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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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Page 1: distributed quantum computing (1)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

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

Page 2: distributed quantum computing (1)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

These slides are just an addition to the math

shown on the blackboard

Page 3: distributed quantum computing (1)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

Motivation

Page 4: distributed quantum computing (1)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

Communication Complexity

n Alice Bob

Page 5: distributed quantum computing (1)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

Communication Complexity

? Alice Bob

Page 6: distributed quantum computing (1)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

Communication Complexity

Classical Computer Quantum Computer

Disjointness n

Equality (Promise) n log(n)

Page 7: distributed quantum computing (1)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

Speedup with Quantum Computers

Classical Computer Quantum Computer

Factorization

Search n

Deutsch-Jozsa n 1

Page 8: distributed quantum computing (1)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

Basics

The qubit

Superposition

Entanglement

Quantum Gate

Page 9: distributed quantum computing (1)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

Deutsch-Josza Algorithm

Promise:

Function is constant or balanced

Page 10: distributed quantum computing (1)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

Deutsch-Josza Algorithm

n Classcial Computer Classical randomized Quantum Computer

2 2 1 1

n n Log(n) 1

Page 11: distributed quantum computing (1)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

Communication

Page 12: distributed quantum computing (1)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

Qubit

Communication

Alice Bob

Page 13: distributed quantum computing (1)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

Communication Types

Entanglement

Communication

Page 14: distributed quantum computing (1)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

Classical bits with EPR Pairs

Communication

Alice Bob

Page 15: distributed quantum computing (1)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

Communication Types

Qubit with shared EPR Pairs

Communication

Alice Bob

Page 16: distributed quantum computing (1)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

Deutsch-Jozsa Communication

Page 17: distributed quantum computing (1)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

Deutsch-Josza Communication

Y: 00101100

Alice Bob

X: 00101100

Page 18: distributed quantum computing (1)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

Deutsch-Josza Communication

Alice Bob

X = Y ? Y: 00101100 X: 00101100

Page 19: distributed quantum computing (1)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

Deutsch-Josza Communication

Y: 00101100

Alice Bob

X: 00101100 X = Y ?

n

Page 20: distributed quantum computing (1)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

Deutsch-Josza Communication

Y: 00101100 X: 00101100 X = Y ?

? Alice Bob

Page 21: distributed quantum computing (1)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

Deutsch-Josza Communication

Y: 00101100 X: 00101100 X = Y ? Promise: Hamming Distance = n/2 or 0

Alice Bob

Page 22: distributed quantum computing (1)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

Deutsch-Josza Communication

Y: 00101100 X: 00101100 X = Y ? Promise: Hamming Distance = n/2 or 0

XOR

Alice Bob

Page 23: distributed quantum computing (1)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

Deutsch-Josza Communication

Y: 00101100 X: 00101100 X = Y ? Promise: Hamming Distance = n/2 or 0

Alice Bob

Page 24: distributed quantum computing (1)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

Alice

Page 25: distributed quantum computing (1)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

Alice Bob log(n)+1

Page 26: distributed quantum computing (1)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

Bob

Page 27: distributed quantum computing (1)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

Bob

Page 28: distributed quantum computing (1)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

Bob

Deutsch-Jozsa Algorithm

Page 29: distributed quantum computing (1)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

What else is possible?

• Leader Election

• Disjointness

• […]

Page 30: distributed quantum computing (1)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

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

Page 31: distributed quantum computing (1)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

Questions?


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