## Tags
- Part of: [[Computing]] [[Computer science]] [[Computational complexity theory]] [[Quantum mechanics]]
- Related:
- Includes:
- Additional:
## Main resources
- [Quantum computing - Wikipedia](https://en.wikipedia.org/wiki/Quantum_computing)
<iframe src="https://en.wikipedia.org/wiki/Quantum_computing" allow="fullscreen" allowfullscreen="" style="height:100%;width:100%; aspect-ratio: 16 / 5; "></iframe>
Quantum computing
[Introduction to Quantum Computing and Quantum Hardware - YouTube](https://youtube.com/playlist?list=PLOFEBzvs-VvrXTMy5Y2IqmSaUjfnhvBHR&si=Bq9rCHmndwlHcx2e)
## Landscapes
- [The Map of Quantum Computing - Quantum Computing Explained - YouTube](https://www.youtube.com/watch?v=-UlxHPIEVqA)
<iframe title="The Map of Quantum Computing - Quantum Computing Explained" src="https://www.youtube.com/embed/-UlxHPIEVqA?feature=oembed" height="113" width="200" allowfullscreen="" allow="fullscreen" style="aspect-ratio: 1.76991 / 1; width: 100%; height: 100%;"></iframe>
- [[Artificial Intelligence x Quantum computing]]
## Additional resources
- [Timeline of quantum computing and communication - Wikipedia](https://en.wikipedia.org/wiki/Timeline_of_quantum_computing_and_communication)
## Related resources
- [Quantum Simulation Explained in 9 Slides - YouTube](https://www.youtube.com/watch?v=kD370qyxTyw)
## Written by AI (may include factually incorrect information)
- Quantum computing is a field of study focused on the development of [[Computing|computer]] technologies based on the principles of [[Quantum mechanics|quantum theory]], which explains the nature and behavior of energy and matter at the quantum level. This field encompasses various branches and specialized topics, reflecting its interdisciplinary nature that spans [[Physics]], [[Computer science]], and [[Mathematics]]. Here's a comprehensive list of various branches and topics within the theory of quantum computing:
### 1. Quantum Algorithms
- Shor's Algorithm: Breaks down large numbers into prime factors, posing a threat to traditional cryptography.
- Grover's Algorithm: Significantly speeds up searches within unsorted databases.
- Quantum Simulation Algorithms: Simulates complex quantum systems, which are intractable for classical computers.
- Quantum Fourier Transform: A quantum version of the classical Fourier transform, essential in many quantum algorithms.
- Quantum Machine Learning Algorithms: Enhances machine learning using quantum computing's parallelism and entanglement.
- Amplitude Amplification: Increases the probability of finding desired outcomes in quantum algorithms.
- Quantum Walk Algorithms: Quantum counterparts of classical random walks, useful in algorithmic applications.
### 2. Quantum Computation Models
- Quantum Circuit Model: Utilizes quantum gates and circuits, the most common model for quantum computing.
- Quantum Turing Machine: Theoretical model that extends the concept of classical Turing machines to quantum computing.
- Adiabatic Quantum Computation: Solves optimization problems by slowly evolving quantum states.
- One-way Quantum Computer: Computes using a highly entangled initial state and single-qubit measurements.
- Topological Quantum Computing: Relies on braiding of anyons, which are quasi-particles, for fault-tolerant computation.
### 3. Quantum Information Theory
- Quantum Entanglement: A phenomenon where quantum states of particles are interdependent, regardless of distance.
- Quantum Teleportation: Transfers quantum information between locations without moving the physical particles.
- Quantum Error Correction: Protects quantum information against errors from decoherence and other quantum noise.
- Quantum Communication Protocols: Methods for securely transmitting quantum information.
- Quantum Key Distribution (QKD): Ensures secure communication using principles of quantum mechanics.
- No-Cloning Theorem: States that it is impossible to create an identical copy of an arbitrary unknown quantum state.
- Quantum Entropy and Information: Extends classical information theory concepts to the quantum domain.
### 4. Quantum Complexity Theory
- Quantum Computational Complexity Classes (BQP, QMA, etc.): Categories of computational problems based on their solvability using quantum computers.
- Complexity of Quantum Algorithms: Studies the resources needed for quantum computations.
- Quantum vs Classical Complexity: Compares computational complexities between quantum and classical algorithms.
- Interactive Proof Systems in Quantum Computing: Studies computational verification methods in a quantum context.
### 5. Quantum Hardware and Implementation
- Quantum Bits (Qubits): Fundamental units of quantum information, analogous to classical bits.
- Quantum Gates and Circuits: Basic operations for manipulating qubits in quantum computers.
- Physical Realizations of Quantum Computers: Various technologies like superconducting qubits and trapped ions used to build quantum computers.
- Quantum Annealing and Quantum Optimization: Techniques for finding minimum energy states of a quantum system, useful in optimization problems.
### 6. Quantum Cryptography
- Quantum Cryptographic Protocols: Secure communication methods based on quantum principles.
- Post-Quantum Cryptography: Developing cryptographic systems secure against quantum computer attacks.
- Quantum-Safe Security Models: Security frameworks resistant to both quantum and classical computational threats.
- Device-Independent Quantum Cryptography: Cryptography that doesn't rely on trusting the hardware used.
### 7. Quantum Error Correction and Fault Tolerance
- Quantum Error-Correcting Codes: Methods to protect quantum information from errors in computation.
- Fault-Tolerant Quantum Computation: Ensures reliable quantum computing even with faulty components.
- Decoherence and Quantum Noise: Study of how quantum information degrades over time due to environmental interactions.
- Error Thresholds and Error Analysis: Determines acceptable levels of errors in quantum computing processes.
### 8. Quantum Programming Languages and Software
- Quantum Programming Paradigms: Different approaches to writing programs for quantum computers.
- Quantum Software Development: Creating software to run and simulate quantum algorithms.
- Quantum Programming Languages and Frameworks: Specialized languages and tools for quantum computing.
- Quantum Circuit Design and Optimization: Techniques to efficiently design and optimize quantum circuits.
### 9. Quantum Systems and Control Theory
- Quantum Control: Manipulation and control of quantum systems for desired outcomes.
- Quantum Feedback Networks: Networks where quantum information is fed back for system control.
- Open Quantum Systems: Study of quantum systems interacting with their environment.
- Quantum Dynamics and Evolution: Analysis of how quantum systems change over time.
### 10. Quantum Entanglement Theory
- Entanglement Measures: Quantifying the degree of entanglement in quantum states.
- Entanglement Entropy: A measure of entanglement in terms of information theory.
- Bell Inequalities: Tests to distinguish between quantum entanglement and classical correlations.
- Quantum Nonlocality: Phenomenon where quantum particles show correlations that defy classical physics.
### 11. Topological Quantum Computation
- Anyons and Braiding: Utilizes exotic quasi-particles (anyons) and their paths (braiding) for computation.
- Topological Quantum Field Theory: Theoretical framework for describing topological phases of matter.
- Topological Quantum Error Correction: Error correction approach using topological properties of quantum states.
### 12. Quantum Measurement Theory
- Quantum Observables and Measurement Models: Studies how quantum states are affected by measurements.
- Weak Measurement: Measurement method that minimally disturbs the quantum state.
- Quantum State Tomography: Technique for reconstructing the state of a quantum system.
### 13. Quantum Foundations and Interpretations
- Quantum Mechanics Interpretations (Copenhagen, Many-Worlds, etc.): Different philosophical perspectives on the meaning of quantum mechanics.
- Quantum-to-Classical Transition: Understanding how quantum phenomena give rise to classical reality.
- Quantum Mechanics Foundations: Basic principles and postulates underlying quantum mechanics.
### 14. Quantum Simulation
- Quantum Simulators: Devices that mimic complex quantum systems.
- Quantum Simulation of Physical Systems: Using quantum computers to simulate physical phenomena.
- Quantum Chemistry Simulation: Simulating molecular and chemical processes using quantum computers.
### 15. Quantum Networking and Communications
- Quantum Repeaters: Devices to extend the range of quantum communication.
- Quantum Networks and Protocols: Frameworks for connecting quantum computers and transferring quantum information.
- Quantum Internet: A proposed network of quantum computers interconnected by quantum communication lines.
Quantum computing is a rapidly evolving field, pushing the frontiers of computation, information processing, and fundamental physics. Its development promises to revolutionize various areas, including cryptography, materials science, and complex system modeling.