from the original counting audio files data subset to train the model for the deep breathing subset.

Figure 1.

Classic neural network processing images down to 50 nodes then 2 nodes for decision of COVID-19 positive or negative in original research from Bakhitov et al. [5].

Figure 2.

Addition of quantum layer for hybrid for the research done for this chapter.

The original research resulted in data model summary measurements as seen in Ref. [5]. This data model was simplified for the purposes of illustrating classical and quantum transfer learning for this chapter. The classical transfer learning resulted in the data model summary measurements as seen in Table 1.

Measurements from original model
Layer(type)	Output shape	Param #
Conv2d-1	[−1, 16, 256, 256]	160
ReLU-2	[−1, 16, 256, 256]	0
MaxPool2d-3	[−1, 16, 128, 128]	4640
Conv2d-7	[−1, 64, 64, 64]	18,496
ReLU-8	[−1, 64, 64, 64]	0
MaxPool2d-9	[−1, 64, 32, 32]	0
Conv2d-10	[−1, 128, 32, 32]	73,856
ReLU-11	[−1, 128, 32, 32]	0
MaxPool2d-12	[−1, 128, 16, 16]	0
Linear-13	[−1, 512]	16,777,728
ReLU-14	[−1, 512]	0
Linear-15	[−1, 2]	1026

Table 1.

Original classical neural network without the quantum transfer learning.

Total Params: 16,875,906.

Trainable Params: 16,875,906.

Non-trainable Params: 0.

Input size (MB): 0.25.

Forward/backward pass size (MB): 33.76.

Params size (MB): 64.38.

Estimated total size (MB): 98.38.

The classical model, originally adept at processing and classifying audio files for medical screening, provided a solid foundation due to its effective pattern recognition in audio data. By incorporating a quantum circuit to process the extracted features, the goal was to leverage quantum computing’s potential to handle high-dimensional data and execute computations beyond the reach of classical systems alone.

This hybrid approach was not only a test of quantum transfer learning’s feasibility but also an investigation into its potential to enrich classical machine learning models with quantum efficiency. The process involved addressing the distinctive challenges of quantum computing, such as error rates and qubit coherence, with the Pennylane simulator, while also scrutinizing the model’s scalability and performance against purely classical or quantum solutions.

The outcome of this case study illustrated the practical application of quantum-enhanced machine learning models, shedding light on both the obstacles and advantages of integrating quantum circuits into classical neural networks. By successfully implementing this hybrid model, the team contributed to the quantum machine learning field, showcasing an effective strategy for employing quantum computing to augment classical machine learning tasks. This case study not only demonstrated the model’s high accuracy in the specific context of medical screening but also underscored the broader potential of quantum computing to revolutionize various sectors, marking a significant step forward in the fusion of quantum and classical computing technologies.

The addition of the quantum layer resulted in the data model summary measurements as seen in Table 2.

Measurements from quantum hybrid model
Layer (type)	Output shape	Param #
Conv2d-1	[−1, 16, 256, 256]	160
ReLU-2	[−1, 16, 256, 256]	0
MaxPool2d-3	[−1, 16, 128, 128]	0
Conv2d-4	[−1, 32, 128, 128]	4640
ReLU-5	[−1, 32, 128, 128]	0
MaxPool2d-6	[−1, 32, 64, 64]	0
Conv2d-7	[−1, 64, 64, 64]	18,496
ReLU-8	[−1, 64, 64, 64]	0
MaxPool2d-9	[−1, 64, 32, 32]	0
Conv2d-10	[−1, 128, 32, 32]	73,856
ReLU-11	[−1, 128, 32, 32]	0
MaxPool2d-12	[−1, 128, 16, 16]	0
Linear-13	[−1, 512]	16,777,728
ReLU-14	[−1, 512]	0
SpectrogramCNN-15	[−1, 512]	0
Linear-16	[−1, 4]	2052
Linear-17	[−1, 2]	10
DressedQuantumNet-18	[−1, 2]	0

Table 2.

Measurements of quantum transfer learning: Note the great reduction in the trainable parameters with the pre-trained model.

Total Params: 16,876,942.

Trainable Params: 2062.

Non-trainable Params: 16,874,880.

Input size (mB): 0.25.

Forward/backward pass size (MB): 33.76.

Params size (MB): 64.38.

Estimated total size (MB): 98.39.

2.6 Cross-domain applications

Although in our example we did not cross domains outside of the Coswara dataset to apply our trained model to a new domain of data, there are examples of this done in “Hybrid model of quantum transfer learning to classify face images with a COVID-19 mask,” Soto-Paredes and Sulla-Torres [10], in which the classic transfer learning model chosen was ResNet-18 and the quantum layers of the target model was used with a basic entangler layers template for four qubits using the Pennylane quantum simulator. Their main finding was 99.05% accuracy in classifying the correct protective mask images (no mask, incorrectly worn mask, correctly worn mask). Mari et al. “Transfer learning in hybrid classical-quantum neural networks,” which is a foundational paper that is posted on the Pennylane site and describes the theory of transfer learning in hybrid classical-quantum and quantum-quantum neural networks [11]. In “Quantum deep transfer learning,” by Wang et al. [12] which describes the theory of transfere learning in four steps of transfer learning across domains as “(1) For a given task with the dataset, find a source domain dataset for knowledge transfer. (2) Train a model on source domain dataset. (3) Build a criteria for the transfer process…depending on the specific task… (4) Train the target task model on the target domain dataset using the learning information obtained by (3).” In “COVID-19 detection on IBM quantum computer with classical-quantum transfer learning,” by Acar and Yilmaz [13], describes using transfer learning on MRI images of lungs of people positive for COVID-19 as compared to healthy individuals. Leider et al. “Quantum machine learning classifier,” uses the Iris dataset and the Pennylane simulator [14] and Leider et al. “Hybrid Quantum Machine Learning Classifier with Classical Neural Network Transfer Learning.” that uses the wine dataset and the Pennylane simulator [15].

2.7 Current quantum computers limitations on efficiency and scalability

The reason for using the quantum simulator of Pennylane is to overcome the current constraints to the capabilities of quantum computing, which is known as the Noisy Intermediate-Scale Quantum (NISQ) era. This is because today’s quantum computers are still quite primitive, error prone and therefore most research work done on them is academic at this time, because of said noise creating inconsistent results. Quantum computers are considered probabilistic, meaning that quantum programs have to be run repeatedly in “shots” of 1000 times or more in order to get the most probable result.

3. Conclusions

Figure 3 shows that when using quantum machine transfer learning, in the earlier epochs the learning rate is much faster and more accurate. This is the major reason that transfer learning is attractive; it saves computing time. Figure 4 shows that the loss rate is also reduced in the earlier epochs using transfer learning. Quantum machine transfer learning currently uses “dressed” quantum circuits that have classical layers of the hybrid neural network before and after the quantum circuit layer, and there is significant slowdown in translating the information from classical to quantum and back to classical information. Because of this slowdown, it is possible that a hybrid quantum transfer learning network will produce less satisfying results than a purely classical network, however, quantum computing is advancing rapidly and these challenges may soon be solved.

Figure 3.

Accuracy of the fully connected (fc) layer to the quantum layer is better in the earlier epochs in the pre-trained model.

Figure 4.

Loss of the fully connected layer to the quantum layer is better in the earlier epochs in the transfer learning example.

Acknowledgments

The authors would like to acknowledge Dmitrii Bakhitov, Adjunct Professor of Data Science at Pace University who contributed the hybrid approach illustrative data model using Pennylane. This was an extension of his data model used for Ref. [5] and includes the hugging face data models in Ref. [8, 9] and code in GitHub at Ref. [16].

The authors would also like to acknowledge Pace University Seidenberg School of Computer Science and Information Systems for the funding to conduct and publish this research.

Conflict of interest

The authors declare no conflict of interest.