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Categorical Quantum Computing

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Joe Mathes

Alex Lang from the University of Oxford presented on categorical quantum computing. He studies category theory and quantum computing. His work develops a graphical language called the ZX-calculus to represent quantum programs and circuits using red and green dots and wires. The rules of the ZX-calculus allow determining if two programs are equivalent and how to execute programs. This approach is simple yet universal for representing quantum computations.

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Categorical Quantum Computing Alex Lang Department of Computer Science University of Oxford July 31 2011 / SuperHappyDevHouse 45.5 Alex Lang Categorical Quantum Computing
Outline Alex Lang Categorical Quantum Computing
Who am I? I study Category theory I study Quantum computing Alex Lang Categorical Quantum Computing
Who am I? I study Category theory I study Quantum computing Alex Lang Categorical Quantum Computing
What I want to talk about Quantum computing Without assuming (much) QM Alex Lang Categorical Quantum Computing
What I want to talk about Quantum computing Without assuming (much) QM Alex Lang Categorical Quantum Computing
What is QC? Like classical computing But faster! (potentially) By taking advantage of quantum mechanics Alex Lang Categorical Quantum Computing
What is QC? Like classical computing But faster! (potentially) By taking advantage of quantum mechanics Alex Lang Categorical Quantum Computing
What is QC? Like classical computing But faster! (potentially) By taking advantage of quantum mechanics Alex Lang Categorical Quantum Computing
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
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
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
A proposal We can program with red and green dots and wires. H H ¦Ð {v3} H {v2} ¦Ð ¦Ð {v3} ¦Ð {v2} Alex Lang Categorical Quantum Computing
What does this represent? Think of the wires as circuit wires Think of the dots as circuit gates Alex Lang Categorical Quantum Computing
What does this represent? Think of the wires as circuit wires Think of the dots as circuit gates Alex Lang Categorical Quantum Computing
Some rules Figure 1. Rules for the ZX-calculus Lang Alex Categorical Quantum Computing
What do the rules mean? Tells you what programs are ¡°equivalent¡± Tells you how to execute the program Alex Lang Categorical Quantum Computing
What do the rules mean? Tells you what programs are ¡°equivalent¡± Tells you how to execute the program Alex Lang Categorical Quantum Computing
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
What¡¯s the point? It¡¯s simple! It¡¯s universal Alex Lang Categorical Quantum Computing
What¡¯s the point? It¡¯s simple! It¡¯s universal Alex Lang Categorical Quantum Computing
The End Ask me questions! Alex Lang Categorical Quantum Computing

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Categorical Quantum Computing

  • 1. Categorical Quantum Computing Alex Lang Department of Computer Science University of Oxford July 31 2011 / SuperHappyDevHouse 45.5 Alex Lang Categorical Quantum Computing
  • 2. Outline Alex Lang Categorical Quantum Computing
  • 3. Who am I? I study Category theory I study Quantum computing Alex Lang Categorical Quantum Computing
  • 4. Who am I? I study Category theory I study Quantum computing Alex Lang Categorical Quantum Computing
  • 5. What I want to talk about Quantum computing Without assuming (much) QM Alex Lang Categorical Quantum Computing
  • 6. What I want to talk about Quantum computing Without assuming (much) QM Alex Lang Categorical Quantum Computing
  • 7. What is QC? Like classical computing But faster! (potentially) By taking advantage of quantum mechanics Alex Lang Categorical Quantum Computing
  • 8. What is QC? Like classical computing But faster! (potentially) By taking advantage of quantum mechanics Alex Lang Categorical Quantum Computing
  • 9. What is QC? Like classical computing But faster! (potentially) By taking advantage of quantum mechanics Alex Lang Categorical Quantum Computing
  • 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. 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. 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. A proposal We can program with red and green dots and wires. H H ¦Ð {v3} H {v2} ¦Ð ¦Ð {v3} ¦Ð {v2} Alex Lang Categorical Quantum Computing
  • 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. What does this represent? Think of the wires as circuit wires Think of the dots as circuit gates Alex Lang Categorical Quantum Computing
  • 16. Some rules Figure 1. Rules for the ZX-calculus Lang Alex Categorical Quantum Computing
  • 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. What do the rules mean? Tells you what programs are ¡°equivalent¡± Tells you how to execute the program Alex Lang Categorical Quantum Computing
  • 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. What¡¯s the point? It¡¯s simple! It¡¯s universal Alex Lang Categorical Quantum Computing
  • 21. What¡¯s the point? It¡¯s simple! It¡¯s universal Alex Lang Categorical Quantum Computing
  • 22. The End Ask me questions! Alex Lang Categorical Quantum Computing