Conventional
Quantum ALgorithms
Outline
Introduction
algorithms
Techniques
- Crafting tools
... with other tools
Why I'm talking about this?
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Complexity theory
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Big O notation (O,\(\Theta\),\(\Omega\),o,\(\omega\))
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NP = P?
- Oracles
- Axioms of Quantum Computing
- Quantum Gates
- Single qubit gates + CNOT
- CNOT + H + T (Clifford Gates?)
Classical Computing
Quantum Computing
Introduction
Algorithms
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Deutsch-Jozsa
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Bernstein-Vazirani
-
Simon
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Grover
Techniques
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Simple phase estimation
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Full phase estimation
...
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Quantum Fourier Transform
... And back to Algorithms
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Shor
(Mixed with techniques)
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Amplitude Amplification and Estimation
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Maximum-Finding Algorithm
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Quantum Singular Value Transformation
(?)
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Counting
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Quantum Arithmetrics
Materials
Materials
Gilles Brassard, Peter Hoyer, Michele Mosca (3), Alain Tapp, Quantum Amplitude Amplification and Estimation,
https://arxiv.org/abs/quant-ph/0005055v1
Samuel J. Lomonaco Jr, Grover's, Quantum search algorithm,
https://arxiv.org/abs/quant-ph/0010040
Richard Jozsa, Searching in Grover's Algorithm, https://arxiv.org/abs/quant-ph/9901021
Samuel J. Lomonaco Jr., Louis H. Kauffman, Quantum Hidden Subgroup Problems: A Mathematical Perspective,
https://arxiv.org/abs/quant-ph/0201095
Samuel J. Lomonaco Jr, Shor's Quantum Factoring Algorithm,
https://arxiv.org/abs/quant-ph/0010034
Michele Mosca, Quantum Algorithms, PhD thesis,
https://arxiv.org/abs/0808.0369
presentation tips
Solution
VS
Problem
1.
2.
presentation tips
Check Complexity, Proof (if possible)
Application (if possible)
3.
4.
-1. complexity + NP=P + oracles
0. quantum mechanics axioms (computer science perspective) + decompositions
1.Deutsch-Jozsa
2. Bernstein-Vazirani
3. Simon
4. Grover
4.5 simple phase est + QFT
4.75 full phase est. (finite binary and not)
5. Counting
5.5 quantum arithmethic (+, *, ?)
6. Shor
7. Amp. amplification and estimation
8. Maximum-finding algorithm
9. Optimality of Grover
10. QSVT (?)
-1. complexity + NP=P + oracles
0. quantum mechanics axioms (computer science perspective) + decompositions
1.Deutsch-Jozsa
2. Bernstein-Vazirani
3. Simon
4. Grover
4.5 simple phase est + QFT
4.75 full phase est. (finite binary and not)
5. Counting
5.5 quantum arithmethic (+, *, ?)
6. Shor
7. Amp. amplification and estimation
8. Maximum-finding algorithm
9. Optimality of Grover
10. QSVT (?)
Paulina & Akash
Ryszard +Mohameed + Adam