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Quantum computing principles
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Module 1
Foundations: From Vectors to Qubits
1
Quantum States as Vectors
Represent quantum states as column vectors with complex numbers.
2
Matrix Multiplication Essentials
Perform matrix-vector and matrix-matrix multiplication (up to 4x4).
3
Tensor Products for Multi-Qubit States
Compute the tensor product of two vectors to represent multi-qubit states.
4
Unitary Matrices & Reversible Quantum Gates
Explain the meaning of a unitary matrix and its implication for the reversibility of quantum gates.
5
Qubits vs. Classical Bits: The Superposition Advantage
Describe how a qubit differs from a classical bit, focusing on superposition.
6
Qubit Representation: Dirac Notation and Bloch Sphere
Represent a single qubit state using Dirac (ket) notation and visualize it on the Bloch sphere.
7
Quantum Measurement Probabilities
Calculate the probabilities of measurement outcomes from a given single-qubit state vector.
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Manipulating Qubits with Quantum Gates