Quantum Math Fundamentals

Essential mathematical concepts for quantum computing: linear algebra, complex numbers, Hilbert spaces, and quantum logic.

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Quantum Vector Math

Ket & Bra Vectors

The foundation of quantum state representation. Explore Dirac notation for quantum states with complex number vectors. 

                        // Simple qubit notation

                        |0> = [1]

                        |1> = [0]
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Inner Product

Calculate probabilities and entanglement using complex conjugates and tensor products in Hilbert space.

Advanced Examples
|0> |1> |ψ> = α|0> + β|1> |α|² + |β|² = 1

Quantum Probabilities

Quantum Probability

Calculate probabilities from quantum state superpositions and interference patterns.

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Matrix Operators

Quantum logic gates as unitary matrices acting on state vectors.

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Hilbert Space

Understand infinite-dimensional vector spaces for continuous quantum states.

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Math Quick References

Complex Numbers

Quantum probability amplitudes require complex vector space manipulation.

z = a + bi
|z| = √(a² + b²)
More Examples

Pauli Matrices

Fundamental matrices representing quantum spin operators for qubits.

σx = [[0 1],[1 0]]
σy = [[0 -i],[i 0]]
σz = [[1 0],[0 -1]]
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