Dynex

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# Machine Learning

#### Next Generation Algorithms for Machine Learning

Quantum computing algorithms for machine learning harness the power of quantum mechanics to enhance various aspects of machine learning tasks. As both, quantum computing and neuromorphic computing are sharing similar features, these algorithms can also be computed efficiently on the Dynex platform – but **without the limitations** of limited qubits, error correction or availability:

**Quantum Support Vector Machine (QSVM):**QSVM is a quantum-inspired algorithm that aims to classify data using a quantum kernel function. It leverages the concept of quantum superposition and quantum feature mapping to potentially provide computational advantages over classical SVM algorithms in certain scenarios.**Quantum Principal Component Analysis (QPCA):**QPCA is a quantum version of the classical Principal Component Analysis (PCA) algorithm. It utilizes quantum linear algebra techniques to extract the principal components from high-dimensional data, potentially enabling more efficient dimensionality reduction in quantum machine learning.**Quantum Neural Networks (QNN):**QNNs are quantum counterparts of classical neural networks. They leverage quantum principles, such as quantum superposition and entanglement, to process and manipulate data. QNNs hold the potential to learn complex patterns and perform tasks like classification and regression, benefiting from quantum parallelism.**Quantum K-Means Clustering:**Quantum K-means is a quantum-inspired variant of the classical K-means clustering algorithm. It uses quantum algorithms to accelerate the clustering process by exploring multiple solutions simultaneously. Quantum K-means has the potential to speed up clustering tasks for large-scale datasets.**Quantum Boltzmann Machines (QBMs):**QBMs are quantum analogues of classical Boltzmann Machines, which are generative models used for unsupervised learning. QBMs employ quantum annealing to sample from a probability distribution and learn patterns and structures in the data.**Quantum Support Vector Regression (QSVR):**QSVR extends the concept of QSVM to regression tasks. It uses quantum computing techniques to perform regression analysis, potentially offering advantages in terms of efficiency and accuracy over classical regression algorithms.

##### Examples

> Example: Quantum-Support-Vector-Machine Implementation on Dynex **Scientific background**: Rounds, Max and Phil Goddard. “Optimal feature selection in credit scoring and classification using a quantum annealer.” (2017)

> Example: Quantum-Support-Vector-Machine (PyTorch) on Dynex

**Scientific background**: Rounds, Max and Phil Goddard. “Optimal feature selection in credit scoring and classification using a quantum annealer.” (2017)

> Example: Quantum-Boltzmann-Machine (PyTorch) on Dynex **Scientific background**: Dixit V, Selvarajan R, Alam MA, Humble TS and Kais S (2021) Training Restricted Boltzmann Machines With a D-Wave Quantum Annealer. Front. Phys. 9:589626. doi: 10.3389/fphy.2021.589626; Sleeman, Jennifer, John E. Dorband and Milton Halem. “A Hybrid Quantum enabled RBM Advantage: Convolutional Autoencoders For Quantum Image Compression and Generative Learning.” Defense + Commercial Sensing (2020)

> Example: Quantum-Boltzmann-Machine Implementation (3-step QUBO) on Dynex **Scientific background**: Dixit V, Selvarajan R, Alam MA, Humble TS and Kais S (2021) Training Restricted Boltzmann Machines With a D-Wave Quantum Annealer. Front. Phys. 9:589626. doi: 10.3389/fphy.2021.589626; Sleeman, Jennifer, John E. Dorband and Milton Halem. “A Hybrid Quantum enabled RBM Advantage: Convolutional Autoencoders For Quantum Image Compression and Generative Learning.” Defense + Commercial Sensing (2020)

> Example: Mode-Assisted Unsupervised Quantum-Boltzmann-Machine Implementation (PyTorch) on Dynex**Scientific background**: Manukian, Haik, et al. "Mode-assisted unsupervised learning of restricted Boltzmann machines." *Communications Physics* 3.1 (2020): 105.; Dixit V, Selvarajan R, Alam MA, Humble TS and Kais S (2021) Training Restricted Boltzmann Machines With a D-Wave Quantum Annealer. Front. Phys. 9:589626. doi: 10.3389/fphy.2021.589626

> Example: Quantum-Boltzmann-Machine (Collaborative Filtering) on Dynex **Scientific background**: Dixit V, Selvarajan R, Alam MA, Humble TS and Kais S (2021) Training Restricted Boltzmann Machines With a D-Wave Quantum Annealer. Front. Phys. 9:589626. doi: 10.3389/fphy.2021.589626; Sleeman, Jennifer, John E. Dorband and Milton Halem. “A Hybrid Quantum enabled RBM Advantage: Convolutional Autoencoders For Quantum Image Compression and Generative Learning.” Defense + Commercial Sensing (2020)

> Example: Quantum-Boltzmann-Machine Implementation on Dynex **Scientific background**: Dixit V, Selvarajan R, Alam MA, Humble TS and Kais S (2021) Training Restricted Boltzmann Machines With a D-Wave Quantum Annealer. Front. Phys. 9:589626. doi: 10.3389/fphy.2021.589626; Sleeman, Jennifer, John E. Dorband and Milton Halem. “A Hybrid Quantum enabled RBM Advantage: Convolutional Autoencoders For Quantum Image Compression and Generative Learning.” Defense + Commercial Sensing (2020)

> Example: Feature Selection - Titanic Survivals **Scientific background**: Xuan Vinh Nguyen, Jeffrey Chan, Simone Romano, and James Bailey. 2014. Effective global approaches for mutual information based feature selection. In Proceedings of the 20th ACM SIGKDD international conference on Knowledge discovery and data mining (KDD ‘14). Association for Computing Machinery, New York, NY, USA, 512–521

> Example: Breast Cancer Prediction using the Dynex scikit-learn Plugin **Scientific background**: Bhatia, H.S., Phillipson, F. (2021). Performance Analysis of Support Vector Machine Implementations on the D-Wave Quantum Annealer. In: Paszynski, M., Kranzlmüller, D., Krzhizhanovskaya, V.V., Dongarra, J.J., Sloot, P.M.A. (eds) Computational Science – ICCS 2021. ICCS 2021. Lecture Notes in Computer Science(), vol 12747. Springer, Cham

**Quantum & Neuromorphic Computing Outperform Traditional Methods**

A new approach using simulated quantum annealing (SQA) to numerically simulate quantum sampling in a deep Boltzmann machine (DBM) was presented in [1]. The authors proposed a framework for training the network as a quantum Boltzmann machine (QBM) in the presence of a significant transverse field for reinforcement learning. However, they demonstrated that the process of embedding Boltzmann machines in larger quantum annealer architectures is problematic when huge weights and biases are needed to emulate the Boltzmann machine’s logical nodes using chains and clusters of physical qubits. On the other hand, quantum annealing has the potential to speed up the sampling process exponentially.

The Dynex Neuromorphic Platform **does not have these physical limitations** and can therefore overcome such scaling problems and expand to large, real-world datasets and problems.

##### Example: Quantum-Boltzmann-Machine (QBM)

This example demonstrates a Quantum-Boltzmann-Machine (QBM) implementation using the Dynex platform to perform the computations and compare it with a traditional Restricted-Boltzmann-Machine (RBM). RBM is a well-known probabilistic unsupervised learning model which is learned by an algorithm called Contrastive Divergence. An important step of this algorithm is called Gibbs sampling – a method that returns random samples from a given probability distribution. We decided to conduct our experiments on the popular MNIST dataset considered a standard benchmark in many of the machine learning and image recognition subfields. The implementation follows a highly optimised QUBO formulation.

Figure: The QBM evolves much faster to an attractive Mean Squared Error (MSE) than the traditional RBM, which means a significant lower amount of training iterations is required. In addition is the achieved MSE much lower, meaning the QBM created models have higher accuracy. This finding is in line with the results from the papers referenced. However, [1] demonstrated that the process of embedding Boltzmann machines in larger quantum annealer architectures is problematic when huge weights and biases are needed to emulate the Boltzmann machine’s logical nodes using chains and clusters of physical qubits because of the limited number of qubits available. The Dynex Neuromorphic platform provides a more scalable alternative and can used to train models with millions of variables. Especially when real-world models are to be trained, the number of training iterations and accuracy are important.

**Scientific background:** Dixit V, Selvarajan R, Alam MA, Humble TS and Kais S (2021) Training Restricted Boltzmann Machines With a D-Wave Quantum Annealer. *Front. Phys.* 9:589626. doi: 10.3389/fphy.2021.589626; Sleeman, Jennifer, John E. Dorband and Milton Halem. “A Hybrid Quantum enabled RBM Advantage: Convolutional Autoencoders For Quantum Image Compression and Generative Learning.” *Defense + Commercial Sensing* (2020).

##### Example: Quantum-Support-Vector-Machine (QSVM)

In another example, we ran simulations for the Standard Banknote Authentication dataset and measured the following Key Performing Indicators (KPIs) using a Quantum Support Vector Machine (QSVM):

**Accuracy:**the fraction of samples that have been classified correctly**Precision:**proportion of correct positive identifications over all positive identifications**Recall:**proportion of correct positive identifications over all actual positives**F1 score:**harmonic mean of the model’s precision and recall

Here are the results:

Figure: Quantum (D-Wave) and Neuromorphic (Dynex) based SVM model training is superior to traditional support vector machines. We used Scikit-learn’s LIBSVM using Sequential Minimal Optimisation as benchmark

**Scientific background**: Rounds, Max and Phil Goddard. “Optimal feature selection in credit scoring and classification using a quantum annealer.” (2017).

#### Next Generation Algorithms for Machine Learning

Quantum computing algorithms for machine learning harness the power of quantum mechanics to enhance various aspects of machine learning tasks. As both, quantum computing and neuromorphic computing are sharing similar features, these algorithms can also be computed efficiently on the Dynex platform – but **without the limitations** of limited qubits, error correction or availability:

**Quantum Support Vector Machine (QSVM):**QSVM is a quantum-inspired algorithm that aims to classify data using a quantum kernel function. It leverages the concept of quantum superposition and quantum feature mapping to potentially provide computational advantages over classical SVM algorithms in certain scenarios.**Quantum Principal Component Analysis (QPCA):**QPCA is a quantum version of the classical Principal Component Analysis (PCA) algorithm. It utilizes quantum linear algebra techniques to extract the principal components from high-dimensional data, potentially enabling more efficient dimensionality reduction in quantum machine learning.**Quantum Neural Networks (QNN):**QNNs are quantum counterparts of classical neural networks. They leverage quantum principles, such as quantum superposition and entanglement, to process and manipulate data. QNNs hold the potential to learn complex patterns and perform tasks like classification and regression, benefiting from quantum parallelism.**Quantum K-Means Clustering:**Quantum K-means is a quantum-inspired variant of the classical K-means clustering algorithm. It uses quantum algorithms to accelerate the clustering process by exploring multiple solutions simultaneously. Quantum K-means has the potential to speed up clustering tasks for large-scale datasets.**Quantum Boltzmann Machines (QBMs):**QBMs are quantum analogues of classical Boltzmann Machines, which are generative models used for unsupervised learning. QBMs employ quantum annealing to sample from a probability distribution and learn patterns and structures in the data.**Quantum Support Vector Regression (QSVR):**QSVR extends the concept of QSVM to regression tasks. It uses quantum computing techniques to perform regression analysis, potentially offering advantages in terms of efficiency and accuracy over classical regression algorithms.

##### Examples

> Example: Quantum-Support-Vector-Machine Implementation on Dynex **Scientific background**: Rounds, Max and Phil Goddard. “Optimal feature selection in credit scoring and classification using a quantum annealer.” (2017)

> Example: Quantum-Support-Vector-Machine (PyTorch) on Dynex

**Scientific background**: Rounds, Max and Phil Goddard. “Optimal feature selection in credit scoring and classification using a quantum annealer.” (2017)

> Example: Quantum-Boltzmann-Machine (PyTorch) on Dynex **Scientific background**: Dixit V, Selvarajan R, Alam MA, Humble TS and Kais S (2021) Training Restricted Boltzmann Machines With a D-Wave Quantum Annealer. Front. Phys. 9:589626. doi: 10.3389/fphy.2021.589626; Sleeman, Jennifer, John E. Dorband and Milton Halem. “A Hybrid Quantum enabled RBM Advantage: Convolutional Autoencoders For Quantum Image Compression and Generative Learning.” Defense + Commercial Sensing (2020)

> Example: Quantum-Boltzmann-Machine Implementation (3-step QUBO) on Dynex **Scientific background**: Dixit V, Selvarajan R, Alam MA, Humble TS and Kais S (2021) Training Restricted Boltzmann Machines With a D-Wave Quantum Annealer. Front. Phys. 9:589626. doi: 10.3389/fphy.2021.589626; Sleeman, Jennifer, John E. Dorband and Milton Halem. “A Hybrid Quantum enabled RBM Advantage: Convolutional Autoencoders For Quantum Image Compression and Generative Learning.” Defense + Commercial Sensing (2020)

> Example: Mode-Assisted Unsupervised Quantum-Boltzmann-Machine Implementation (PyTorch) on Dynex**Scientific background**: Manukian, Haik, et al. "Mode-assisted unsupervised learning of restricted Boltzmann machines." *Communications Physics* 3.1 (2020): 105.; Dixit V, Selvarajan R, Alam MA, Humble TS and Kais S (2021) Training Restricted Boltzmann Machines With a D-Wave Quantum Annealer. Front. Phys. 9:589626. doi: 10.3389/fphy.2021.589626

> Example: Quantum-Boltzmann-Machine (Collaborative Filtering) on Dynex **Scientific background**: Dixit V, Selvarajan R, Alam MA, Humble TS and Kais S (2021) Training Restricted Boltzmann Machines With a D-Wave Quantum Annealer. Front. Phys. 9:589626. doi: 10.3389/fphy.2021.589626; Sleeman, Jennifer, John E. Dorband and Milton Halem. “A Hybrid Quantum enabled RBM Advantage: Convolutional Autoencoders For Quantum Image Compression and Generative Learning.” Defense + Commercial Sensing (2020)

> Example: Quantum-Boltzmann-Machine Implementation on Dynex **Scientific background**: Dixit V, Selvarajan R, Alam MA, Humble TS and Kais S (2021) Training Restricted Boltzmann Machines With a D-Wave Quantum Annealer. Front. Phys. 9:589626. doi: 10.3389/fphy.2021.589626; Sleeman, Jennifer, John E. Dorband and Milton Halem. “A Hybrid Quantum enabled RBM Advantage: Convolutional Autoencoders For Quantum Image Compression and Generative Learning.” Defense + Commercial Sensing (2020)

> Example: Feature Selection - Titanic Survivals **Scientific background**: Xuan Vinh Nguyen, Jeffrey Chan, Simone Romano, and James Bailey. 2014. Effective global approaches for mutual information based feature selection. In Proceedings of the 20th ACM SIGKDD international conference on Knowledge discovery and data mining (KDD ‘14). Association for Computing Machinery, New York, NY, USA, 512–521

> Example: Breast Cancer Prediction using the Dynex scikit-learn Plugin **Scientific background**: Bhatia, H.S., Phillipson, F. (2021). Performance Analysis of Support Vector Machine Implementations on the D-Wave Quantum Annealer. In: Paszynski, M., Kranzlmüller, D., Krzhizhanovskaya, V.V., Dongarra, J.J., Sloot, P.M.A. (eds) Computational Science – ICCS 2021. ICCS 2021. Lecture Notes in Computer Science(), vol 12747. Springer, Cham

**Quantum & Neuromorphic Computing Outperform Traditional Methods**

A new approach using simulated quantum annealing (SQA) to numerically simulate quantum sampling in a deep Boltzmann machine (DBM) was presented in [1]. The authors proposed a framework for training the network as a quantum Boltzmann machine (QBM) in the presence of a significant transverse field for reinforcement learning. However, they demonstrated that the process of embedding Boltzmann machines in larger quantum annealer architectures is problematic when huge weights and biases are needed to emulate the Boltzmann machine’s logical nodes using chains and clusters of physical qubits. On the other hand, quantum annealing has the potential to speed up the sampling process exponentially.

The Dynex Neuromorphic Platform **does not have these physical limitations** and can therefore overcome such scaling problems and expand to large, real-world datasets and problems.

##### Example: Quantum-Boltzmann-Machine (QBM)

This example demonstrates a Quantum-Boltzmann-Machine (QBM) implementation using the Dynex platform to perform the computations and compare it with a traditional Restricted-Boltzmann-Machine (RBM). RBM is a well-known probabilistic unsupervised learning model which is learned by an algorithm called Contrastive Divergence. An important step of this algorithm is called Gibbs sampling – a method that returns random samples from a given probability distribution. We decided to conduct our experiments on the popular MNIST dataset considered a standard benchmark in many of the machine learning and image recognition subfields. The implementation follows a highly optimised QUBO formulation.

Figure: The QBM evolves much faster to an attractive Mean Squared Error (MSE) than the traditional RBM, which means a significant lower amount of training iterations is required. In addition is the achieved MSE much lower, meaning the QBM created models have higher accuracy. This finding is in line with the results from the papers referenced. However, [1] demonstrated that the process of embedding Boltzmann machines in larger quantum annealer architectures is problematic when huge weights and biases are needed to emulate the Boltzmann machine’s logical nodes using chains and clusters of physical qubits because of the limited number of qubits available. The Dynex Neuromorphic platform provides a more scalable alternative and can used to train models with millions of variables. Especially when real-world models are to be trained, the number of training iterations and accuracy are important.

**Scientific background:** Dixit V, Selvarajan R, Alam MA, Humble TS and Kais S (2021) Training Restricted Boltzmann Machines With a D-Wave Quantum Annealer. *Front. Phys.* 9:589626. doi: 10.3389/fphy.2021.589626; Sleeman, Jennifer, John E. Dorband and Milton Halem. “A Hybrid Quantum enabled RBM Advantage: Convolutional Autoencoders For Quantum Image Compression and Generative Learning.” *Defense + Commercial Sensing* (2020).

##### Example: Quantum-Support-Vector-Machine (QSVM)

In another example, we ran simulations for the Standard Banknote Authentication dataset and measured the following Key Performing Indicators (KPIs) using a Quantum Support Vector Machine (QSVM):

**Accuracy:**the fraction of samples that have been classified correctly**Precision:**proportion of correct positive identifications over all positive identifications**Recall:**proportion of correct positive identifications over all actual positives**F1 score:**harmonic mean of the model’s precision and recall

Here are the results:

Figure: Quantum (D-Wave) and Neuromorphic (Dynex) based SVM model training is superior to traditional support vector machines. We used Scikit-learn’s LIBSVM using Sequential Minimal Optimisation as benchmark

**Scientific background**: Rounds, Max and Phil Goddard. “Optimal feature selection in credit scoring and classification using a quantum annealer.” (2017).

#### Next Generation Algorithms for Machine Learning

Quantum computing algorithms for machine learning harness the power of quantum mechanics to enhance various aspects of machine learning tasks. As both, quantum computing and neuromorphic computing are sharing similar features, these algorithms can also be computed efficiently on the Dynex platform – but **without the limitations** of limited qubits, error correction or availability:

**Quantum Support Vector Machine (QSVM):**QSVM is a quantum-inspired algorithm that aims to classify data using a quantum kernel function. It leverages the concept of quantum superposition and quantum feature mapping to potentially provide computational advantages over classical SVM algorithms in certain scenarios.**Quantum Principal Component Analysis (QPCA):**QPCA is a quantum version of the classical Principal Component Analysis (PCA) algorithm. It utilizes quantum linear algebra techniques to extract the principal components from high-dimensional data, potentially enabling more efficient dimensionality reduction in quantum machine learning.**Quantum Neural Networks (QNN):**QNNs are quantum counterparts of classical neural networks. They leverage quantum principles, such as quantum superposition and entanglement, to process and manipulate data. QNNs hold the potential to learn complex patterns and perform tasks like classification and regression, benefiting from quantum parallelism.**Quantum K-Means Clustering:**Quantum K-means is a quantum-inspired variant of the classical K-means clustering algorithm. It uses quantum algorithms to accelerate the clustering process by exploring multiple solutions simultaneously. Quantum K-means has the potential to speed up clustering tasks for large-scale datasets.**Quantum Boltzmann Machines (QBMs):**QBMs are quantum analogues of classical Boltzmann Machines, which are generative models used for unsupervised learning. QBMs employ quantum annealing to sample from a probability distribution and learn patterns and structures in the data.**Quantum Support Vector Regression (QSVR):**QSVR extends the concept of QSVM to regression tasks. It uses quantum computing techniques to perform regression analysis, potentially offering advantages in terms of efficiency and accuracy over classical regression algorithms.

##### Examples

> Example: Quantum-Support-Vector-Machine Implementation on Dynex **Scientific background**: Rounds, Max and Phil Goddard. “Optimal feature selection in credit scoring and classification using a quantum annealer.” (2017)

> Example: Quantum-Support-Vector-Machine (PyTorch) on Dynex

**Scientific background**: Rounds, Max and Phil Goddard. “Optimal feature selection in credit scoring and classification using a quantum annealer.” (2017)

> Example: Quantum-Boltzmann-Machine (PyTorch) on Dynex **Scientific background**: Dixit V, Selvarajan R, Alam MA, Humble TS and Kais S (2021) Training Restricted Boltzmann Machines With a D-Wave Quantum Annealer. Front. Phys. 9:589626. doi: 10.3389/fphy.2021.589626; Sleeman, Jennifer, John E. Dorband and Milton Halem. “A Hybrid Quantum enabled RBM Advantage: Convolutional Autoencoders For Quantum Image Compression and Generative Learning.” Defense + Commercial Sensing (2020)

> Example: Quantum-Boltzmann-Machine Implementation (3-step QUBO) on Dynex **Scientific background**: Dixit V, Selvarajan R, Alam MA, Humble TS and Kais S (2021) Training Restricted Boltzmann Machines With a D-Wave Quantum Annealer. Front. Phys. 9:589626. doi: 10.3389/fphy.2021.589626; Sleeman, Jennifer, John E. Dorband and Milton Halem. “A Hybrid Quantum enabled RBM Advantage: Convolutional Autoencoders For Quantum Image Compression and Generative Learning.” Defense + Commercial Sensing (2020)

> Example: Mode-Assisted Unsupervised Quantum-Boltzmann-Machine Implementation (PyTorch) on Dynex**Scientific background**: Manukian, Haik, et al. "Mode-assisted unsupervised learning of restricted Boltzmann machines." *Communications Physics* 3.1 (2020): 105.; Dixit V, Selvarajan R, Alam MA, Humble TS and Kais S (2021) Training Restricted Boltzmann Machines With a D-Wave Quantum Annealer. Front. Phys. 9:589626. doi: 10.3389/fphy.2021.589626

> Example: Quantum-Boltzmann-Machine (Collaborative Filtering) on Dynex **Scientific background**: Dixit V, Selvarajan R, Alam MA, Humble TS and Kais S (2021) Training Restricted Boltzmann Machines With a D-Wave Quantum Annealer. Front. Phys. 9:589626. doi: 10.3389/fphy.2021.589626; Sleeman, Jennifer, John E. Dorband and Milton Halem. “A Hybrid Quantum enabled RBM Advantage: Convolutional Autoencoders For Quantum Image Compression and Generative Learning.” Defense + Commercial Sensing (2020)

> Example: Quantum-Boltzmann-Machine Implementation on Dynex **Scientific background**: Dixit V, Selvarajan R, Alam MA, Humble TS and Kais S (2021) Training Restricted Boltzmann Machines With a D-Wave Quantum Annealer. Front. Phys. 9:589626. doi: 10.3389/fphy.2021.589626; Sleeman, Jennifer, John E. Dorband and Milton Halem. “A Hybrid Quantum enabled RBM Advantage: Convolutional Autoencoders For Quantum Image Compression and Generative Learning.” Defense + Commercial Sensing (2020)

> Example: Feature Selection - Titanic Survivals **Scientific background**: Xuan Vinh Nguyen, Jeffrey Chan, Simone Romano, and James Bailey. 2014. Effective global approaches for mutual information based feature selection. In Proceedings of the 20th ACM SIGKDD international conference on Knowledge discovery and data mining (KDD ‘14). Association for Computing Machinery, New York, NY, USA, 512–521

> Example: Breast Cancer Prediction using the Dynex scikit-learn Plugin **Scientific background**: Bhatia, H.S., Phillipson, F. (2021). Performance Analysis of Support Vector Machine Implementations on the D-Wave Quantum Annealer. In: Paszynski, M., Kranzlmüller, D., Krzhizhanovskaya, V.V., Dongarra, J.J., Sloot, P.M.A. (eds) Computational Science – ICCS 2021. ICCS 2021. Lecture Notes in Computer Science(), vol 12747. Springer, Cham

**Quantum & Neuromorphic Computing Outperform Traditional Methods**

A new approach using simulated quantum annealing (SQA) to numerically simulate quantum sampling in a deep Boltzmann machine (DBM) was presented in [1]. The authors proposed a framework for training the network as a quantum Boltzmann machine (QBM) in the presence of a significant transverse field for reinforcement learning. However, they demonstrated that the process of embedding Boltzmann machines in larger quantum annealer architectures is problematic when huge weights and biases are needed to emulate the Boltzmann machine’s logical nodes using chains and clusters of physical qubits. On the other hand, quantum annealing has the potential to speed up the sampling process exponentially.

The Dynex Neuromorphic Platform **does not have these physical limitations** and can therefore overcome such scaling problems and expand to large, real-world datasets and problems.

##### Example: Quantum-Boltzmann-Machine (QBM)

This example demonstrates a Quantum-Boltzmann-Machine (QBM) implementation using the Dynex platform to perform the computations and compare it with a traditional Restricted-Boltzmann-Machine (RBM). RBM is a well-known probabilistic unsupervised learning model which is learned by an algorithm called Contrastive Divergence. An important step of this algorithm is called Gibbs sampling – a method that returns random samples from a given probability distribution. We decided to conduct our experiments on the popular MNIST dataset considered a standard benchmark in many of the machine learning and image recognition subfields. The implementation follows a highly optimised QUBO formulation.

Figure: The QBM evolves much faster to an attractive Mean Squared Error (MSE) than the traditional RBM, which means a significant lower amount of training iterations is required. In addition is the achieved MSE much lower, meaning the QBM created models have higher accuracy. This finding is in line with the results from the papers referenced. However, [1] demonstrated that the process of embedding Boltzmann machines in larger quantum annealer architectures is problematic when huge weights and biases are needed to emulate the Boltzmann machine’s logical nodes using chains and clusters of physical qubits because of the limited number of qubits available. The Dynex Neuromorphic platform provides a more scalable alternative and can used to train models with millions of variables. Especially when real-world models are to be trained, the number of training iterations and accuracy are important.

**Scientific background:** Dixit V, Selvarajan R, Alam MA, Humble TS and Kais S (2021) Training Restricted Boltzmann Machines With a D-Wave Quantum Annealer. *Front. Phys.* 9:589626. doi: 10.3389/fphy.2021.589626; Sleeman, Jennifer, John E. Dorband and Milton Halem. “A Hybrid Quantum enabled RBM Advantage: Convolutional Autoencoders For Quantum Image Compression and Generative Learning.” *Defense + Commercial Sensing* (2020).

##### Example: Quantum-Support-Vector-Machine (QSVM)

In another example, we ran simulations for the Standard Banknote Authentication dataset and measured the following Key Performing Indicators (KPIs) using a Quantum Support Vector Machine (QSVM):

**Accuracy:**the fraction of samples that have been classified correctly**Precision:**proportion of correct positive identifications over all positive identifications**Recall:**proportion of correct positive identifications over all actual positives**F1 score:**harmonic mean of the model’s precision and recall

Here are the results:

Figure: Quantum (D-Wave) and Neuromorphic (Dynex) based SVM model training is superior to traditional support vector machines. We used Scikit-learn’s LIBSVM using Sequential Minimal Optimisation as benchmark

**Scientific background**: Rounds, Max and Phil Goddard. “Optimal feature selection in credit scoring and classification using a quantum annealer.” (2017).

Design by Onur Oztaskiran