As quantum computing technology matures and becomes more accessible, its integration into various industries is set to revolutionize multiple fields. In the pharmaceutical industry, Dynex enables breakthroughs in drug discovery and personalized treatments through advanced examples like Quantum Protein Folding and Quantum RNA Folding, improving our ability to combat disease. The automotive and aerospace sectors benefit from enhanced Computational Fluid Dynamics (CFD) simulations and optimized satellite positioning, pushing the boundaries of design and efficiency. Financial services can harness Dynex for quantum portfolio optimization, leading to superior risk management and fraud detection. In telecommunications, Dynex enhances network performance with applications like optimal WiFi hotspot positioning. Furthermore, algorithms such as MaxCut, Quantum Single Image Super-Resolution, and Quantum Integer Factorization showcase Dynex's prowess in solving complex computational problems.

##### Examples by Industry

> Artificial Intelligence

> Pharmaceutical

> Automotive, Aerospace, Super-Sports and Space

> Financial Services

> Telecommunication

> Research & Science

##### Quantum Computation of Fluid Dynamics on Dynex (QCFD)

Dynex offers an innovative platform for the efficient simulation of Computational Fluid Dynamics (QCFD), a powerful discipline within engineering and physics. With Dynex, QCFD simulations can be conducted seamlessly, providing engineers and researchers with a robust tool for analyzing fluid flow, heat transfer, and related phenomena. This capability is invaluable in numerous industries, including aerospace, automotive, and energy, where understanding and optimizing fluid behavior is crucial. By utilizing Dynex’s advanced computational capabilities, users can gain insights into aerodynamics, thermal management, and fluid interactions, ultimately aiding in the design and optimization of various systems and devices. Dynex empowers engineers to accelerate the QCFD simulation process, fostering innovation and driving advancements in fields reliant on fluid dynamics analyses.

> Github Repository Dynex QCFD

**Scientific background**: An Introduction to Algorithms in Quantum Computation of Fluid Dynamics, Sachin S. Bharadwaj and Katepalli R. Sreenivasan, Department of Mechanical and Aerospace Engineering, STO - Educational Notes Paper, 2022.

##### 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

##### Quantum Protein Folding on Dynex

Protein folding is the physical process by which a protein chain attains its functional three-dimensional structure from a simple sequence of amino acids. This folding occurs spontaneously, guided by interactions among the amino acids and the surrounding environment, which determine the protein's final shape. Correct folding is crucial for a protein's function, as misfolding can lead to diseases like Alzheimer's and Parkinson's.

> Jupyter Notebook: Quantum Protein Folding

**Scientific background**: Irbäck, Anders & Knuthson, Lucas & Mohanty, Sandipan & Peterson, Carsten. (2022). Folding lattice proteins with quantum annealing.

##### Drug Repurposing With 3D Molecular Quantum Methods

From concept to treating a patient, it can take 10 years for a single treatment. Drug repositioning, repurposing, re-tasking, re-profiling or drug rescue is the process by which approved drugs are employed to treat a disease they were not initially intended/designed for. Virtual screening has become essential at the early stages of drug discovery. However, the process still typically takes a long time to execute since it generally relies on measuring chemical similarities among molecules. Even for today’s processors, this exercise comprises a major challenge since it is computationally heavy and expensive. Accordingly, most of the well-known methods typically use 2D molecular fingerprints to include structural information that represents substructural characteristics of molecules as vectors. These methods do not take into consideration relevant aspects of molecular structures such as 3D folding, although they are efficient in terms of execution times. At the expense of higher computing times, considering 3D structural properties of molecules substantially increases the accuracy of results. The 3D molecular Quantum method is computed efficiently on the Dynex platform and provides a superior virtual screening method.

**Scientific background**: Drug repurposing based on a quantum-inspired method versus classical fingerprinting uncovers potential antivirals against SARS-CoV-2, Jimenez-Guardeño JM, Ortega-Prieto AM, Menendez Moreno B, Maguire TJA, Richardson A, Diaz-Hernandez JI, et al. (2022); PLoS Comput Biol 18(7): e1010330

##### Quantum 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

##### Efficient Exploration of Phenol Derivatives with Dynex

Molecule screening from a vast number of possible compounds is a challenging task. The emergence of quadratic unconstrained binary optimization (QUBO) solvers provides alternatives to address this issue. We propose a process for screening molecules by integrating QUBO solvers and density functional theory (DFT) calculations. As a proof-of-concept work, we map the problem of screening phenolic inhibitors onto the QUBO model. We approximate the bond dissociation energy (BDE) of the −OH bond, an indicator of good polymeric inhibitors, into the QUBO model by modifying the group contribution method (GCM) with the aid of DFT calculations. We demonstrate a strong correlation between this QUBO model and the data from DFT, with the correlation coefficient and Spearman’s coefficient of 0.82 and 0.86, respectively, when tested on the 85 given molecules. This mapping allows us to identify the candidates through the QUBO solver, whose BDEs are validated through DFT calculations, as well. Our work provides a promising direction for incorporating the GCM into QUBO solvers to tackle the molecule screening problems.

Scientific background: Efficient Exploration of Phenol Derivatives Using QUBO Solvers with Group Contribution-Based Approaches; Chien-Hung Cho, Jheng-Wei Su, Lien-Po Yu, Ching-Ray Chang, Pin-Hong Chen, Tzu-Wei Lin, Shin-Hong Liu, Tsung-Hui Li, and Ying-Yuan Lee; Industrial & Engineering Chemistry Research 2024 63 (10), 4248-4256; DOI: 10.1021/acs.iecr.3c03331

##### Quantum 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

##### Quantum 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

##### Quantum Self-Attention Transformer

The Quantum Self-Attention Transformer leverages the principles of quantum computing to perform tasks typically handled by classical transformers, particularly in the domain of NLP and LLM. Classical transformers rely heavily on the self-attention mechanism, which allows the model to weigh the importance of different words in a sentence when making predictions or generating new text.

The quantum self-attention transformer circuit is designed to process word embeddings derived from sentences and generate new sentences based on quantum operations. The circuit begins by embedding the binary representation of input vectors into quantum states, followed by multiple layers of rotation and controlled gates to capture complex relationships between the inputs. After applying the Quantum Fourier Transform (QFT) and Grover's operator, the circuit uses a combination of Hadamard, T, and rotation gates to further process the information. The final output is a set of expectation values, which are processed with softmax to generate attention-weighted outputs. These outputs are then used to generate a new sentence by combining the embeddings with word vectors similar to the quantum-generated outputs, ensuring a coherent and contextually relevant sentence.

This circuit essentially uses quantum computation to perform the role of attention in a transformer model, which is crucial for tasks like natural language processing, where understanding the importance of different words in a sentence is key to generating meaningful text. The quantum approach aims to leverage the potential speedups and parallelism inherent in quantum computing to perform these tasks more efficiently.

##### Grover Integer Factorisation on Dynex

Grover's algorithm is a quantum search algorithm that offers a quadratic speedup over classical search methods, making it one of the most significant algorithms in quantum computing. Traditionally, searching through an unsorted database of 𝑁 elements requires 𝑂(𝑁) time, as each element must be checked individually. However, Grover's algorithm can find the desired element in 𝑂(√𝑁) time, using the principles of quantum superposition and interference. The algorithm works by iteratively applying two main operations: the oracle, which marks the correct solution by flipping its phase, and the amplitude amplification, which increases the probability amplitude of the correct solution while decreasing that of the incorrect ones. These steps are repeated a number of times proportional to 𝑁, and a measurement at the end of the process will reveal the correct solution with high probability. This makes Grover's algorithm particularly powerful for applications like cryptography, where it can significantly reduce the time required to search through large keyspaces, posing a potential threat to classical encryption methods.

> Simple Grover Integer Factorisation Circuit

**Scientific background**: Grover, L.K. From Schrödinger’s equation to the quantum search algorithm. *Pramana - J Phys* **56**, 333–348 (2001). https://doi.org/10.1007/s12043-001-0128-3

##### Shor Integer Factorisation on Dynex

Shor's algorithm is a groundbreaking quantum algorithm that efficiently factors large integers, a problem that is classically hard to solve and forms the basis of many encryption schemes, such as RSA. The algorithm leverages quantum parallelism and the Quantum Fourier Transform (QFT) to find the period of a specific function related to the integer to be factored. This period is crucial for determining the factors of the integer. Shor's algorithm runs exponentially faster than the best-known classical algorithms, solving the factorization problem in polynomial time. This poses a significant threat to classical cryptographic systems, as it can break widely-used encryption methods by efficiently discovering prime factors of large numbers, something that would take classical computers an infeasible amount of time. Shor's algorithm consists of two main parts: classical pre- and post-processing, and a quantum phase estimation subroutine, which finds the order of a modular exponentiation function. Once the order is determined, the factors of the number can be computed using classical methods. Shor's algorithm is one of the most significant demonstrations of the potential power of quantum computing and has profound implications for the future of cryptography and information security.

> Simple Shor Integer Factorisation Circuit

**Scientific background**: Shor, P.W. (1994). "Algorithms for quantum computation: Discrete logarithms and factoring". *Proceedings 35th Annual Symposium on Foundations of Computer Science*. pp. 124–134.

##### Quantum 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)

##### Quantum Satellite Positioning

This quantum algorithm explores the problem of optimally grouping a set of satellites into constellations to observe specific targets on Earth. Each satellite has unique observational capabilities, influencing how effectively it can monitor a designated area for a certain duration. The goal of the algorithm is to demonstrate quantum superiority on how to maximize the Earth coverage of each constellation, ensuring that all targets are monitored as efficiently as possible.

> Jupyter Notebook: Quantum Satellite Positioning

**Scientific background**: G. Bass, C. Tomlin, V. Kumar, P. Rihaczek, J. Dulny III. Heterogeneous Quantum Computing for Satellite Constellation Optimization: Solving the Weighted K-Clique Problem. 2018 Quantum Sci. Technol. 3 024010.

##### Stock Portfolio Optimisation with Quantum Algorithms on the Dynex Platform

Portfolio Optimization (PO) is a standard problem in the financial industry. The computational complexity of such combinatorial optimization problems tend to increase exponentially with the number of variables — here, the number of assets — which at large scale can make solvers incapable of providing only optimal solutions. Instead, the results are likely suboptimal. This article provides detailed introduction on how stock portfolio optimisation can be performed by using quantum computing algorithm on the Dynex Neuromorphic Computing Cloud overcoming these limitations.

> Real World Use Case: Stock Portfolio Optimisation with Quantum Algorithms on the Dynex Platform

##### 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.

##### Quantum 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)