Welcome to the Quantum Computing Explained repository! This comprehensive guide introduces key concepts, characteristics, and applications of quantum computing. Explore from basic principles to advanced quantum algorithms and programming using Microsoft Q#.
- Quantum Computing Basics
- Definition
- Applications
- Characteristics of a Computational System
- Superposition
- Entanglement
- Interference
- Complex Numbers in Quantum Computing
- Importance and Usage
- Properties
- Linear Algebra in Quantum Computing
- Linear Combination
- Linear Dependence
- Linear Independence
- Span and Basis
- Matrix
- Projection
- Introduction to Qubits
- Qubit Creation
- Utility of Qubits
- Building a Qubit
- Basic Math Behind Qubits
- Quantum Computing Algorithms
- Quantum Fourier Transform
- Amplitude Amplification
- Quantum Walk
- Microsoft Q#
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Quantum computers are controllable quantum mechanical devices that exploit the properties of quantum physics to perform computations. For some computational tasks, quantum computing provides exponential speedups.
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Qubits (quantum bits) are the fundamental object of information in quantum computing.
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Quantum computing leverages the principles of superposition, entanglement, and interference to process information in ways classical computers cannot.
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Quantum theory can be interpreted as saying that matter, at a quantum level, is in a multitude of possible configurations (known as states).
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These many configurations of the quantum state, may interfere with each other, and this interference prevents the use of statistical sampling to obtain the quantum state configurations.
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The foundational core of quantum computing to store Information in quantum states of matter and to use quantum gate operations to compute on that information. by harnessing and learning to 'program' quantum interference.
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Quantum computers harness the unique behavior of quantum physics—such as superposition, entanglement, and quantum interference—and apply it to computing. This introduces new concepts to traditional programming methods.
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With Azure Quantum, you can make use of the advantages of quantum computing today, in a full-stack open cloud ecosystem with access to software, hardware, and pre-built solutions. Azure Quantum offers two types of solutions: quantum computing and optimization.
Unlock the potential of quantum computing in cryptography, artificial intelligence, finance, and particle physics.
Definition: Existence of one element in many states or places simultaneously.
Example: A basic water molecule exhibiting superposition.
Definition: Quantum mechanical phenomenon where the states of two or more objects are interconnected.
Example: Two spinning electrons demonstrating entanglement.
Definition: Control the probability of a qubit system collapsing into measurement states.
Example:
Explore the role of complex numbers in quantum computing and understand why they are crucial for quantum operations.
- Commutative
- Associative
- Distributive
Definition: Combination of vectors through scalar multiplication and addition.
Example:
Definition: Vectors are linearly dependent if one vector can be expressed as a combination of others.
Example:
Definition: Vectors are linearly independent if no vector can be expressed as a combination of others.
Example:
Explore the concepts of span and basis in linear algebra and understand their significance.
Definition: Mathematical representation used in various real-life applications. Mainly we are used two kind of matricies.
- Unitary Matricies: U^t * U = I, inverse of U is U^T means when acting on a vector, unitary matricies rotate/flip the vector, keeping the magnitude of the vector the same
- Hermitian Matricies: H = H^t
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Eigenvectors and Eigenvalues:
Where matrices are used:
Definition: The process of projecting a vector onto a subspace.
Real-life applications:
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Classical Computers use 0's and 1's bits in different times. In Quantum Computers also follow same scenerio but it can be use 0 and 1 at the samw time.
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The fundamental difference between Classical Computers and Quantum Computers is that programs in Quantum Computers are intrinsically probabilistic, whereas Classical Computers are usually deterministic.
- Physically, a qubit can be amde from any quantum particle that has 2 distinct states. A Qubit is in a Superposition, if it is both 0 and 1 at same time.
Learn how qubits enhance computational power in quantum computing compared to classical bits.
Delve into the possibility and challenges of building a qubit at home.
Understand the mathematical concepts behind qubits, including working with multiple qubits and their various states.
Definition: Linear transformation on qubits, analogous to the inverse discrete Fourier transform.
Associated algorithms: Shor's and Simon's algorithms.
Definition: Generalization of Grover's search algorithm, applicable to counting and probability tasks.
Algorithms: Grover's and quantum counting algorithms.
Definition: Quantum version of the classic random walk, formulated in continuous and discrete time.
Problem: Element distinctness problem.
Explore Microsoft Q#, an open-source programming language designed for developing and running quantum algorithms. It is part of the Quantum Development Kit, allowing you to create quantum programs and simulations.
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