## INTRODUCTION

Quantum computing is an emerging field of computing that is based on the utilization of microscopic phenomena of quantum mechanics to solve complex problems.

It differs from classical computing which uses only bits 0 and 1.

In contrast, quantum uses the qubits which can be in several states at the same time, allowing computation to run parallel.

This idea can be attributed to Richard Feynman and David Deutsch in the least but it was not until the 21st century that a serious breakthrough was put in place to lead to the experimental quantum computers of today.

Quantum computing based on the principles of qubits and gates holds the potential to solve problems that classical computers cannot solve and could find usage in cryptography, optimization, and drug synthesis.

## Quantum Mechanics Basics

Quantum mechanics is the theory that is used to explain the characteristics of particles at the sub microscopic level having an application of superposition and duality of wave and particle.

**Superposition** : Superposition makes qubits able to be in state 0 and state 1 simultaneously, making quantum computers solve multiple scenarios at once.

**Entanglement** : Sharing connects qubits in such a way that the state of one is dependent on the other; no matter the distance, boosting its quantum computational ability.

**Quantum Bits (Qubits**) : Qubits are unique units of quantum computers that can represent the states of 0 & 1 at the same time contrary to bits.

**Quantum Gates** : Quantum gates control qubits by applying quantum operations including superposition and entanglement to operate quantum algorithms.

## Quantum Algorithms

**Grover’s Algorithm (Search)** : Grover’s Algorithm showed a quadratic speed-up in the case of searching unsorted databases so that the number of queries that are required is considerably less than the previous methods.

**Shor’s Algorithm (Factoring)** : Shor’s Algorithm factors large integers with significant efficiency and, therefore, is a menace to classical uses of cryptography that entail dependency on factors of large numbers.

**Quantum Fourier Transform** : Quantum Fourier Transform is an extension of the Fourier transform, which is required in several quantities of quantum algorithms such as Shor’s Algorithm.

## Quantum Hardware

Quantum hardware is the actual objects that realize quantum computing. Among them are the superconducting qubits, trapped ions, and topological qubits. This technology is aimed at preserving quantum states, implementing quantum gates, and increasing the system complexity of quantum computations while overcoming problems, such as error correction and coherence.**Superconducting Qubits** : Superconducting qubits are based on circuits created by superconducting material that allows maintaining quantum states with low loss of energy, it is one of the leading technologies to implement quantum computing.

**Trapped Ion Qubits** : Trapped ion qubits enclose ions by electric and magnetic fields, they offer coherent and accurate quantum control in individual qubits.

**Topological Qubits** : Topological qubits utilize the characteristics of topological phases for storing/retrieving the quantum bit, which is supposed to be immune to most errors.

**Photonic Qubits** : This photonic qubit implements the use of particles of light (photons) to convey the quantum information, which allows for quantum communication over long distances and at the same time can easily be scaled up.

## Applications of Quantum Computing

**Cryptography: **Capability for the disruption of the classic encryption methodologies and development of quantum-resistant cryptographic schemes.

**Optimization:** This is more effective than the classical approach in solving complicated optimization issues in such cur-cles as logistics, finance, and manufacturing.

**Drug Discovery:** Replicates the things at a molecular level and how they interact, leading to a faster process of discovering new drugs.

**Material Science:** Creates new materials for products and chemical processes that result in improvements to productivity in manufacturing and energy storage systems.**Artificial Intelligence:** Improves artificial intelligence techniques particularly in the field of machine learning and data analytics by enabling them to process large amounts of data in the shortest time possible.

## Optimization Problems of Quantum Computing

**Scheduling:**Solves complex scheduling issues like flight and manufacturing schedules more efficiently.**Supply Chain:**Optimizes inventory, routing, and distribution for better logistics management.**Finance:**Enhances investment strategies and risk management by analysing financial data.**Traffic:**Improves urban traffic flow and reduces congestion.**Energy:**Optimizes energy distribution in smart grids for better efficiency.

## Challenges and Limitations of Quantum Computing

**Bit Stability:** Qubit coherence and therefore keeping it from getting decohered requires some level of control since the environment causes interference.

**Error Correction: **The deployment of efficient methods for the actual quantum error correction is known to be a rather challenging and time-consuming process.

**Scalability: **Quantum Systems: In the case of using quantum gates, for instance, scaling up the system to use more than one qubit poses certain challenges in that the performance and reliability of the larger system may be compromised.

**Algorithm Development: **The latter, which consists of developing optimal quantum algorithms for real use, is still an active research field.

**Cost:** Quantum hardware creation and maintenance is expensive and acts as a serious drawback since it requires huge capital investment.

## Conclusion

Quantum computing has the potency of revolutionizing many disciplines including cryptography, drug development, optimization, and artificial intelligence. Quantum computing remains on the right track as development goes on with qubit technology, error correction, and application in industries whereby quantum computers are estimated to tackle problems that cannot be solved using classical computers indicating the dawn of a new-age computational ability and innovation.