Blog 5: Modern emerging algorithms
Modern emerging algorithms
In Blog 4: Quantum Algorithms Unleashed: Shor’s, Grover’s, and More , we provided a introduction to two important early stage algorithms which have influenced Quantum computing. Some of the the early algorithms, such as Shor's algorithm for factoring large numbers and Grover's algorithm for searching unsorted data, demonstrated the potential of quantum computing to outperform classical systems in specific tasks. By establishing the basic principles and capabilities of quantum computation, they have paved the way for modern advancements and their adaptation to real-world business challenges. Let’s look at some of the more recent innovations in quantum algorithms :
In this blog we will take a quick tour of some of the emerging algorithms which hold significant promise for various industries. With growing interest in the transformative potential of quantum computing, businesses are starting to investigate how Quantum could potentially reshape their operations by solving complex problems that to date have been difficult to resolve with classical computing. In traditional terminology, an algorithm simply refers to a set of instructions. But when we refer to quantum algorithms, we mean instructions that enable the translation of quantum properties and mechanics into practical applications for business and industry.
Algorithms therefore serve as one of the key pillars in the design of quantum solutions.. Quantum algorithms act as the crucial link between real-world problems and the potential solutions offered by quantum computers. They involve identifying suitable problems, mapping them into quantum-compatible models, designing algorithms that leverage quantum phenomena, and integrating these algorithms with classical systems for execution and optimization. This process requires expertise in quantum mechanics, computer science, and often collaboration with domain-specific experts. By bridging the gap between complex challenges and quantum solutions, quantum algorithms play a vital role in unlocking the transformative potential of quantum computing across various industries and scientific domains.
Many quantum algorithms, such as the Quantum Approximate Optimization Algorithm (QAOA) or the Variational Quantum Eigensolver (VQE), hold significant promise for industries like logistics, finance, and drug discovery. The current blog post will explore some groundbreaking quantum algorithms, from those that paved the way, to those with short term variability that are breaking ground. Each of these algorithms has unique use cases that highlight their potential impact on various sectors. Let us know if you have experience of any of these algorithms or if you want to share more details on your use case.
The design of quantum computing solutions starts with identifying problems that classical computers find challenging due to their complexity. These problems are then translated into a mathematical model suitable for quantum operations. Next, experts in quantum mechanics and computer science craft a quantum algorithm, detailing the sequence of operations to be performed on quantum bits. This algorithm is integrated with classical systems, where the quantum computer focuses on the computationally intensive tasks. Finally, the algorithm is implemented on a quantum computer or simulator, rigorously tested, and continuously optimized as technology advances.
Quantum algorithms play a pivotal role in the design of quantum computing solutions. They are the blueprints that translate real-world problems into a language that quantum computers can understand and process.
Here's how algorithms are utilised in designing quantum computing solutions:
Problem Identification & Mapping: The first step is to identify a problem suitable for quantum computing. This typically involves problems with inherent computational complexity that classical computers struggle to solve efficiently. Once a problem is identified, it needs to be mapped or translated into a mathematical model that can be expressed in terms of quantum operations.
Algorithm Design: The next step involves designing a quantum algorithm to solve the mapped problem. This requires expertise in quantum mechanics, linear algebra, and computer science. The algorithm specifies a sequence of quantum gates and measurements that will be applied to quantum bits to perform the computation.
Integration with Classical Systems: Quantum algorithms typically work in tandem with classical computing systems. The quantum computer handles the computationally intensive quantum parts of the algorithm, while the classical computer manages the input/output, data processing, and overall control of the computation.
Implementation & Testing: The designed algorithm is then implemented on a quantum computer or simulator. This involves translating the abstract quantum operations into specific instructions for the chosen quantum hardware. Rigorous testing is crucial to verify the algorithm's correctness and performance.
Optimization & Refinement: As quantum hardware improves and new techniques emerge, quantum algorithms are continuously optimised and refined to increase their efficiency and accuracy.
Quantum Approximate Optimization Algorithm (QAOA)
The Quantum Approximate Optimization Algorithm (QAOA) is a modern algorithm designed to tackle combinatorial optimization problems. In simple terms, solving optimization problems that involve establishing the best solution from a vast set of possibilities. QAOA works to solve complex optimization problems by transforming them into more manageable, continuous problems. These types of problems usually require selecting the best choice from a finite set of options, like scheduling tasks, determining routes, or optimising a portfolio. Rather than evaluating every possible solution one by one, QAOA employs a quantum circuit with tunable parameters. These parameters can be adjusted smoothly, allowing for a more efficient search for the optimal solution. In order to do this the algorithm encodes the problem’s objective, known as its cost function, into a mathematical model called a Hamiltonian, which represents the energy of the quantum system. The lowest energy, known as the ground state, corresponds to the optimal solution. By adjusting the circuit’s parameters, QAOA lowers the system’s energy, gradually getting closer to the ground state, which represents the best solution to the problem. In essence, QAOA leverages quantum mechanics to streamline the search for an optimal solution, making it faster and more efficient than classical approaches.
Recent advancements in QAOA include the development of hybrid approaches that combine classical optimizers with quantum circuits, in this context a classical computer is used to adjust circuit parameters to ensure accuracy. For instance, researchers have introduced a gradient-free classical optimizer called Double Adaptive-Region Bayesian Optimization (DARBO) that significantly enhances QAOA's performance in terms of speed, accuracy, and stability when solving combinatorial problems, this is particularly valuable in situations where data is noisy or discontinuous, making it hard to compute gradients. This adaptability makes QAOA a promising candidate for real-world applications where finding optimal solutions quickly is critical.
Variational Quantum Eigensolver (VQE)
The Variational Quantum Eigensolver (VQE) is another pivotal algorithm in the quantum computing landscape, primarily used for calculating the ground state energy of quantum systems. Similarly to the hybrid approach to the QAOA, VQE also employs classical methods to optimise the parameters of a quantum circuit in order to minimise the expectation value of a Hamiltonian.
In contrast to the QAOA, which is primarily used in areas such as supply chain management, logistics and finance, VQE is particularly useful in materials science and chemistry, where understanding specific molecular properties can lead to breakthroughs in drug discovery and material design. By simulating molecular structures more accurately than classical methods allow, VQE can help identify new compounds with desirable properties or predict reaction pathways with greater precision. Its ability to handle noisy intermediate-scale quantum (NISQ) devices makes it an attractive option for immediate applications in research and industry.
Quantum Machine Learning (QML) Algorithms
Quantum Machine Learning (QML) represents an exciting intersection between quantum computing and artificial intelligence. QML algorithms leverage quantum mechanics to enhance machine learning tasks such as classification, clustering, and regression.
One notable QML approach is the Quantum Support Vector Machine (QSVM), which utilises quantum states for faster processing of high-dimensional data. By exploiting the exponential scaling capabilities of quantum systems, QSVM can potentially outperform classical machine learning models in specific scenarios, particularly when dealing with complex datasets.
Another promising area within QML is quantum neural networks (QNNs), which aim to integrate neural network architectures with quantum computing principles. These networks could revolutionise fields such as image recognition and natural language processing by enabling faster training times and improved accuracy through enhanced feature extraction capabilities.
Conclusion
As quantum computing continues to evolve, the development of innovative algorithms like QAOA, VQE, Shor's algorithm, Grover's algorithm, and QML methods will play a pivotal role in integrating this technology into everyday business practices. These algorithms and many more emerging ones not only harness the unique capabilities of quantum systems but also address real-world challenges across various sectors.
. As we move toward a future where quantum computers become more accessible and practical for everyday use, understanding these algorithms will be essential for organisations looking to thrive in an increasingly complex and competitive technological landscape. At Fathom, we're embarking on an exciting exploration into the realm of quantum computing. We’re eager to delve into its potential and uncover its vast potential to drive innovation and advancement.
Companies tend to keep details about their R&D initiatives confidential for competitive reasons, we hope to shine a light on more of the algorithms and deviations of them being used by businesses as we develop an opensource community of sharing knowledge and collaboration in industry.. We invite you to be part of this journey. Subscribe to our blog, engage with us on social media, and share your thoughts and insights on the use of modern quantum algorithms.
