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_posts/2023-10-09-theory-of-quantum-information.md

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As we start off thinking about thinking and the physics of quantum computation, we can frame what will necessarily be nebulous and theoretical discussions about about this still rapidly evolving field of thought using something like the structure provided by [Dr. Mark M Wilde's new text in pdf form, but still built *from the ground up* and entitled "From Classical to Quantum Shannon Theory"](https://arxiv.org/pdf/1106.1445.pdf) OR ... we can look at [Peter Shor](https://arxiv.org/find/quant-ph/1/Shor/0/1/0/all/1/0)'s [MIT course on Quantum Conputation](https://math.mit.edu/~shor/435-LN/) and professor Shor's course lecture notes.
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1) [Introduction and History](https://math.mit.edu/~shor/435-LN/Lecture_01.pdf)
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2) --- [The Superposition Principle](https://math.mit.edu/~shor/435-LN/Lecture_02.pdf)
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* Lecture 3 --- [Unitary Evolution and the Bloch Sphere](https://math.mit.edu/~shor/435-LN/Lecture_03.pdf)
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* Lecture 4 --- [Quantum Measurements](https://math.mit.edu/~shor/435-LN/Lecture_04.pdf)
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Lecture 5) --- [Joint Quantum Systems and Tensor Products](https://math.mit.edu/~shor/435-LN/Lecture_05.pdf)
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Lecture 6 --- [More Tensor Products (Measurements of Joint Systems)](https://math.mit.edu/~shor/435-LN/Lecture_06.pdf)
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Lecture 7 --- [Classical Boolean circuits](https://math.mit.edu/~shor/435-LN/Lecture_07.pdf)
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Lecture 8 --- [Reversible Boolean circuits](https://math.mit.edu/~shor/435-LN/Lecture_08.pdf)
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Lecture 9 --- [Quantum gates I](https://math.mit.edu/~shor/435-LN/Lecture_09.pdf)
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Lecture 10 --- [Quantum gates II](https://math.mit.edu/~shor/435-LN/Lecture_10.pdf)
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Lecture 11 --- [Quantum Teleportation](https://math.mit.edu/~shor/435-LN/Lecture_11.pdf)
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Lecture 12 --- [Density Matrices I](https://math.mit.edu/~shor/435-LN/Lecture_12.pdf)
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Lecture 13 --- [Density Matrices II](https://math.mit.edu/~shor/435-LN/Lecture_13.pdf)
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Lecture 14 --- [The GHZ Experiment (theory)](https://math.mit.edu/~shor/435-LN/Lecture_14.pdf)
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Lecture 15 --- [Quantum Optics and the GHZ Experiment](https://math.mit.edu/~shor/435-LN/Lecture_15.pdf)
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Lecture 16 --- [The Deutsch-Jozsa Algorithm](https://math.mit.edu/~shor/435-LN/Lecture_16.pdf)
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Lecture 17 --- [Classical computational complexity theory](https://math.mit.edu/~shor/435-LN/Lecture_17.pdf)
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Lecture 18 --- [Simon's algorithm](https://math.mit.edu/~shor/435-LN/Lecture_18.pdf)
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Lecture 19 --- [The quantum Fourier transform](https://math.mit.edu/~shor/435-LN/Lecture_19.pdf)
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Lecture 20 --- [Phase Estimation](https://math.mit.edu/~shor/435-LN/Lecture_20.pdf)
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Lecture 21 --- [Quantum factoring algorithm](https://math.mit.edu/~shor/435-LN/Lecture_21.pdf)
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Lecture 22 --- [The Number Theory Needed for the Factoring Algorithm](https://math.mit.edu/~shor/435-LN/Lecture_22.pdf)
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Lecture 23 --- [The Discrete Log Algorithm](https://math.mit.edu/~shor/435-LN/Lecture_23.pdf)
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Lecture 24 --- [Grover's search algorithm](https://math.mit.edu/~shor/435-LN/Lecture_24.pdf)
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Lecture 25 --- [Proof that Grover Search is Optimal](https://math.mit.edu/~shor/435-LN/Lecture_25.pdf)
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Lecture 26 --- [Lecture on Hamiltonian Simulation; ***Notes Unwritten***
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Lecture 27 --- [Introduction to Quantum error correcting codes --- the 9-qubit code](https://math.mit.edu/~shor/435-LN/Lecture_27.pdf)
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Lecture 28 --- [More on the 9-qubit code](https://math.mit.edu/~shor/435-LN/Lecture_28.pdf)
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Lecture 29 --- [The 7-qubit Quantum Hamming Code](https://math.mit.edu/~shor/435-LN/Lecture_29.pdf)
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Lecture 30 --- [Quantum CSS Codes](https://math.mit.edu/~shor/435-LN/Lecture_30.pdf)
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Lecture 31 --- [The BB84 Quantum Key Distribution Protocol and the Proof of Its Security](https://math.mit.edu/~shor/435-LN/Lecture_31.pdf)
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2) [The Superposition Principle](https://math.mit.edu/~shor/435-LN/Lecture_02.pdf)
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3) [Unitary Evolution and the Bloch Sphere](https://math.mit.edu/~shor/435-LN/Lecture_03.pdf)
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4) [Quantum Measurements](https://math.mit.edu/~shor/435-LN/Lecture_04.pdf)
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5) [Joint Quantum Systems and Tensor Products](https://math.mit.edu/~shor/435-LN/Lecture_05.pdf)
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6) [More Tensor Products (Measurements of Joint Systems)](https://math.mit.edu/~shor/435-LN/Lecture_06.pdf)
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7) [Classical Boolean circuits](https://math.mit.edu/~shor/435-LN/Lecture_07.pdf)
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8) [Reversible Boolean circuits](https://math.mit.edu/~shor/435-LN/Lecture_08.pdf)
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9) [Quantum gates I](https://math.mit.edu/~shor/435-LN/Lecture_09.pdf)
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10) [Quantum gates II](https://math.mit.edu/~shor/435-LN/Lecture_10.pdf)
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11) [Quantum Teleportation](https://math.mit.edu/~shor/435-LN/Lecture_11.pdf)
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12) [Density Matrices I](https://math.mit.edu/~shor/435-LN/Lecture_12.pdf)
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13) [Density Matrices II](https://math.mit.edu/~shor/435-LN/Lecture_13.pdf)
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14) [The GHZ Experiment (theory)](https://math.mit.edu/~shor/435-LN/Lecture_14.pdf)
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15) [Quantum Optics and the GHZ Experiment](https://math.mit.edu/~shor/435-LN/Lecture_15.pdf)
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16) [The Deutsch-Jozsa Algorithm](https://math.mit.edu/~shor/435-LN/Lecture_16.pdf)
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17) [Classical computational complexity theory](https://math.mit.edu/~shor/435-LN/Lecture_17.pdf)
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18) [Simon's algorithm](https://math.mit.edu/~shor/435-LN/Lecture_18.pdf)
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19) [The quantum Fourier transform](https://math.mit.edu/~shor/435-LN/Lecture_19.pdf)
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20) [Phase Estimation](https://math.mit.edu/~shor/435-LN/Lecture_20.pdf)
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21) [Quantum factoring algorithm](https://math.mit.edu/~shor/435-LN/Lecture_21.pdf)
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22) [The Number Theory Needed for the Factoring Algorithm](https://math.mit.edu/~shor/435-LN/Lecture_22.pdf)
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23) [The Discrete Log Algorithm](https://math.mit.edu/~shor/435-LN/Lecture_23.pdf)
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24) [Grover's search algorithm](https://math.mit.edu/~shor/435-LN/Lecture_24.pdf)
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25) [Proof that Grover Search is Optimal](https://math.mit.edu/~shor/435-LN/Lecture_25.pdf)
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26) On Hamiltonian Simulation ***Notes Unwritten By Dr. Shor*** ... *but, don't worry* ... there other sources, like [UW-Madison CS 880 Quantum Algorithms](https://pages.cs.wisc.edu/~dieter/Courses/2022s-CS710/Scribes/) that do cover this topic of [Hamiltonian Simulation](https://pages.cs.wisc.edu/~dieter/Courses/2022s-CS710/Scribes/scribe14.pdf)
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27) [Introduction to Quantum error correcting codes) the 9-qubit code](https://math.mit.edu/~shor/435-LN/Lecture_27.pdf)
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28) [More on the 9-qubit code](https://math.mit.edu/~shor/435-LN/Lecture_28.pdf)
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29) [The 7-qubit Quantum Hamming Code](https://math.mit.edu/~shor/435-LN/Lecture_29.pdf)
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30) [Quantum CSS Codes](https://math.mit.edu/~shor/435-LN/Lecture_30.pdf)
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31) [The BB84 Quantum Key Distribution Protocol and the Proof of Its Security](https://math.mit.edu/~shor/435-LN/Lecture_31.pdf)
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OR ... if you prefer the seminal course which has spawned lots of excellent notes and influenced lots of people now working in the quantum computation field, eg such as [Umesh V. Vazirnai](https://people.eecs.berkeley.edu/~vazirani/) and [N. David Mermin](https://www.thriftbooks.com/w/quantum-computer-science-an-introduction_n-david-mermin/13913761/?resultid=b79b59d1-adee-4d9a-8d6c-f655f52a8625#edition=14734495&idiq=32814053) ... but, a currently taught course which is still more than just current, in spite of being the most mature take on this new topic out there, we can go *back* to the foundation of Dr. John Preskil's outline for CalTech's [Phys 219 Quantum Computation](http://theory.caltech.edu/~preskill/ph219/ph219_2023.html)
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