Elements of Quantum Annealing (1)

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Contents：
1.1 Social background
1.2 Whai is Quantum Annealing ?
1.3 Purpose of Quantum Annealing
1.4 How to solve the optimization problem

Transcript

1. Elements of Quantum Annealing (1) Chapter 1 What is Quantum Annealing ? B3 English Seminar 2019/1/22 Nagaoka University of Technology Atom Yoshizawa
2. References Hidetoshi Nishimori , Masayuki Ohzeki “Elements of Quantum Annealing” , Kyouritu Publishing Ltd. (2018) 2
3. Contents 1.1 Social background 1.2 What is Quantum Annealing ? 1.3 Purpose of Quantum Annealing 1.4 How to solve the optimization problem 3
4. 1.1 Social background ◦ Problem 1 : The limits of transistor’s scale Moore's law : The number of transistors doubles every two years. However, It is becoming difficult to make the transistor small. ◦ Problem 2 : The increase in power consumption IT consumes 10% of the total electricity generation in the world. Especially the server uses huge amount of power. 4
5. 1.1 Social background Qbit using superconductors use little power except small chips. Supercomputer K (京) 's power consumption is about 12 MW. On the other hand, the power consumption of the D-wave quantum annealing machine is about 20 kW. 5 Quantum annealing is an ecological computer.
6. Two types of systems ◦ Quantum Gates Target issue : Generic quantum computation ◦ Quantum Annealing Target issue : Combinatorial optimization problems 6 1.2 What is Quantum Annealing Both systems use Qbit.
7. Quantum Annealing is different from Quantum Gates in that quantum bits are always coupled to each other. Because noise acts on the entire system, it is smaller than it works individually. 7 1.2 What is Quantum Annealing Quantum Annealing is easy to operate stably. http://obeidlab.blogspot.com/2011/06/ising-model-quantum-mechanics-and-very.html
8. Trends are beginning to use quantum annealing beyond combinatorial optimization problems. 8 1.3 Purpose of Quantum Annealing If Quantum Annealing is expanded, in principle it can be the same as the Quantum Gates and greatly speed up certain problems.
9. The combination optimization problem is, a problem of minimizing or maximizing their single-valued cost function when there are many variables taking discrete values. Example : Ising model = − � < 𝑖𝑖 − � =1 ℎ = 1 , 2 , ⋯ , 9 1.4 How to solve the optimization problem
10. The problem of finding the ground state of the Ising model belongs to the combinatorial optimization problem. Each Ising spin takes two values of ± 1. So, the total number of combinations is 2. 10 1.4 How to solve the optimization problem https://www.zaikei.co.jp/photo/237081.html
11. How to solve the optimization problem. 1. Make the state of each spin quantum mechanically uncertain. Initial setting to take two states at the same time in the sense of quantum mechanics. 11 1.4 How to solve the optimization problem
12. 2. Reduce quantum fluctuation and strengthen exchange interaction between spins 𝑖𝑖 and the local magnetic field ℎ . Each Ising spin selects autonomously confirmed state. 3. Block quantum fluctuation. The ground state of Hamiltonian is chosen. 12 1.4 How to solve the optimization problem