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Quantum computing

1. Quantum Computing Ft. Number systems Rana Muhammad Amaan Mir Huzaifah Ali 103 Abdullah Dar Class 1-A

2. Introduction Qubits vs. Classical Bits: Quantum computing uses qubits instead of classical bits . Unlike classical bits, which are strictly 0 or 1, qubits can be in a state of 0, 1, or a superposition of both. Quantum Superposition: A qubit can exist in multiple states simultaneously, representing both 0 and 1 with different probabilities until it is measured. Quantum Entanglement: Qubits can become entangled, meaning the state of one qubit can instantaneously affect the state of another, even over long distances.

3. Quantum Number Systems Quantum Superposition for Number System: A single qubit can represent more information than a classical bit because of superposition. n qubits can represent 2^n states simultaneously. This property allows quantum computers to process a massive number of possibilities in parallel. Quantum Gates (Analogous to Boolean Logic Gates): Quantum operations are performed using quantum gates (like Hadamard, Pauli-X, etc.), which manipulate the states of qubits. These gates operate on superposition states and entangled qubits, unlike classical gates that work on binary inputs.

4. A Quantum circuit: A Quantum Algorithm: Currently very complicated and hard to decipher which is why quantum technology is not that widely used at the moment and is a highly specialized field

5. Classical vs Quantum Number Systems Classical Systems: Deterministic: A bit is either 0 or 1, with each operation having a predictable outcome. Limited by binary representation and classical logic gates. Quantum Systems: Probabilistic: A qubit exists in a superposition of states until measured. Quantum gates perform operations on a superposition of inputs, offering exponential speedup for specific types of problems (e.g., Shor’s algorithm for factoring large numbers).

6. Applications and Advantages Classical Computing: Efficient for tasks like arithmetic, data processing, and Boolean logic operations .Uses binary logic for operations, leading to limitations in solving certain types of problems (e.g., factoring large numbers, simulating quantum systems). Quantum Computing: Offers potential for exponentially faster algorithms for problems like cryptography, optimization, and simulation of quantum systems .The ability to process multiple states simultaneously offers significant advantages over classical number systems.

7. Current Challenges Quantum Error Correction: Maintaining quantum states and performing precise calculations is difficult. Research is also pretty costly and most ideas are currently just theoretical Scalability: Quantum systems are currently in early stages with limited numbers of qubits, making it difficult to perform large-scale computations.

8. Future Outlook Classical Computing: Will remain dominant for traditional computational tasks and everyday applications. Advancements in AI and Machine Learning, Cloud Computing etc Quantum Computing: Quantum computing will complement classical systems by solving problems that are computationally intractable for classical systems .Integration of classical and quantum systems could lead to hybrid computational architectures, where quantum processors handle complex tasks (e.g., cryptography, machine learning) and classical systems manage routine tasks.

9. Hybrid Systems: Classical and Quantum Integration A hybrid system uses the classical toolbox for routine tasks like making sure everything runs smoothly and correcting errors while saving the fancy quantum tools for the heavy lifting, such as solving complicated problems that would take classical computers a long time. This way, we can solve a wider range of problems more efficiently by using both types of computing together.

10. Cryptography w.r.t Quantum Computing “Cryptography is the practice of using mathematical and computational techniques to protect information from unauthorized access.” While quantum computers can threaten our current methods of keeping information safe, they also push us to create stronger, more secure systems. It’s like a high-tech game of cat and mouse: as quantum technology advances, cryptography must evolve to stay one step ahead and protect our data.