The backbone of Computing — Math
Day 3 — Quantum30 2.0
Mathematics, despite its reputation for being challenging, is an indispensable tool with incredible potential. It underpins not only traditional calculations but also plays a pivotal role in emerging fields like Artificial Intelligence (AI) and Quantum Computing. Even our trusty (but sometimes not so trusty) friend, ChatGPT, relies on mathematics as its foundation!
Today, let’s delve into some key mathematical concepts that form the core of two exciting disciplines: Machine Learning (ML) and Quantum Computing.
Machine Learning
Machine Learning is the beating heart of AI, responsible for a wide range of tasks such as optimization, predictions, data processing, and more. There are four fundamental mathematical concepts that drive ML algorithms:
- Calculus: This is the core of many ML algorithms and mostly focuses on optimization of the given problem statement and data set. One of the optimization methods, Gradient Descent, is used to adjust the data parameters iteratively that helps in improving accuracy and minimizing the prediction errors.
- Linear Algebra: Whenever I hear this name, the first thing that comes in my mind are vectors. Well, indeed, linear algebra uses Vectors and Methods to solve a multivariate problem i.e. a problem that has multiple parameters or variables
- Probability: This is used to make probabilistic predictions according to the given dataset.
- Statistics: Statistics forms the bedrock of ML. The above mentioned three topics are essential for comprehending data. Statistics integrates the results from these fields to analyze data, draw inferences, and arrive at meaningful conclusions.
Quantum Computing
In the previous day post, we talked about quantum representations of quantum states. Based on that, can you guess which mathematical tool we use for quantum mechanics, and hence, quantum computing?
If your guess was Linear Algebra, then indeed, that is correct! Linear algebra, in layman, deals with vectors and matrices and that is how we will be representing our states from now on. Quantum computing uses qubits which are the quantum states in superposition. The gate operations manipulates our states without disturbing it and is also represented as matrices.
This is where the power of mathematics shines through. While we may not yet have scalable quantum computers, mathematics allows us to envision what it would be like if such systems were developed. We can make predictions regarding the manipulation and measurement of quantum states, paving the way for future breakthroughs in quantum computing technology
Conclusion
Mathematics forms the backbone of both Machine Learning and Quantum Computing, showcasing its versatility and indispensability in shaping the future of technology.