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Distributed Quantum Computing
Using the most precise description of our world
to solve some of the hardest problems
by Matthias Egli
Based on the paper „Distributed Quantum Computing“ by Harry Buhrman and Hein Röhrig
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These slides are just an addition to the math
shown on the blackboard
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Motivation
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Communication Complexity
n Alice Bob
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Communication Complexity
? Alice Bob
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Communication Complexity
Classical Computer Quantum Computer
Disjointness n
Equality (Promise) n log(n)
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Speedup with Quantum Computers
Classical Computer Quantum Computer
Factorization
Search n
Deutsch-Jozsa n 1
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Basics
The qubit
Superposition
Entanglement
Quantum Gate
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Deutsch-Josza Algorithm
Promise:
Function is constant or balanced
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Deutsch-Josza Algorithm
n Classcial Computer Classical randomized Quantum Computer
2 2 1 1
n n Log(n) 1
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Communication
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Qubit
Communication
Alice Bob
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Communication Types
Entanglement
Communication
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Classical bits with EPR Pairs
Communication
Alice Bob
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Communication Types
Qubit with shared EPR Pairs
Communication
Alice Bob
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Deutsch-Jozsa Communication
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Deutsch-Josza Communication
Y: 00101100
Alice Bob
X: 00101100
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Deutsch-Josza Communication
Alice Bob
X = Y ? Y: 00101100 X: 00101100
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Deutsch-Josza Communication
Y: 00101100
Alice Bob
X: 00101100 X = Y ?
n
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Deutsch-Josza Communication
Y: 00101100 X: 00101100 X = Y ?
? Alice Bob
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Deutsch-Josza Communication
Y: 00101100 X: 00101100 X = Y ? Promise: Hamming Distance = n/2 or 0
Alice Bob
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Deutsch-Josza Communication
Y: 00101100 X: 00101100 X = Y ? Promise: Hamming Distance = n/2 or 0
XOR
Alice Bob
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Deutsch-Josza Communication
Y: 00101100 X: 00101100 X = Y ? Promise: Hamming Distance = n/2 or 0
Alice Bob
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Alice
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Alice Bob log(n)+1
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Bob
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Bob
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Bob
Deutsch-Jozsa Algorithm
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What else is possible?
• Leader Election
• Disjointness
• […]
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Sources
• Caltech Introduction to Quantum Computing
http://www.theory.caltech.edu/people/preskill/ph229/notes/chap1.pdf
• Distributed Quantum Computing
Harry Buhrmann and Hein Röhrig
• Can quantum mechanics help distributed computing?
Anne Broadbent and Alain Tapp
• Distributed Quantum Computing: A New Frontier in Distributed Systems
or Science Fiction?
Vasil S. Denchev and Gopal Pandurangan
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Questions?