**Context: **We often hear that quantum computers efficiently solve problems that are very difficult to solve with a classical computer. But even if the hardware is available to build a quantum computer, exploiting its quantum features requires us to write smart algorithms.

**What is Quantum computing?**

- Quantum computing is a field of study focused on the development of computer-based technologies centred around the principles of quantum theory.
- Quantum theory, a subfield of physics, describes the nature of energy and matter on the quantum (atomic and subatomic) scale.

**Principles of Quantum Computing:**

**Superposition:**A qubit can represent both 0 and 1 state simultaneously.**Entanglement:**States of qubits become interlinked allowing coordinated processing.**Interference:**Quantum states combine to amplify correct solutions and cancel out wrong ones.**Tunnelling:**Particles can pass through barriers aiding in optimisation tasks.**Measurement:**Extracts a result from a qubit collapsing its state to either 0 or 1.**Quantum Gates:**Operations that manipulate qubits, analogous to classical logic gates.**No-Cloning:**Qubits cannot be precisely copied.**Decoherence:**External influences can cause errors requiring error correction.

**Application of Quantum computing**

**What is Classical Computing?**

Classical computing refers to the traditional model of computing based on classical physics principles and the binary system.

**Bits:**The fundamental unit of classical computing. A bit can be in one of two states: 0 or 1.**Logic Gates:**Operations that manipulate bits. Common gates include AND, OR, NOT, XOR, and others. These gates form the building blocks of digital circuits and processors.**Binary System:**Classical computers operate using the binary numeral system, where data and instructions are represented using combinations of 0s and 1s.**Deterministic:**Classical computers operate in a deterministic manner, meaning given the same input, they will always produce the same output.**Stored-Program Concept:**Modern classical computers follow this concept, where instructions (software) and data are stored in memory and processed by a central processing unit (CPU).**Architecture:**Classical computers typically have a CPU, memory (RAM), storage (hard drive or SSD), input/output devices, and other components interconnected by a system bus.**Applications:**Classical computing encompasses a wide range of devices, from simple calculators to supercomputers, and is used in virtually every industry and aspect of modern life.**Limitations:**There are problems that classical computers find challenging or time-consuming, such as factoring very large numbers or simulating quantum systems. This is where quantum computing may offer advantages.

**Quantum computing vs Classical computing**

Feature/Aspect | Quantum Computing | Classical Computing |

Basic Unit | Quantum bits (qubits) | Binary bits (0 or 1) |

State Representation | 0, 1, or a superposition of both | Either 0 or 1 |

Parallelism | Can process multiple possibilities simultaneously | Processes tasks sequentially or with limited parallelism |

Entanglement | Qubits can be entangled | No equivalent phenomenon |

Operations | Uses quantum gates | Uses logic gates (AND, OR, NOT, etc.) |

Determinism | Probabilistic outcomes | Deterministic outcomes |

Data Storage | Quantum states (fragile) | Electronic storage (RAM, SSDs, hard drives) |

Error Correction | Requires quantum error correction | Uses classical error correction methods |

Maturity & Applications | Early stages with specific potential applications | Mature, used in countless applications |

Hardware | Specialised conditions (E.g., very low temperatures) | Operates at room temperature with semiconductor technology |

**Benefits of Quantum Computing:**

**Speed:**Solve specific problems exponentially faster.**Parallelism:**Process vast information simultaneously.**Optimisation:**Efficiently tackle complex optimization tasks.**Simulation:**Directly simulate quantum systems for research.**Cryptography:**Enable ultra-secure quantum encryption.**Machine Learning:**Accelerate training and improve accuracy.**Material Discovery:**Efficiently find new materials with desired properties.**Climate Modelling:**Achieve more accurate environmental simulations.**Enhanced Search:**Quickly search through unsorted databases.**Error Correction:**Advanced techniques applicable beyond just quantum computing.

**Limitations of Quantum Computing:**

**Decoherence:**Qubits are unstable and lose information over time.**Error Rates:**High error rates compromise computation reliability.**Scalability:**Difficult to build large-scale quantum systems.**Quantum-to-Classical Transition:**Information loss when translating quantum results into classical data.**Selective Speedup:**Not universally faster; speed benefits apply to specific problems.**Algorithm Complexity:**Quantum algorithms are intricate and hard to design.**Hardware Demands:**Requires extreme conditions (**E.g.,**very low temperatures) to function.**Error Correction:**Needs many extra qubits, complicating the design.**Immature Software:**Lacks a robust software ecosystem.**Cryptography Risks:**Threatens current encryption methods.**Practicality:**Many quantum solutions have limited immediate real-world use.