Categorical Quantum Computing

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Categorical Quantum Computing

  1. 1. Categorical Quantum Computing Alex Lang Department of Computer Science University of OxfordJuly 31 2011 / SuperHappyDevHouse 45.5 Alex Lang Categorical Quantum Computing
  2. 2. Outline Alex Lang Categorical Quantum Computing
  3. 3. Who am I? I study Category theory I study Quantum computing Alex Lang Categorical Quantum Computing
  4. 4. Who am I? I study Category theory I study Quantum computing Alex Lang Categorical Quantum Computing
  5. 5. What I want to talk about Quantum computing Without assuming (much) QM Alex Lang Categorical Quantum Computing
  6. 6. What I want to talk about Quantum computing Without assuming (much) QM Alex Lang Categorical Quantum Computing
  7. 7. What is QC? Like classical computing But faster! (potentially) By taking advantage of quantum mechanics Alex Lang Categorical Quantum Computing
  8. 8. What is QC? Like classical computing But faster! (potentially) By taking advantage of quantum mechanics Alex Lang Categorical Quantum Computing
  9. 9. What is QC? Like classical computing But faster! (potentially) By taking advantage of quantum mechanics Alex Lang Categorical Quantum Computing
  10. 10. What I do in QC We haven’t really built a quantum computer yet But I don’t really care! Once (if) we can a quantum computer, what will quantum programs mean? (semantics) Alex Lang Categorical Quantum Computing
  11. 11. What I do in QC We haven’t really built a quantum computer yet But I don’t really care! Once (if) we can a quantum computer, what will quantum programs mean? (semantics) Alex Lang Categorical Quantum Computing
  12. 12. What I do in QC We haven’t really built a quantum computer yet But I don’t really care! Once (if) we can a quantum computer, what will quantum programs mean? (semantics) Alex Lang Categorical Quantum Computing
  13. 13. A proposal We can program with red and green dots and wires. H H π {v3} H {v2} π π {v3} π {v2} Alex Lang Categorical Quantum Computing
  14. 14. What does this represent? Think of the wires as circuit wires Think of the dots as circuit gates Alex Lang Categorical Quantum Computing
  15. 15. What does this represent? Think of the wires as circuit wires Think of the dots as circuit gates Alex Lang Categorical Quantum Computing
  16. 16. Some rules Figure 1. Rules for the ZX-calculus Lang Alex Categorical Quantum Computing
  17. 17. What do the rules mean? Tells you what programs are “equivalent” Tells you how to execute the program Alex Lang Categorical Quantum Computing
  18. 18. What do the rules mean? Tells you what programs are “equivalent” Tells you how to execute the program Alex Lang Categorical Quantum Computing
  19. 19. What can you do with this? Quantum Teleportation in in in in Alice Bob Alice Bob Alice Bob Alice Bob H out out out out Alex Lang Categorical Quantum Computing
  20. 20. What’s the point? It’s simple! It’s universal Alex Lang Categorical Quantum Computing
  21. 21. What’s the point? It’s simple! It’s universal Alex Lang Categorical Quantum Computing
  22. 22. The End Ask me questions! Alex Lang Categorical Quantum Computing

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