Math Needed for Quantum Computing

Shaila Nasrin

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2 min read

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Oct 21, 2024

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Linear Algebra

• Vectors and Matrices: Understanding vector spaces, basis vectors, and matrix operations (addition, multiplication).
• Eigenvalues and Eigenvectors: Crucial for understanding quantum measurements.
• Hermitian and Unitary Matrices: Quantum gates are represented by unitary matrices, and observables by Hermitian matrices.
• Tensor Products: For working with multi-qubit systems.
• Matrix Decompositions: Concepts like the singular value decomposition (SVD) are important for certain quantum algorithms.

Probability Theory

• Random Variables and Probability Distributions: Quantum measurements result in probabilities.
• Expectation Values: Related to the measurement outcomes.
• Bayesian Inference: Can be useful in quantum algorithms and error correction.
• Markov Chains: Useful in some quantum algorithms (e.g., Grover’s algorithm).

Complex Numbers

• Complex Arithmetic: Understanding operations on complex numbers (addition, multiplication, conjugates).
• Euler’s Formula: Understanding the relationship between complex exponentials and trigonometric functions.