Distributed Quantum Computing Using the most precise description of - - PowerPoint PPT Presentation

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Distributed Quantum Computing Using the most precise description of - - PowerPoint PPT Presentation

Jan 16, 2023 640 likes •969 views

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 Rhrig These slides are just

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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
  • r Science Fiction?

Vasil S. Denchev and Gopal Pandurangan

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Questions?