Applications of Quantum Computing

Quantum computing is a mixture of Physics, Mathematics and Computer Science and it has created multiple new subfields in the world of computation. Development in this field is necessary to overcome the limitation of classical computation. Quantum computing has an advantage over traditional classical computation in

• problems that involve too much searching and testing e.g. searching through an unstructured database. A classical approach is to check one element at a time. But a quantum computer can do it quadratically fast. If there are 'n' elements in a list then a classical algorithm needs 'n' operations but Grover's quantum algorithm needs √n operations to find an element in the list.

• problems that require secure encryption. Quantum mechanics can guarantee security in transmitting data based on the laws of quantum physics. Most common encryption protocols are based on a mathematical problem that we can't solve e.g. factoring. Quantum Key Distribution(QKD) can transmit the data securely and it is not based on any mathematical problem that we can't solve.

• problems that involve simulating quantum mechanical systems. Classical computers are really bad at simulating quantum mechanical systems. This gave birth to the idea of quantum computing. Richard Feynmann postulated that it's better to simulate a quantum mechanical system in a quantum computer. Read this amazing article on Richard Feynman and his contributions to Quantum Computing and Nanotechnology.

Today, quantum computing has potential applications in many fields such as Finance, Cyber Security, Chemistry, Biology, Aerospace, Artificial Intelligence and Machine Learning, Music, Optimization etc. Let's explore a few possible applications.

1) Quantum Computing in Cyber Security:

Public key encryption has been virtually unhackable by using a very long pair of keys involving 617 digits( RSA-617 or RSA-2048). It is not factorizable via classical computers. But an advanced quantum computer could crack this in just a few hours using Shor's Quantum Algorithm. Hence quantum computers pose a serious risk to modern-day encryption threatening to break commonly used encryption methods. They also could create unhackable security networks. But we need 10000s of qubits and a fault-tolerant quantum computer to successfully run Shor's algorithm. IBM announced a 433 qubit Osprey quantum processor in 2022. Hence we are far away from breaking all of our security. But this risk has led to the development of a new field called Post Quantum Cryptography.

2) Quantum Computing in Vaccine Development:

The calculations predicting the basic behavior of a medium-sized drug molecule could take a lifetime to compute accurately. However, quantum computers could significantly improve the early stages of drug discovery, reducing the number of development cycles.

3) Quantum Computing in Machine Learning:

It involves using Quantum circuits in neural networks creating a quantum neural network. The main task is to map the problem from classical space to quantum space(Hilbert space) and again project it back to classical space. Read this article on Quantum Machine Learning and the Power of Data. Another way of understanding quantum machine learning is using classical machine learning algorithms to train on quantum data. The type of data and type of the algorithm creates a 2 by 2 matrix given here.

4) Quantum Finance:

It is an interdisciplinary field combining theories and methods of physicists and economists to solve problems of finance. One famous problem is the portfolio optimization problem. This problem involves collecting a few financial assets in a certain proportion to maximize an objective function. Quantum computing uses Variational Quantum Eigensolver(VQE) for this problem. Read this article on Quantum(-inspired) improvement of portfolio optimization.

Conclusion:

The applications mentioned here can be considered as a brim of an ocean. This field is for computer scientists, physicists, artists, electronic and chemical engineers etc. Hence quantum computing will grip its claws in all the domains and its interdisciplinary nature is just fascinating.