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56 lines
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56 lines
1.5 KiB
Markdown
# Math 401, Fall 2025: Thesis notes, R4, Superdense coding and Quantum error correcting codes
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> Progress: 0/NaN=NaN% (denominator and enumerator may change)
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This part may not be a part of "mathematical" research. But that's what I initially begin with.
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> [!TIP]
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>
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> A helpful resource is [The Functional Analysis of Quantum Information Theory](https://arxiv.org/pdf/1410.7188) Section 2.2
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>
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> Or another way in quantum computing [Quantum Computing and Quantum Information](https://www.cambridge.org/highereducation/books/quantum-computation-and-quantum-information/01E10196D0A682A6AEFFEA52D53BE9AE#overview) Section 2.3
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## References to begin with
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### Quantum computing and quantum information
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Every quantum bit is composed of two orthogonal states, denoted by $|0\rangle$ and $|1\rangle$.
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Each state
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$$
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\varphi=\alpha|0\rangle+\beta|1\rangle
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$$
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where $\alpha$ and $\beta$ are complex numbers, and $|\alpha|^2+|\beta|^2=1$.
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### Logic gates
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All the logic gates are unitary operators in $\mathbb{C}^{2\times 2}$.
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Example: the NOT gate is represented by the following matrix:
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$$
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NOT=\begin{pmatrix}
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0 & 1 \\
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1 & 0
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\end{pmatrix}
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$$
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Hadamard gate is represented by the following matrix:
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$$
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H=\frac{1}{\sqrt{2}}\begin{pmatrix}
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1 & 1 \\
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1 & -1
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\end{pmatrix}
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$$
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## Superdense coding
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## Quantum error correcting codes
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This part is intentionally left blank and may be filled near the end of the semester, by assignments given in CSE5313.
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[Link to self-contained report](../../CSE5313/Exam_reviews/CSE5313_F1.md) |