Eternity II puzzle by beginners (Qiskit Camp Asia 2019)

https://community.qiskit.org/events/asia/

Transcript

1. Eternity II Puzzle by Beginners #48 IBM Qiskit Camp Asia 2019 (Nov 18-21, 2019) Kumagai Masahito, Yuki Yamada, Shuta Kobayashi and Ken Wei IBM Qiskit Camp Asia 2019
2. Eternity II Photo Credit: Karen Carr
3. • Edge-matching puzzle ◦ 256 pieces (16 by 16 grid) • Designed to be difficult to solve by brute-force computer search Eternity II → Let’s solve this with quantum computers! Photo Credit: Karen Carr
4. Problem Settings Adjacent edges must match Each piece is unique Pieces can be used in 4 orientations Gray = edge Rules
5. Our Approach • Start from edge → Proceed to inside repeatedly
6. Our Approach • Start from edge → Proceed to inside repeatedly • Fix one corner • Enumerate all possibilities for other positions • Filter the possibilities by requirements • Find a correct combination ? ? ? ? ? ? ? ? ? ? ?
7. Implementation - Simplified Case • Find an answer for 2 by 2 grid ◦ (Original: 16 by 16 grid) Expected output
8. Implementation - Quantum Circuit
9. Implementation - Quantum Circuit 10 qubits & 17 ancilla bits
10. Experimentation Result We got a correct answer https://github.com/kumagaimasahito/Eternity/blob/master/eternity_group2.ipynb
11. Future Works • Decrease the number of ancilla bits in our quantum circuit • Try other experimentations on bigger puzzles • Implement Grover algorithm for finding Directed Hamiltonian Cycle Special thanks: Ken Wei (IBM), Asa Eagle!
12. Blue: 1 Red: 2 Green: 3 ※Clockwise Directed Hamiltonian Cycle
13. Directed Hamiltonian Cycle
14. Directed Hamiltonian Cycle
15. Directed Hamiltonian Cycle