Understanding the Matrices of Quantum Logic Gates

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SUMMARY

Each Quantum Logic Gate corresponds to a specific matrix representation, with single-qubit gates represented as 2x2 matrices and two-qubit gates as 4x4 matrices. Understanding these matrices is crucial for grasping how quantum gates operate within quantum computing. The matrices are utilized in operations involving quantum states, typically through multiplication with state vectors. For a deeper understanding, it is recommended to consult detailed lecture notes, such as those provided by Caltech's Preskill.

PREREQUISITES
  • Basic knowledge of quantum mechanics
  • Understanding of linear algebra, specifically matrix multiplication
  • Familiarity with quantum computing concepts
  • Access to quantum logic gate resources, such as Caltech lecture notes
NEXT STEPS
  • Study the Caltech lecture notes on quantum mechanics and quantum computing
  • Learn about the mathematical foundations of quantum states and operators
  • Explore specific quantum gates like the Hadamard and CNOT gates
  • Investigate the role of matrices in quantum state transformations
USEFUL FOR

Students and professionals in quantum computing, physicists, and anyone interested in the mathematical foundations of quantum logic gates.

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(I am not sure if this is the right section for this).

This question probably is extremely trivial and silly, but I haven't been able to find the answer to it despite going through quite a bit of The Internet.

So, it appears that each Quantum Logic Gate corresponds to a matrix. Ones that interact with one qubit are 2 x 2, two qubits 4 x 4. The problem is, I have no clue what on Earth these matrices do and how they correspond to the gates. Do you multiply them by something? If so, what is that something?
 
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Floating Info said:
(I am not sure if this is the right section for this).

This question probably is extremely trivial and silly, but I haven't been able to find the answer to it despite going through quite a bit of The Internet.

So, it appears that each Quantum Logic Gate corresponds to a matrix. Ones that interact with one qubit are 2 x 2, two qubits 4 x 4. The problem is, I have no clue what on Earth these matrices do and how they correspond to the gates. Do you multiply them by something? If so, what is that something?

I haven't delved into the subject but If you want to really understand them you should work your way through the following lecture notes:

http://www.theory.caltech.edu/people/preskill/ph229/#lecture

My impression is that any type of summary articles (such as Wikipedia) will be too brief to get much understanding.
 

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