SZX-calculus, Scalable Graphical Quantum Reasoning A GTIQ2019 talk - PowerPoint PPT Presentation

❚✐t♦✉❛♥ ❈❛r❡tt❡✱ ▲❖❘■❆✱ ❯♥✐✈❡rs✐té ❞❡ ▲♦rr❛✐♥❡ ❉♦♠✐♥✐❝ ❍♦rs♠❛♥✱ ❯♥✐✈❡rs✐té ❞❡ ❣r❡♥♦❜❧❡ ❙✐♠♦♥ P❡r❞r✐①✱ ▲❖❘■❆✱ ❈◆❘❙ presents SZX-calculus, Scalable Graphical Quantum Reasoning A GTIQ2019 talk

❚r❛♥s❢♦r♠❛t✐♦♥ ▼❛tr✐① ❈♦♠♣♦s✐t✐♦♥ ♠❛tr✐① ♣r♦❞✉❝t ■❞❡♥t✐t② ■❞❡♥t✐t② ♠❛tr✐① ❚❡♥s♦r ❑r♦♥❡❝❦❡r ♣r♦❞✉❝t ❙✇❛♣ ❇❛s✐s ♣❡r♠✉t❛t✐♦♥ ❯♥✐t ❙❝❛❧❛rs Picturing processes ◆❛♠❡ ❙②♠❜♦❧ ❉✐❛❣r❛♠ ❍✐❧❜❡rt s♣❛❝❡ Chapitre 1: Graphical Reasoning � ✵✵✵✶ ⑤ ✶✶✵✶ � ✶

▼❛tr✐① ❈♦♠♣♦s✐t✐♦♥ ♠❛tr✐① ♣r♦❞✉❝t ■❞❡♥t✐t② ■❞❡♥t✐t② ♠❛tr✐① ❚❡♥s♦r ❑r♦♥❡❝❦❡r ♣r♦❞✉❝t ❙✇❛♣ ❇❛s✐s ♣❡r♠✉t❛t✐♦♥ ❯♥✐t ❙❝❛❧❛rs Picturing processes ◆❛♠❡ ❙②♠❜♦❧ ❉✐❛❣r❛♠ ❍✐❧❜❡rt s♣❛❝❡ ❚r❛♥s❢♦r♠❛t✐♦♥ f Chapitre 1: Graphical Reasoning � ✵✵✵✶ ⑤ ✶✶✵✶ � ✶

❈♦♠♣♦s✐t✐♦♥ ♠❛tr✐① ♣r♦❞✉❝t ■❞❡♥t✐t② ■❞❡♥t✐t② ♠❛tr✐① ❚❡♥s♦r ❑r♦♥❡❝❦❡r ♣r♦❞✉❝t ❙✇❛♣ ❇❛s✐s ♣❡r♠✉t❛t✐♦♥ ❯♥✐t ❙❝❛❧❛rs Picturing processes ◆❛♠❡ ❙②♠❜♦❧ ❉✐❛❣r❛♠ ❍✐❧❜❡rt s♣❛❝❡ ❚r❛♥s❢♦r♠❛t✐♦♥ f ▼❛tr✐① f Chapitre 1: Graphical Reasoning � ✵✵✵✶ ⑤ ✶✶✵✶ � ✶

♠❛tr✐① ♣r♦❞✉❝t ■❞❡♥t✐t② ■❞❡♥t✐t② ♠❛tr✐① ❚❡♥s♦r ❑r♦♥❡❝❦❡r ♣r♦❞✉❝t ❙✇❛♣ ❇❛s✐s ♣❡r♠✉t❛t✐♦♥ ❯♥✐t ❙❝❛❧❛rs Picturing processes ◆❛♠❡ ❙②♠❜♦❧ ❉✐❛❣r❛♠ ❍✐❧❜❡rt s♣❛❝❡ ❚r❛♥s❢♦r♠❛t✐♦♥ f ▼❛tr✐① f ❈♦♠♣♦s✐t✐♦♥ g ◦ f Chapitre 1: Graphical Reasoning � ✵✵✵✶ ⑤ ✶✶✵✶ � ✶

■❞❡♥t✐t② ■❞❡♥t✐t② ♠❛tr✐① ❚❡♥s♦r ❑r♦♥❡❝❦❡r ♣r♦❞✉❝t ❙✇❛♣ ❇❛s✐s ♣❡r♠✉t❛t✐♦♥ ❯♥✐t ❙❝❛❧❛rs Picturing processes ◆❛♠❡ ❙②♠❜♦❧ ❉✐❛❣r❛♠ ❍✐❧❜❡rt s♣❛❝❡ ❚r❛♥s❢♦r♠❛t✐♦♥ f ▼❛tr✐① f g ❈♦♠♣♦s✐t✐♦♥ g ◦ f ♠❛tr✐① ♣r♦❞✉❝t f Chapitre 1: Graphical Reasoning � ✵✵✵✶ ⑤ ✶✶✵✶ � ✶

■❞❡♥t✐t② ♠❛tr✐① ❚❡♥s♦r ❑r♦♥❡❝❦❡r ♣r♦❞✉❝t ❙✇❛♣ ❇❛s✐s ♣❡r♠✉t❛t✐♦♥ ❯♥✐t ❙❝❛❧❛rs Picturing processes ◆❛♠❡ ❙②♠❜♦❧ ❉✐❛❣r❛♠ ❍✐❧❜❡rt s♣❛❝❡ ❚r❛♥s❢♦r♠❛t✐♦♥ f ▼❛tr✐① f g ❈♦♠♣♦s✐t✐♦♥ g ◦ f ♠❛tr✐① ♣r♦❞✉❝t f ■❞❡♥t✐t② id Chapitre 1: Graphical Reasoning � ✵✵✵✶ ⑤ ✶✶✵✶ � ✶

❚❡♥s♦r ❑r♦♥❡❝❦❡r ♣r♦❞✉❝t ❙✇❛♣ ❇❛s✐s ♣❡r♠✉t❛t✐♦♥ ❯♥✐t ❙❝❛❧❛rs Picturing processes ◆❛♠❡ ❙②♠❜♦❧ ❉✐❛❣r❛♠ ❍✐❧❜❡rt s♣❛❝❡ ❚r❛♥s❢♦r♠❛t✐♦♥ f ▼❛tr✐① f g ❈♦♠♣♦s✐t✐♦♥ g ◦ f ♠❛tr✐① ♣r♦❞✉❝t f ■❞❡♥t✐t② id ■❞❡♥t✐t② ♠❛tr✐① Chapitre 1: Graphical Reasoning � ✵✵✵✶ ⑤ ✶✶✵✶ � ✶

❑r♦♥❡❝❦❡r ♣r♦❞✉❝t ❙✇❛♣ ❇❛s✐s ♣❡r♠✉t❛t✐♦♥ ❯♥✐t ❙❝❛❧❛rs Picturing processes ◆❛♠❡ ❙②♠❜♦❧ ❉✐❛❣r❛♠ ❍✐❧❜❡rt s♣❛❝❡ ❚r❛♥s❢♦r♠❛t✐♦♥ f ▼❛tr✐① f g ❈♦♠♣♦s✐t✐♦♥ g ◦ f ♠❛tr✐① ♣r♦❞✉❝t f ■❞❡♥t✐t② id ■❞❡♥t✐t② ♠❛tr✐① ❚❡♥s♦r f ⊗ g Chapitre 1: Graphical Reasoning � ✵✵✵✶ ⑤ ✶✶✵✶ � ✶

❙✇❛♣ ❇❛s✐s ♣❡r♠✉t❛t✐♦♥ ❯♥✐t ❙❝❛❧❛rs Picturing processes ◆❛♠❡ ❙②♠❜♦❧ ❉✐❛❣r❛♠ ❍✐❧❜❡rt s♣❛❝❡ ❚r❛♥s❢♦r♠❛t✐♦♥ f ▼❛tr✐① f g ❈♦♠♣♦s✐t✐♦♥ g ◦ f ♠❛tr✐① ♣r♦❞✉❝t f ■❞❡♥t✐t② id ■❞❡♥t✐t② ♠❛tr✐① f ❚❡♥s♦r f ⊗ g ❑r♦♥❡❝❦❡r ♣r♦❞✉❝t g Chapitre 1: Graphical Reasoning � ✵✵✵✶ ⑤ ✶✶✵✶ � ✶

❇❛s✐s ♣❡r♠✉t❛t✐♦♥ ❯♥✐t ❙❝❛❧❛rs Picturing processes ◆❛♠❡ ❙②♠❜♦❧ ❉✐❛❣r❛♠ ❍✐❧❜❡rt s♣❛❝❡ ❚r❛♥s❢♦r♠❛t✐♦♥ f ▼❛tr✐① f g ❈♦♠♣♦s✐t✐♦♥ g ◦ f ♠❛tr✐① ♣r♦❞✉❝t f ■❞❡♥t✐t② id ■❞❡♥t✐t② ♠❛tr✐① f ❚❡♥s♦r f ⊗ g ❑r♦♥❡❝❦❡r ♣r♦❞✉❝t g ❙✇❛♣ σ Chapitre 1: Graphical Reasoning � ✵✵✵✶ ⑤ ✶✶✵✶ � ✶

❯♥✐t ❙❝❛❧❛rs Picturing processes ◆❛♠❡ ❙②♠❜♦❧ ❉✐❛❣r❛♠ ❍✐❧❜❡rt s♣❛❝❡ ❚r❛♥s❢♦r♠❛t✐♦♥ f ▼❛tr✐① f g ❈♦♠♣♦s✐t✐♦♥ g ◦ f ♠❛tr✐① ♣r♦❞✉❝t f ■❞❡♥t✐t② id ■❞❡♥t✐t② ♠❛tr✐① f ❚❡♥s♦r f ⊗ g ❑r♦♥❡❝❦❡r ♣r♦❞✉❝t g ❙✇❛♣ ❇❛s✐s ♣❡r♠✉t❛t✐♦♥ σ Chapitre 1: Graphical Reasoning � ✵✵✵✶ ⑤ ✶✶✵✶ � ✶

❙❝❛❧❛rs Picturing processes ◆❛♠❡ ❙②♠❜♦❧ ❉✐❛❣r❛♠ ❍✐❧❜❡rt s♣❛❝❡ ❚r❛♥s❢♦r♠❛t✐♦♥ f ▼❛tr✐① f g ❈♦♠♣♦s✐t✐♦♥ g ◦ f ♠❛tr✐① ♣r♦❞✉❝t f ■❞❡♥t✐t② id ■❞❡♥t✐t② ♠❛tr✐① f ❚❡♥s♦r f ⊗ g ❑r♦♥❡❝❦❡r ♣r♦❞✉❝t g ❙✇❛♣ ❇❛s✐s ♣❡r♠✉t❛t✐♦♥ σ ❯♥✐t I Chapitre 1: Graphical Reasoning � ✵✵✵✶ ⑤ ✶✶✵✶ � ✶

Picturing processes ◆❛♠❡ ❙②♠❜♦❧ ❉✐❛❣r❛♠ ❍✐❧❜❡rt s♣❛❝❡ ❚r❛♥s❢♦r♠❛t✐♦♥ f ▼❛tr✐① f g ❈♦♠♣♦s✐t✐♦♥ g ◦ f ♠❛tr✐① ♣r♦❞✉❝t f ■❞❡♥t✐t② id ■❞❡♥t✐t② ♠❛tr✐① f ❚❡♥s♦r f ⊗ g ❑r♦♥❡❝❦❡r ♣r♦❞✉❝t g ❙✇❛♣ ❇❛s✐s ♣❡r♠✉t❛t✐♦♥ σ ❯♥✐t ❙❝❛❧❛rs I Chapitre 1: Graphical Reasoning � ✵✵✵✶ ⑤ ✶✶✵✶ � ✶

❚❤❡② ❛r❡ ♣r♦♣s ✿ ❖♥❡ ✇✐r❡ t②♣❡ s♣❛♥s ❛❧❧ t❤❡ ♦t❤❡rs✳ ❋♦r ✉s t❤✐s ✐s t❤❡ ◗✉❜✐t t②♣❡ r❡♣r❡s❡♥t❡❞ ❜② ❛ t✇♦ ❞✐♠❡♥s✐♦♥❛❧ ❍✐❧❜❡rt s♣❛❝❡✳ ❙②♥t❛① ✿ ❞✐❛❣r❛♠s ✇✐t❤ ✐♥♣✉ts ❛♥❞ ♦✉t♣✉ts ❜✉✐❧t ❢r♦♠ ❛ s❡t ♦❢ ❣❡♥❡r❛t♦rs✳ ❙❡♠❛♥t✐❝ ✿ ✳ ✳ ✳ ✳ ✷ ✷ ✳ ✳ ❍✐❧❜❡rt s♣❛❝❡ ✐s ❛ ❜✐❣ ♣❧❛❝❡ ❈❛r❧t♦♥ ❈❛✈❡s ❇✉t ✇❡ ♦♥❧② ♥❡❡❞ ❛ s♠❛❧❧ ♣❛rt ♦❢ ✐t✦ Diagrammatic languages and categories ❉✐❛❣r❛♠s ❛r❡ ♠♦♥♦✐❞❛❧ s②♠♠❡tr✐❝ ❝❛t❡❣♦r✐❡s✳ Chapitre 1: Graphical Reasoning � ✵✵✶✵ ⑤ ✶✶✵✶ � ✷

❋♦r ✉s t❤✐s ✐s t❤❡ ◗✉❜✐t t②♣❡ r❡♣r❡s❡♥t❡❞ ❜② ❛ t✇♦ ❞✐♠❡♥s✐♦♥❛❧ ❍✐❧❜❡rt s♣❛❝❡✳ ❙②♥t❛① ✿ ❞✐❛❣r❛♠s ✇✐t❤ ✐♥♣✉ts ❛♥❞ ♦✉t♣✉ts ❜✉✐❧t ❢r♦♠ ❛ s❡t ♦❢ ❣❡♥❡r❛t♦rs✳ ❙❡♠❛♥t✐❝ ✿ ✳ ✳ ✳ ✳ ✷ ✷ ✳ ✳ ❍✐❧❜❡rt s♣❛❝❡ ✐s ❛ ❜✐❣ ♣❧❛❝❡ ❈❛r❧t♦♥ ❈❛✈❡s ❇✉t ✇❡ ♦♥❧② ♥❡❡❞ ❛ s♠❛❧❧ ♣❛rt ♦❢ ✐t✦ Diagrammatic languages and categories ❉✐❛❣r❛♠s ❛r❡ ♠♦♥♦✐❞❛❧ s②♠♠❡tr✐❝ ❝❛t❡❣♦r✐❡s✳ ❚❤❡② ❛r❡ ♣r♦♣s ✿ ❖♥❡ ✇✐r❡ t②♣❡ s♣❛♥s ❛❧❧ t❤❡ ♦t❤❡rs✳ Chapitre 1: Graphical Reasoning � ✵✵✶✵ ⑤ ✶✶✵✶ � ✷