Dynex

Compute on Dynex

# Advanced Examples

Here are some advanced code examples and notebooks to be used to compute them on the Dynex neuromorphic computing platform:

#### RNA Folding

Finds the optimal stem configuration of the RNA sequence from the HIV virus and the Tobacco Mild Green Mosaic Virus using the Dynex platform. The example takes an RNA sequence and applies a quadratic model in pursuit of the optimal stem configuration.

> Jupyter Notebook**Scientific background**: Fox DM, MacDermaid CM, Schreij AMA, Zwierzyna M, Walker RC. RNA folding using quantum computers,. PLoS Comput Biol. 2022 Apr 11;18(4):e1010032. doi: 10.1371/journal.pcbi.1010032. PMID: 35404931; PMCID: PMC9022793

#### Breast Cancer Prediction

This examples shows using the Dynex SDK Scikit package which provides a scikit-learn transformer for feature selection using the Dynex Neuromorphic Computing Platform. The number of features have impact on neural network training and accuracy. It will be demonstrated how a significant reduction of features lead to similar (or even better) results.

> Jupyter Notebook**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

#### Enzyme-Target Prediction on the Dynex Platform

The Dynex SDK based program predicts potential interactions between enzymes and target molecules and leverages the principles of quantum mechanics.

> Jupyter Notebook**Scientific background**: Hoang M Ngo, My T Thai, Tamer Kahveci, QuTIE: Quantum optimization for Target Identification by Enzymes, *Bioinformatics Advances*, 2023;, vbad112

#### Single Image Super-Resolution on the Dynex Platform

Implementation of a Quantum Single Image Super-Resolution algorithm to use on the Dynex platform. One of the well-known classical approaches for SISR relies on the well-established patch-wise sparse modeling of the problem. Yet, this field’s current state of affairs is that deep neural networks (DNNs) have demonstrated far superior results than traditional approaches. Nevertheless, quantum computing is expected to become increasingly prominent for machine learning problems soon. Among the two paradigms of quantum computing, namely universal gate quantum computing and adiabatic quantum computing (AQC), the latter has been successfully applied to practical computer vision problems, in which quantum parallelism has been exploited to solve combinatorial optimization efficiently. This algorithm demonstrates formulating quantum SISR as a sparse coding optimization problem, which is solved using the Dynex Neuromorphic Computing Platform via the Dynex SDK. This AQC-based algorithm is demonstrated to achieve improved SISR accuracy.

**Scientific background**: Choong HY, Kumar S, Van Gool L. Quantum Annealing for Single Image Super-Resolution. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition 2023 (pp. 1150-1159)

#### Recommender System on the Dynex Platform

This example shows a recommender system exploiting community detection. Community detection, by partitioning users and items into densely connected clusters, can boost the accuracy of non-personalised recommendation by assuming that users within each community share similar tastes.

**Scientific background**: Nembrini, Riccardo & Carugno, Costantino & Ferrari Dacrema, Maurizio & Cremonesi, Paolo. (2022). Towards Recommender Systems with Community Detection and Quantum Computing. 579-585. 10.1145/3523227.3551478

#### Reinforcement Learning Using QBM on the Dynex Platform

We associate a transverse field Ising spin Hamiltonian with a layout of qubits similar to that of a deep Boltzmann machine (DBM) and use the Dynex Platform for sampling. We design a reinforcement learning algorithm in which the set of visible nodes representing the states and actions of an optimal policy are the first and last layers of the deep network. In absence of a transverse field, our simulations show that DBMs are trained more effectively than restricted Boltzmann machines (RBM) with the same number of nodes.

**Scientific background**: Crawford, Daniel & Levit, Anna & Ghadermarzy, Navid & Oberoi, Jaspreet Singh & Ronagh, Pooya. (2018). Reinforcement learning using quantum Boltzmann machines. Quantum Information and Computation. 18. 51-74. 10.26421/QIC18.1-2-3.

#### Optimal WiFi Hotspot positioning with the Dynex Platform

This notebook performs analysis on architectural plans, particularly focusing on identifying zones, walls, and other features. It then applies graph theory to optimise the placement of WiFi hotspots. It performs processing of the plan, applying edge detection and walls baselines extraction and finally calls the Dynex SDK sampler to find the optimum position of the WIFI hotspot.

#### Quantum-Boltzmann-Machine (QBM) on the Dynex Platform

We demonstrate a Quantum-Boltzmann-Machine (QBM) implementation using the Dynex platform to perform the computations and compare it with a traditional Restricted-Boltzmann-Machine (RBM) applied on the MNIST dataset of handwritten digital images with 60,000 training and 10,000 testing samples.

> Jupyter Notebook**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).

#### Quantum Support-Vector-Machine (QSVM) on the Dynex Platform

In this example a classical classiﬁcation model, Kernel-Support Vector machine, is implemented as a Quadratic Unconstrained Binary Optimisation problem. Here, data points are classiﬁed by a separating hyperplane while maximizing the function margin. The problem is solved for a public Banknote Authentication dataset and the well- known Iris Dataset using the **Dynex Neuromorphic Computing Platform**.

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

#### Placement of EV Charging Stations

Determining optimal locations to build new electric vehicle charging stations is a complex optimization problem. Many factors should be taken into consideration, like existing charger locations, points of interest (POIs), quantity to build, etc. In this example, we take a look at how we might formulate this optimization problem and solve it using the Dynex Neuromorphic Platform.

> Jupyter Notebook**Scientific background**: Pagany, Raphaela & Marquardt, Anna & Zink, Roland. (2019). Electric Charging Demand Location Model—A User-and Destination-Based Locating Approach for Electric Vehicle Charging Stations. Sustainability. 11. 2301. 10.3390/su11082301

#### Feature Selection

Feature selection for machine learning using mutual information to predict survivals of Titanic passengers. The method used is applicable to problems from a wide range of domains, for example financial portfolio optimization.

> Jupyter Notebook**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

##### Quantum Integer Factorization on the Dynex Platform

Identifying new methods for integer factorization plays an important role in modern information security. Shor’s algorithm is perhaps the most well-known method for integer factorization. An equally powerful model of quantum computing is the adiabatic quantum computing (AQC) model, which can also solve the integer factorization problem. In this example, we show how to convert an arbitrary integer factorization problem to an executable Ising model and tested it on the Dynex Neuromorphic Platform.

> Jupyter Notebook**Scientific background**: Jiang, S., Britt, K.A., McCaskey, A.J. *et al.* Quantum Annealing for Prime Factorization. *Sci Rep* **8**, 17667 (2018)

Here are some advanced code examples and notebooks to be used to compute them on the Dynex neuromorphic computing platform:

#### RNA Folding

Finds the optimal stem configuration of the RNA sequence from the HIV virus and the Tobacco Mild Green Mosaic Virus using the Dynex platform. The example takes an RNA sequence and applies a quadratic model in pursuit of the optimal stem configuration.

> Jupyter Notebook**Scientific background**: Fox DM, MacDermaid CM, Schreij AMA, Zwierzyna M, Walker RC. RNA folding using quantum computers,. PLoS Comput Biol. 2022 Apr 11;18(4):e1010032. doi: 10.1371/journal.pcbi.1010032. PMID: 35404931; PMCID: PMC9022793

#### Breast Cancer Prediction

This examples shows using the Dynex SDK Scikit package which provides a scikit-learn transformer for feature selection using the Dynex Neuromorphic Computing Platform. The number of features have impact on neural network training and accuracy. It will be demonstrated how a significant reduction of features lead to similar (or even better) results.

> Jupyter Notebook**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

#### Enzyme-Target Prediction on the Dynex Platform

The Dynex SDK based program predicts potential interactions between enzymes and target molecules and leverages the principles of quantum mechanics.

> Jupyter Notebook**Scientific background**: Hoang M Ngo, My T Thai, Tamer Kahveci, QuTIE: Quantum optimization for Target Identification by Enzymes, *Bioinformatics Advances*, 2023;, vbad112

#### Single Image Super-Resolution on the Dynex Platform

Implementation of a Quantum Single Image Super-Resolution algorithm to use on the Dynex platform. One of the well-known classical approaches for SISR relies on the well-established patch-wise sparse modeling of the problem. Yet, this field’s current state of affairs is that deep neural networks (DNNs) have demonstrated far superior results than traditional approaches. Nevertheless, quantum computing is expected to become increasingly prominent for machine learning problems soon. Among the two paradigms of quantum computing, namely universal gate quantum computing and adiabatic quantum computing (AQC), the latter has been successfully applied to practical computer vision problems, in which quantum parallelism has been exploited to solve combinatorial optimization efficiently. This algorithm demonstrates formulating quantum SISR as a sparse coding optimization problem, which is solved using the Dynex Neuromorphic Computing Platform via the Dynex SDK. This AQC-based algorithm is demonstrated to achieve improved SISR accuracy.

**Scientific background**: Choong HY, Kumar S, Van Gool L. Quantum Annealing for Single Image Super-Resolution. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition 2023 (pp. 1150-1159)

#### Recommender System on the Dynex Platform

This example shows a recommender system exploiting community detection. Community detection, by partitioning users and items into densely connected clusters, can boost the accuracy of non-personalised recommendation by assuming that users within each community share similar tastes.

**Scientific background**: Nembrini, Riccardo & Carugno, Costantino & Ferrari Dacrema, Maurizio & Cremonesi, Paolo. (2022). Towards Recommender Systems with Community Detection and Quantum Computing. 579-585. 10.1145/3523227.3551478

#### Reinforcement Learning Using QBM on the Dynex Platform

We associate a transverse field Ising spin Hamiltonian with a layout of qubits similar to that of a deep Boltzmann machine (DBM) and use the Dynex Platform for sampling. We design a reinforcement learning algorithm in which the set of visible nodes representing the states and actions of an optimal policy are the first and last layers of the deep network. In absence of a transverse field, our simulations show that DBMs are trained more effectively than restricted Boltzmann machines (RBM) with the same number of nodes.

**Scientific background**: Crawford, Daniel & Levit, Anna & Ghadermarzy, Navid & Oberoi, Jaspreet Singh & Ronagh, Pooya. (2018). Reinforcement learning using quantum Boltzmann machines. Quantum Information and Computation. 18. 51-74. 10.26421/QIC18.1-2-3.

#### Optimal WiFi Hotspot positioning with the Dynex Platform

This notebook performs analysis on architectural plans, particularly focusing on identifying zones, walls, and other features. It then applies graph theory to optimise the placement of WiFi hotspots. It performs processing of the plan, applying edge detection and walls baselines extraction and finally calls the Dynex SDK sampler to find the optimum position of the WIFI hotspot.

#### Quantum-Boltzmann-Machine (QBM) on the Dynex Platform

We demonstrate a Quantum-Boltzmann-Machine (QBM) implementation using the Dynex platform to perform the computations and compare it with a traditional Restricted-Boltzmann-Machine (RBM) applied on the MNIST dataset of handwritten digital images with 60,000 training and 10,000 testing samples.

> Jupyter Notebook**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).

#### Quantum Support-Vector-Machine (QSVM) on the Dynex Platform

In this example a classical classiﬁcation model, Kernel-Support Vector machine, is implemented as a Quadratic Unconstrained Binary Optimisation problem. Here, data points are classiﬁed by a separating hyperplane while maximizing the function margin. The problem is solved for a public Banknote Authentication dataset and the well- known Iris Dataset using the **Dynex Neuromorphic Computing Platform**.

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

#### Placement of EV Charging Stations

Determining optimal locations to build new electric vehicle charging stations is a complex optimization problem. Many factors should be taken into consideration, like existing charger locations, points of interest (POIs), quantity to build, etc. In this example, we take a look at how we might formulate this optimization problem and solve it using the Dynex Neuromorphic Platform.

> Jupyter Notebook**Scientific background**: Pagany, Raphaela & Marquardt, Anna & Zink, Roland. (2019). Electric Charging Demand Location Model—A User-and Destination-Based Locating Approach for Electric Vehicle Charging Stations. Sustainability. 11. 2301. 10.3390/su11082301

#### Feature Selection

Feature selection for machine learning using mutual information to predict survivals of Titanic passengers. The method used is applicable to problems from a wide range of domains, for example financial portfolio optimization.

> Jupyter Notebook**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

##### Quantum Integer Factorization on the Dynex Platform

Identifying new methods for integer factorization plays an important role in modern information security. Shor’s algorithm is perhaps the most well-known method for integer factorization. An equally powerful model of quantum computing is the adiabatic quantum computing (AQC) model, which can also solve the integer factorization problem. In this example, we show how to convert an arbitrary integer factorization problem to an executable Ising model and tested it on the Dynex Neuromorphic Platform.

> Jupyter Notebook**Scientific background**: Jiang, S., Britt, K.A., McCaskey, A.J. *et al.* Quantum Annealing for Prime Factorization. *Sci Rep* **8**, 17667 (2018)

Here are some advanced code examples and notebooks to be used to compute them on the Dynex neuromorphic computing platform:

#### RNA Folding

Finds the optimal stem configuration of the RNA sequence from the HIV virus and the Tobacco Mild Green Mosaic Virus using the Dynex platform. The example takes an RNA sequence and applies a quadratic model in pursuit of the optimal stem configuration.

> Jupyter Notebook**Scientific background**: Fox DM, MacDermaid CM, Schreij AMA, Zwierzyna M, Walker RC. RNA folding using quantum computers,. PLoS Comput Biol. 2022 Apr 11;18(4):e1010032. doi: 10.1371/journal.pcbi.1010032. PMID: 35404931; PMCID: PMC9022793

#### Breast Cancer Prediction

This examples shows using the Dynex SDK Scikit package which provides a scikit-learn transformer for feature selection using the Dynex Neuromorphic Computing Platform. The number of features have impact on neural network training and accuracy. It will be demonstrated how a significant reduction of features lead to similar (or even better) results.

> Jupyter Notebook**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

#### Enzyme-Target Prediction on the Dynex Platform

The Dynex SDK based program predicts potential interactions between enzymes and target molecules and leverages the principles of quantum mechanics.

> Jupyter Notebook**Scientific background**: Hoang M Ngo, My T Thai, Tamer Kahveci, QuTIE: Quantum optimization for Target Identification by Enzymes, *Bioinformatics Advances*, 2023;, vbad112

#### Single Image Super-Resolution on the Dynex Platform

Implementation of a Quantum Single Image Super-Resolution algorithm to use on the Dynex platform. One of the well-known classical approaches for SISR relies on the well-established patch-wise sparse modeling of the problem. Yet, this field’s current state of affairs is that deep neural networks (DNNs) have demonstrated far superior results than traditional approaches. Nevertheless, quantum computing is expected to become increasingly prominent for machine learning problems soon. Among the two paradigms of quantum computing, namely universal gate quantum computing and adiabatic quantum computing (AQC), the latter has been successfully applied to practical computer vision problems, in which quantum parallelism has been exploited to solve combinatorial optimization efficiently. This algorithm demonstrates formulating quantum SISR as a sparse coding optimization problem, which is solved using the Dynex Neuromorphic Computing Platform via the Dynex SDK. This AQC-based algorithm is demonstrated to achieve improved SISR accuracy.

**Scientific background**: Choong HY, Kumar S, Van Gool L. Quantum Annealing for Single Image Super-Resolution. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition 2023 (pp. 1150-1159)

#### Recommender System on the Dynex Platform

This example shows a recommender system exploiting community detection. Community detection, by partitioning users and items into densely connected clusters, can boost the accuracy of non-personalised recommendation by assuming that users within each community share similar tastes.

**Scientific background**: Nembrini, Riccardo & Carugno, Costantino & Ferrari Dacrema, Maurizio & Cremonesi, Paolo. (2022). Towards Recommender Systems with Community Detection and Quantum Computing. 579-585. 10.1145/3523227.3551478

#### Reinforcement Learning Using QBM on the Dynex Platform

We associate a transverse field Ising spin Hamiltonian with a layout of qubits similar to that of a deep Boltzmann machine (DBM) and use the Dynex Platform for sampling. We design a reinforcement learning algorithm in which the set of visible nodes representing the states and actions of an optimal policy are the first and last layers of the deep network. In absence of a transverse field, our simulations show that DBMs are trained more effectively than restricted Boltzmann machines (RBM) with the same number of nodes.

**Scientific background**: Crawford, Daniel & Levit, Anna & Ghadermarzy, Navid & Oberoi, Jaspreet Singh & Ronagh, Pooya. (2018). Reinforcement learning using quantum Boltzmann machines. Quantum Information and Computation. 18. 51-74. 10.26421/QIC18.1-2-3.

#### Optimal WiFi Hotspot positioning with the Dynex Platform

This notebook performs analysis on architectural plans, particularly focusing on identifying zones, walls, and other features. It then applies graph theory to optimise the placement of WiFi hotspots. It performs processing of the plan, applying edge detection and walls baselines extraction and finally calls the Dynex SDK sampler to find the optimum position of the WIFI hotspot.

#### Quantum-Boltzmann-Machine (QBM) on the Dynex Platform

We demonstrate a Quantum-Boltzmann-Machine (QBM) implementation using the Dynex platform to perform the computations and compare it with a traditional Restricted-Boltzmann-Machine (RBM) applied on the MNIST dataset of handwritten digital images with 60,000 training and 10,000 testing samples.

> Jupyter Notebook**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).

#### Quantum Support-Vector-Machine (QSVM) on the Dynex Platform

In this example a classical classiﬁcation model, Kernel-Support Vector machine, is implemented as a Quadratic Unconstrained Binary Optimisation problem. Here, data points are classiﬁed by a separating hyperplane while maximizing the function margin. The problem is solved for a public Banknote Authentication dataset and the well- known Iris Dataset using the **Dynex Neuromorphic Computing Platform**.

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

#### Placement of EV Charging Stations

Determining optimal locations to build new electric vehicle charging stations is a complex optimization problem. Many factors should be taken into consideration, like existing charger locations, points of interest (POIs), quantity to build, etc. In this example, we take a look at how we might formulate this optimization problem and solve it using the Dynex Neuromorphic Platform.

> Jupyter Notebook**Scientific background**: Pagany, Raphaela & Marquardt, Anna & Zink, Roland. (2019). Electric Charging Demand Location Model—A User-and Destination-Based Locating Approach for Electric Vehicle Charging Stations. Sustainability. 11. 2301. 10.3390/su11082301

#### Feature Selection

Feature selection for machine learning using mutual information to predict survivals of Titanic passengers. The method used is applicable to problems from a wide range of domains, for example financial portfolio optimization.

> Jupyter Notebook**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

##### Quantum Integer Factorization on the Dynex Platform

Identifying new methods for integer factorization plays an important role in modern information security. Shor’s algorithm is perhaps the most well-known method for integer factorization. An equally powerful model of quantum computing is the adiabatic quantum computing (AQC) model, which can also solve the integer factorization problem. In this example, we show how to convert an arbitrary integer factorization problem to an executable Ising model and tested it on the Dynex Neuromorphic Platform.

> Jupyter Notebook**Scientific background**: Jiang, S., Britt, K.A., McCaskey, A.J. *et al.* Quantum Annealing for Prime Factorization. *Sci Rep* **8**, 17667 (2018)

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