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Compute on Dynex

Dynex

Industries

Compute on Dynex

Dynex

Industries

Compute on Dynex

# Artificial Intelligence

### Artificial Intelligence

#### Artificial Intelligence

Quantum computing is on the verge of revolutionizing the field of Artificial Intelligence (AI), heralding a new era where AI systems can process information and learn at speeds and depths previously unimaginable. By leveraging the principles of quantum mechanics, quantum computing can perform complex calculations at exponentially faster rates than traditional computers, enabling AI to analyze vast datasets more efficiently. This quantum acceleration will significantly enhance machine learning models, making them more accurate and capable of solving highly complex problems, from understanding natural languages with greater nuance to predicting trends and behaviors in data that were once considered too intricate to decode.

In particular, quantum computing can transform deep learning, a subset of AI that involves training large neural networks. These networks, which mimic the human brain's ability to learn and make decisions, could be trained much faster and on a scale that is currently unattainable. This means that AI systems could evolve to understand and interact with the world in more sophisticated and human-like ways, potentially unlocking breakthroughs in AI's ability to automate complex tasks, enhance decision-making, and innovate across sectors like healthcare, finance, environmental science, and beyond.

Furthermore, the fusion of quantum computing and AI holds the promise of solving some of the most pressing challenges faced by humanity, including climate change, by optimizing energy consumption and discovering new materials for carbon capture. It could revolutionize drug discovery by simulating the quantum properties of molecules, a task that is incredibly time-consuming and resource-intensive with current technology. The synergy between quantum computing and AI not only paves the way for advancements in existing applications but also opens up new frontiers for exploration and innovation, making what was once science fiction a tangible reality.

#### Using Dynex for particle tracking at the Large Hadron Collider (LHC)

The Large Hadron Collider (LHC) is the world’s largest and most powerful particle accelerator. It aims at discovering what our universe is made of by colliding particle beams at high speed, thus creating ‘mini big bangs’. The result of those collisions is a firework of new particles, whose study can help understand what our universe is made of. This repository uses Dynex for superlinear speedup for particle tracking.

> Github Repository HEPQPR.Qallse on Dynex

#### 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).

#### 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)

#### 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).

**Mode-Assisted Quantum Restricted Boltzmann Machines**

The integration of neuromorphic computing into the Dynex platform signifies a transformative step in computational technology, particularly in the realms of machine learning and optimization. This advanced platform leverages the unique attributes of neuromorphic dynamics, utilising neuromorphic annealing - a technique divergent from conventional computing methods - to adeptly address intricate problems in discrete optimization, sampling, and machine learning.

#### Efficient Quantum State Tomography on Dynex

Quantum state tomography is a process used in quantum physics to characterize and reconstruct the quantum state of a system. In simple terms, it's like taking a snapshot of a quantum system to understand its properties fully. In quantum mechanics, a quantum state represents the complete description of a quantum system, including its position, momentum, energy, and other physical quantities. However, unlike classical systems where properties are well-defined, quantum systems often exist in superposition states, meaning they can simultaneously be in multiple states until measured. While traditional training methods perform rather poorly, Dynex computed training achieves near perfect fidelity.

> Quantum Mode-assisted unsupervised learning of Restricted Boltzmann Machines

**Scientific background**: Yuan-Hang Zhang. Efficient Quantum State Tomography with Mode-assisted Training. Physical Review A. 106. 10.1103/PhysRevA.106.042420.

#### 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.

#### 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

> Automotive, Aerospace, Super-Sports and Space

Quantum computing is on the verge of revolutionizing the field of Artificial Intelligence (AI), heralding a new era where AI systems can process information and learn at speeds and depths previously unimaginable. By leveraging the principles of quantum mechanics, quantum computing can perform complex calculations at exponentially faster rates than traditional computers, enabling AI to analyze vast datasets more efficiently. This quantum acceleration will significantly enhance machine learning models, making them more accurate and capable of solving highly complex problems, from understanding natural languages with greater nuance to predicting trends and behaviors in data that were once considered too intricate to decode.

In particular, quantum computing can transform deep learning, a subset of AI that involves training large neural networks. These networks, which mimic the human brain's ability to learn and make decisions, could be trained much faster and on a scale that is currently unattainable. This means that AI systems could evolve to understand and interact with the world in more sophisticated and human-like ways, potentially unlocking breakthroughs in AI's ability to automate complex tasks, enhance decision-making, and innovate across sectors like healthcare, finance, environmental science, and beyond.

Furthermore, the fusion of quantum computing and AI holds the promise of solving some of the most pressing challenges faced by humanity, including climate change, by optimizing energy consumption and discovering new materials for carbon capture. It could revolutionize drug discovery by simulating the quantum properties of molecules, a task that is incredibly time-consuming and resource-intensive with current technology. The synergy between quantum computing and AI not only paves the way for advancements in existing applications but also opens up new frontiers for exploration and innovation, making what was once science fiction a tangible reality.

#### Using Dynex for particle tracking at the Large Hadron Collider (LHC)

The Large Hadron Collider (LHC) is the world’s largest and most powerful particle accelerator. It aims at discovering what our universe is made of by colliding particle beams at high speed, thus creating ‘mini big bangs’. The result of those collisions is a firework of new particles, whose study can help understand what our universe is made of. This repository uses Dynex for superlinear speedup for particle tracking.

> Github Repository HEPQPR.Qallse on Dynex

#### 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).

#### 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)

#### 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).

**Mode-Assisted Quantum Restricted Boltzmann Machines**

The integration of neuromorphic computing into the Dynex platform signifies a transformative step in computational technology, particularly in the realms of machine learning and optimization. This advanced platform leverages the unique attributes of neuromorphic dynamics, utilising neuromorphic annealing - a technique divergent from conventional computing methods - to adeptly address intricate problems in discrete optimization, sampling, and machine learning.

#### Efficient Quantum State Tomography on Dynex

Quantum state tomography is a process used in quantum physics to characterize and reconstruct the quantum state of a system. In simple terms, it's like taking a snapshot of a quantum system to understand its properties fully. In quantum mechanics, a quantum state represents the complete description of a quantum system, including its position, momentum, energy, and other physical quantities. However, unlike classical systems where properties are well-defined, quantum systems often exist in superposition states, meaning they can simultaneously be in multiple states until measured. While traditional training methods perform rather poorly, Dynex computed training achieves near perfect fidelity.

> Quantum Mode-assisted unsupervised learning of Restricted Boltzmann Machines

**Scientific background**: Yuan-Hang Zhang. Efficient Quantum State Tomography with Mode-assisted Training. Physical Review A. 106. 10.1103/PhysRevA.106.042420.

#### 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.

#### 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

> Automotive, Aerospace, Super-Sports and Space

Quantum computing is on the verge of revolutionizing the field of Artificial Intelligence (AI), heralding a new era where AI systems can process information and learn at speeds and depths previously unimaginable. By leveraging the principles of quantum mechanics, quantum computing can perform complex calculations at exponentially faster rates than traditional computers, enabling AI to analyze vast datasets more efficiently. This quantum acceleration will significantly enhance machine learning models, making them more accurate and capable of solving highly complex problems, from understanding natural languages with greater nuance to predicting trends and behaviors in data that were once considered too intricate to decode.

In particular, quantum computing can transform deep learning, a subset of AI that involves training large neural networks. These networks, which mimic the human brain's ability to learn and make decisions, could be trained much faster and on a scale that is currently unattainable. This means that AI systems could evolve to understand and interact with the world in more sophisticated and human-like ways, potentially unlocking breakthroughs in AI's ability to automate complex tasks, enhance decision-making, and innovate across sectors like healthcare, finance, environmental science, and beyond.

Furthermore, the fusion of quantum computing and AI holds the promise of solving some of the most pressing challenges faced by humanity, including climate change, by optimizing energy consumption and discovering new materials for carbon capture. It could revolutionize drug discovery by simulating the quantum properties of molecules, a task that is incredibly time-consuming and resource-intensive with current technology. The synergy between quantum computing and AI not only paves the way for advancements in existing applications but also opens up new frontiers for exploration and innovation, making what was once science fiction a tangible reality.

#### Using Dynex for particle tracking at the Large Hadron Collider (LHC)

The Large Hadron Collider (LHC) is the world’s largest and most powerful particle accelerator. It aims at discovering what our universe is made of by colliding particle beams at high speed, thus creating ‘mini big bangs’. The result of those collisions is a firework of new particles, whose study can help understand what our universe is made of. This repository uses Dynex for superlinear speedup for particle tracking.

> Github Repository HEPQPR.Qallse on Dynex

#### 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).

#### 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)

#### 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).

**Mode-Assisted Quantum Restricted Boltzmann Machines**

The integration of neuromorphic computing into the Dynex platform signifies a transformative step in computational technology, particularly in the realms of machine learning and optimization. This advanced platform leverages the unique attributes of neuromorphic dynamics, utilising neuromorphic annealing - a technique divergent from conventional computing methods - to adeptly address intricate problems in discrete optimization, sampling, and machine learning.

#### Efficient Quantum State Tomography on Dynex

Quantum state tomography is a process used in quantum physics to characterize and reconstruct the quantum state of a system. In simple terms, it's like taking a snapshot of a quantum system to understand its properties fully. In quantum mechanics, a quantum state represents the complete description of a quantum system, including its position, momentum, energy, and other physical quantities. However, unlike classical systems where properties are well-defined, quantum systems often exist in superposition states, meaning they can simultaneously be in multiple states until measured. While traditional training methods perform rather poorly, Dynex computed training achieves near perfect fidelity.

> Quantum Mode-assisted unsupervised learning of Restricted Boltzmann Machines

**Scientific background**: Yuan-Hang Zhang. Efficient Quantum State Tomography with Mode-assisted Training. Physical Review A. 106. 10.1103/PhysRevA.106.042420.

#### 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.

#### 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

> Automotive, Aerospace, Super-Sports and Space