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# Benchmarks

### Benchmarks

#### Benchmarks

Our Dynex platform has been rigorously benchmarked against both traditional and quantum computing systems, demonstrating consistent superiority in performance. Through comprehensive testing across a variety of complex computational tasks, Dynex has proven to deliver faster processing times and more efficient problem-solving capabilities. This consistent outperformance underscores the robustness of our technology, making it a preferred choice for industries seeking to leverage advanced computing power. By blending the best attributes of quantum and neuromorphic computing, Dynex offers a unique solution that significantly enhances computational efficiency and effectiveness, setting a new standard in the computing landscape.

##### Benchmarking the Dynex n.quantum Platform with the Q-Score

In the context of our study, we employ the Q-score to benchmark the computing capabilities of the Dynex Neuromorphic Quantum Computing Platform, facilitating a comparative evaluation with contemporary state-of-the-art quantum computers. Our findings demonstrate that the Dynex platform exhibits remarkable performance superiority over the presently largest quantum computing systems. While physical quantum computing systems such as Google’s Sycamore, IBM’s Osprey, D-Wave’s Advantage, and Rigetti’s Aspen-M-2 have reportedly achieved Q-scores not surpassing 140, the Dynex Neuromorphic Platform has demonstrated a Q-score exceeding 15,000.

> Medium: Benchmarking the Dynex Neuromorphic Platform with the Q-Score

##### Benchmark: CFD vs. Quantum-CFD

Computational Fluid Dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and algorithms to solve and analyze problems involving fluid flows. By utilizing computational software, CFD simulates the interaction of liquids and gases with surfaces, defined by boundary conditions and initial conditions. This technique allows engineers and scientists to visualize and predict fluid flow behavior, heat transfer, and related phenomena in a virtual setting, without the need for costly and time-consuming physical experiments. CFD is widely used in industries such as aerospace, automotive, and energy, for designing and optimizing processes and products like aircraft wings, engine components, and wind turbines. The Quantum-CFD algorithm is superior to traditional CFD methods, resulting in 95% less computation time required and 90% less costs.

> Github: QCFD Benchmark (independent repo)

##### Dynex finds best-known MaxCut for the Stanford G70 benchmark

The cut size 9,553 for G70 found by Dynex is the best-known MaxCut than previous reported results on June 8th 2024. The previous record of 9,541 was found using a special purpose algorithm designed for MaxCut (Breakout Local Search for the Max-Cut problem) in 2013. This achievement underscores the power and efficiency of our neuromorphic quantum computing platform, especially given that improving the cut size by even one involves exponentially increasing complexity. The following table displays the previously known best MaxCut values for various Gset benchmarks, including the G70 dataset. Results for D-Wave have been computed using the D-Wave Cloud Platform using the Advantage™ quantum computer with 5,000 physical qubits.

> G70 MaxCut Solution on Dynex Github

##### Enhancing MaxCut Solutions: Dynex’s Benchmark Performance on G70 Using Quantum Computing

We conducted an experiment on the G70 MaxCut problem, a complex unweighted MaxCut challenge with 10,000 nodes and 99,999 edges sourced from the publicly available Gset dataset provided by Stanford University. Various algorithms and solvers were evaluated, including commercial solvers like Gurobi and IBM CPLEX, and specialized algorithms such as the SDP solver DSDP, the graph neural network-based PI-GNN, and the tabu search-based KHLWG. Utilizing Dynex’s neuromorphic quantum computing cloud with a single Nvidia RTX3080 GPU, and without any MaxCut-specific enhancements, Dynex achieved a Maximum Cut value of 9,506 — outperforming other algorithms and demonstrating the potential of the Dynex platform. The experiment underscores that additional computational resources or bespoke algorithmic modifications could potentially lead to even higher performance, potentially setting new benchmarks for MaxCut solutions and showcasing the scalability and adaptability of the Dynex platform for tackling such optimization problems.

> Medium: Enhancing MaxCut Solutions: Dynex’s Benchmark Performance on G70 Using Quantum Computing

> Github: Jupyter Notebook

##### MaxCut Quantum Simulation Record

Dynex announced a significant breakthrough in the field of quantum computing, achieved through the Dynex neuromorphic quantum computing platform. By employing a sophisticated quantum algorithm, we successfully solved a graph containing 10,000 vertices, setting a new record that surpasses the previous benchmark by threefold.

> Dynex Sets New World Record for Quantum Computing, Breaking NVIDIA’s Previous Record

##### Benchmark: 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.

> Github: Dynex MA-QRBM Package

**Scientific background**: Advancements in Unsupervised Learning: Mode-Assisted Quantum Restricted Boltzmann Machines Leveraging Neuromorphic Computing on the Dynex Platform; Adam Neumann, Dynex Developers; International Journal of Bioinformatics & Intelligent Computing. 2024; Volume 3(1):91- 103, ISSN 2816-8089

##### Benchmark: 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.

> Github: Quantum Mode-assisted unsupervised learning of Restricted Boltzmann Machines

**Scientific background**: Quantum Frontiers on Dynex: Elevating Deep Restricted Boltzmann Machines with Quantum Mode-Assisted Training; Adam Neumann, Dynex Developers; 116660843, Academia.edu; 2024

##### Benchmark: Quantum-Support-Vector-Machine

The **Dynex QSVM PyTorch Layer** outperforms D-Wave Quantum Machines (HQPU, QPU), Simulated Annealing and Scikit-Learn with 100.00% on all metrics. In this example, a classical classiﬁcation model, Kernel-Support Vector machine, is implemented as a Quadratic Unconstrained Binary Optimisation problem (QSVM). Data-points are classiﬁed by a separating hyperplane while maximizing the function margin. The problem is solved for a public Banknote Authentication dataset.

##### Benchmark: Quantum Restricted Boltzmann Machine

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.

> Medium: Computing on the Dynex Neuromorphic Platform: Image Classification

Our Dynex platform has been rigorously benchmarked against both traditional and quantum computing systems, demonstrating consistent superiority in performance. Through comprehensive testing across a variety of complex computational tasks, Dynex has proven to deliver faster processing times and more efficient problem-solving capabilities. This consistent outperformance underscores the robustness of our technology, making it a preferred choice for industries seeking to leverage advanced computing power. By blending the best attributes of quantum and neuromorphic computing, Dynex offers a unique solution that significantly enhances computational efficiency and effectiveness, setting a new standard in the computing landscape.

##### Benchmarking the Dynex n.quantum Platform with the Q-Score

In the context of our study, we employ the Q-score to benchmark the computing capabilities of the Dynex Neuromorphic Quantum Computing Platform, facilitating a comparative evaluation with contemporary state-of-the-art quantum computers. Our findings demonstrate that the Dynex platform exhibits remarkable performance superiority over the presently largest quantum computing systems. While physical quantum computing systems such as Google’s Sycamore, IBM’s Osprey, D-Wave’s Advantage, and Rigetti’s Aspen-M-2 have reportedly achieved Q-scores not surpassing 140, the Dynex Neuromorphic Platform has demonstrated a Q-score exceeding 15,000.

> Medium: Benchmarking the Dynex Neuromorphic Platform with the Q-Score

##### Benchmark: CFD vs. Quantum-CFD

Computational Fluid Dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and algorithms to solve and analyze problems involving fluid flows. By utilizing computational software, CFD simulates the interaction of liquids and gases with surfaces, defined by boundary conditions and initial conditions. This technique allows engineers and scientists to visualize and predict fluid flow behavior, heat transfer, and related phenomena in a virtual setting, without the need for costly and time-consuming physical experiments. CFD is widely used in industries such as aerospace, automotive, and energy, for designing and optimizing processes and products like aircraft wings, engine components, and wind turbines. The Quantum-CFD algorithm is superior to traditional CFD methods, resulting in 95% less computation time required and 90% less costs.

> Github: QCFD Benchmark (independent repo)

##### Dynex finds best-known MaxCut for the Stanford G70 benchmark

The cut size 9,553 for G70 found by Dynex is the best-known MaxCut than previous reported results on June 8th 2024. The previous record of 9,541 was found using a special purpose algorithm designed for MaxCut (Breakout Local Search for the Max-Cut problem) in 2013. This achievement underscores the power and efficiency of our neuromorphic quantum computing platform, especially given that improving the cut size by even one involves exponentially increasing complexity. The following table displays the previously known best MaxCut values for various Gset benchmarks, including the G70 dataset. Results for D-Wave have been computed using the D-Wave Cloud Platform using the Advantage™ quantum computer with 5,000 physical qubits.

> G70 MaxCut Solution on Dynex Github

##### Enhancing MaxCut Solutions: Dynex’s Benchmark Performance on G70 Using Quantum Computing

We conducted an experiment on the G70 MaxCut problem, a complex unweighted MaxCut challenge with 10,000 nodes and 99,999 edges sourced from the publicly available Gset dataset provided by Stanford University. Various algorithms and solvers were evaluated, including commercial solvers like Gurobi and IBM CPLEX, and specialized algorithms such as the SDP solver DSDP, the graph neural network-based PI-GNN, and the tabu search-based KHLWG. Utilizing Dynex’s neuromorphic quantum computing cloud with a single Nvidia RTX3080 GPU, and without any MaxCut-specific enhancements, Dynex achieved a Maximum Cut value of 9,506 — outperforming other algorithms and demonstrating the potential of the Dynex platform. The experiment underscores that additional computational resources or bespoke algorithmic modifications could potentially lead to even higher performance, potentially setting new benchmarks for MaxCut solutions and showcasing the scalability and adaptability of the Dynex platform for tackling such optimization problems.

> Medium: Enhancing MaxCut Solutions: Dynex’s Benchmark Performance on G70 Using Quantum Computing

> Github: Jupyter Notebook

##### MaxCut Quantum Simulation Record

Dynex announced a significant breakthrough in the field of quantum computing, achieved through the Dynex neuromorphic quantum computing platform. By employing a sophisticated quantum algorithm, we successfully solved a graph containing 10,000 vertices, setting a new record that surpasses the previous benchmark by threefold.

> Dynex Sets New World Record for Quantum Computing, Breaking NVIDIA’s Previous Record

##### Benchmark: 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.

> Github: Dynex MA-QRBM Package

**Scientific background**: Advancements in Unsupervised Learning: Mode-Assisted Quantum Restricted Boltzmann Machines Leveraging Neuromorphic Computing on the Dynex Platform; Adam Neumann, Dynex Developers; International Journal of Bioinformatics & Intelligent Computing. 2024; Volume 3(1):91- 103, ISSN 2816-8089

##### Benchmark: 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.

> Github: Quantum Mode-assisted unsupervised learning of Restricted Boltzmann Machines

**Scientific background**: Quantum Frontiers on Dynex: Elevating Deep Restricted Boltzmann Machines with Quantum Mode-Assisted Training; Adam Neumann, Dynex Developers; 116660843, Academia.edu; 2024

##### Benchmark: Quantum-Support-Vector-Machine

The **Dynex QSVM PyTorch Layer** outperforms D-Wave Quantum Machines (HQPU, QPU), Simulated Annealing and Scikit-Learn with 100.00% on all metrics. In this example, a classical classiﬁcation model, Kernel-Support Vector machine, is implemented as a Quadratic Unconstrained Binary Optimisation problem (QSVM). Data-points are classiﬁed by a separating hyperplane while maximizing the function margin. The problem is solved for a public Banknote Authentication dataset.

##### Benchmark: Quantum Restricted Boltzmann Machine

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.

> Medium: Computing on the Dynex Neuromorphic Platform: Image Classification

Our Dynex platform has been rigorously benchmarked against both traditional and quantum computing systems, demonstrating consistent superiority in performance. Through comprehensive testing across a variety of complex computational tasks, Dynex has proven to deliver faster processing times and more efficient problem-solving capabilities. This consistent outperformance underscores the robustness of our technology, making it a preferred choice for industries seeking to leverage advanced computing power. By blending the best attributes of quantum and neuromorphic computing, Dynex offers a unique solution that significantly enhances computational efficiency and effectiveness, setting a new standard in the computing landscape.

##### Benchmarking the Dynex n.quantum Platform with the Q-Score

In the context of our study, we employ the Q-score to benchmark the computing capabilities of the Dynex Neuromorphic Quantum Computing Platform, facilitating a comparative evaluation with contemporary state-of-the-art quantum computers. Our findings demonstrate that the Dynex platform exhibits remarkable performance superiority over the presently largest quantum computing systems. While physical quantum computing systems such as Google’s Sycamore, IBM’s Osprey, D-Wave’s Advantage, and Rigetti’s Aspen-M-2 have reportedly achieved Q-scores not surpassing 140, the Dynex Neuromorphic Platform has demonstrated a Q-score exceeding 15,000.

> Medium: Benchmarking the Dynex Neuromorphic Platform with the Q-Score

##### Benchmark: CFD vs. Quantum-CFD

Computational Fluid Dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and algorithms to solve and analyze problems involving fluid flows. By utilizing computational software, CFD simulates the interaction of liquids and gases with surfaces, defined by boundary conditions and initial conditions. This technique allows engineers and scientists to visualize and predict fluid flow behavior, heat transfer, and related phenomena in a virtual setting, without the need for costly and time-consuming physical experiments. CFD is widely used in industries such as aerospace, automotive, and energy, for designing and optimizing processes and products like aircraft wings, engine components, and wind turbines. The Quantum-CFD algorithm is superior to traditional CFD methods, resulting in 95% less computation time required and 90% less costs.

> Github: QCFD Benchmark (independent repo)

##### Dynex finds best-known MaxCut for the Stanford G70 benchmark

The cut size 9,553 for G70 found by Dynex is the best-known MaxCut than previous reported results on June 8th 2024. The previous record of 9,541 was found using a special purpose algorithm designed for MaxCut (Breakout Local Search for the Max-Cut problem) in 2013. This achievement underscores the power and efficiency of our neuromorphic quantum computing platform, especially given that improving the cut size by even one involves exponentially increasing complexity. The following table displays the previously known best MaxCut values for various Gset benchmarks, including the G70 dataset. Results for D-Wave have been computed using the D-Wave Cloud Platform using the Advantage™ quantum computer with 5,000 physical qubits.

> G70 MaxCut Solution on Dynex Github

##### Enhancing MaxCut Solutions: Dynex’s Benchmark Performance on G70 Using Quantum Computing

We conducted an experiment on the G70 MaxCut problem, a complex unweighted MaxCut challenge with 10,000 nodes and 99,999 edges sourced from the publicly available Gset dataset provided by Stanford University. Various algorithms and solvers were evaluated, including commercial solvers like Gurobi and IBM CPLEX, and specialized algorithms such as the SDP solver DSDP, the graph neural network-based PI-GNN, and the tabu search-based KHLWG. Utilizing Dynex’s neuromorphic quantum computing cloud with a single Nvidia RTX3080 GPU, and without any MaxCut-specific enhancements, Dynex achieved a Maximum Cut value of 9,506 — outperforming other algorithms and demonstrating the potential of the Dynex platform. The experiment underscores that additional computational resources or bespoke algorithmic modifications could potentially lead to even higher performance, potentially setting new benchmarks for MaxCut solutions and showcasing the scalability and adaptability of the Dynex platform for tackling such optimization problems.

> Medium: Enhancing MaxCut Solutions: Dynex’s Benchmark Performance on G70 Using Quantum Computing

> Github: Jupyter Notebook

##### MaxCut Quantum Simulation Record

Dynex announced a significant breakthrough in the field of quantum computing, achieved through the Dynex neuromorphic quantum computing platform. By employing a sophisticated quantum algorithm, we successfully solved a graph containing 10,000 vertices, setting a new record that surpasses the previous benchmark by threefold.

> Dynex Sets New World Record for Quantum Computing, Breaking NVIDIA’s Previous Record

##### Benchmark: 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.

> Github: Dynex MA-QRBM Package

**Scientific background**: Advancements in Unsupervised Learning: Mode-Assisted Quantum Restricted Boltzmann Machines Leveraging Neuromorphic Computing on the Dynex Platform; Adam Neumann, Dynex Developers; International Journal of Bioinformatics & Intelligent Computing. 2024; Volume 3(1):91- 103, ISSN 2816-8089

##### Benchmark: 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.

> Github: Quantum Mode-assisted unsupervised learning of Restricted Boltzmann Machines

**Scientific background**: Quantum Frontiers on Dynex: Elevating Deep Restricted Boltzmann Machines with Quantum Mode-Assisted Training; Adam Neumann, Dynex Developers; 116660843, Academia.edu; 2024

##### Benchmark: Quantum-Support-Vector-Machine

The **Dynex QSVM PyTorch Layer** outperforms D-Wave Quantum Machines (HQPU, QPU), Simulated Annealing and Scikit-Learn with 100.00% on all metrics. In this example, a classical classiﬁcation model, Kernel-Support Vector machine, is implemented as a Quadratic Unconstrained Binary Optimisation problem (QSVM). Data-points are classiﬁed by a separating hyperplane while maximizing the function margin. The problem is solved for a public Banknote Authentication dataset.

##### Benchmark: Quantum Restricted Boltzmann Machine

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.

> Medium: Computing on the Dynex Neuromorphic Platform: Image Classification