Introduction to Quantum Computing - Jefferson Lab · Introduction to Quantum Computing Stephen...

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Introduction to Quantum Computing Stephen Casey – NASA Langley Research Center Slide template creator – Krysta Svore Langley Research Center

Transcript of Introduction to Quantum Computing - Jefferson Lab · Introduction to Quantum Computing Stephen...

Page 1: Introduction to Quantum Computing - Jefferson Lab · Introduction to Quantum Computing Stephen Casey –NASA Langley Research Center Slide template creator –Krysta Svore Langley

Introduction to Quantum ComputingStephen Casey – NASA Langley Research Center

Slide template creator – Krysta Svore

Langley Research Center

Page 2: Introduction to Quantum Computing - Jefferson Lab · Introduction to Quantum Computing Stephen Casey –NASA Langley Research Center Slide template creator –Krysta Svore Langley

Langley Research Center

Page 3: Introduction to Quantum Computing - Jefferson Lab · Introduction to Quantum Computing Stephen Casey –NASA Langley Research Center Slide template creator –Krysta Svore Langley

Langley Research Center

Page 4: Introduction to Quantum Computing - Jefferson Lab · Introduction to Quantum Computing Stephen Casey –NASA Langley Research Center Slide template creator –Krysta Svore Langley

Langley Research Center

Page 5: Introduction to Quantum Computing - Jefferson Lab · Introduction to Quantum Computing Stephen Casey –NASA Langley Research Center Slide template creator –Krysta Svore Langley

Langley Research Center

Page 6: Introduction to Quantum Computing - Jefferson Lab · Introduction to Quantum Computing Stephen Casey –NASA Langley Research Center Slide template creator –Krysta Svore Langley

Bloch Sphere

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θ

φ

Hadamard basis

Page 7: Introduction to Quantum Computing - Jefferson Lab · Introduction to Quantum Computing Stephen Casey –NASA Langley Research Center Slide template creator –Krysta Svore Langley

Langley Research Center

Quantum Hardware Technologies

Quantum dots

Ion traps

Optical photons

Superconductors

Nitrogen vacancy centers

Topological

Page 8: Introduction to Quantum Computing - Jefferson Lab · Introduction to Quantum Computing Stephen Casey –NASA Langley Research Center Slide template creator –Krysta Svore Langley

Unitary gates

Langley Research Center

Controlled-NOTXPauli-X

HHadamard

YPauli-Y

ZPauli-Z

SPhase

RRotation

Swap

Controlled-swap

Page 9: Introduction to Quantum Computing - Jefferson Lab · Introduction to Quantum Computing Stephen Casey –NASA Langley Research Center Slide template creator –Krysta Svore Langley

Quantum circuit model

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1

0

1

H

H

Page 10: Introduction to Quantum Computing - Jefferson Lab · Introduction to Quantum Computing Stephen Casey –NASA Langley Research Center Slide template creator –Krysta Svore Langley

Entanglement

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Bell states

H

Entangled

Page 11: Introduction to Quantum Computing - Jefferson Lab · Introduction to Quantum Computing Stephen Casey –NASA Langley Research Center Slide template creator –Krysta Svore Langley

Quantum Fourier Transform

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Page 12: Introduction to Quantum Computing - Jefferson Lab · Introduction to Quantum Computing Stephen Casey –NASA Langley Research Center Slide template creator –Krysta Svore Langley

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QFT

Exponential Speedup

Page 13: Introduction to Quantum Computing - Jefferson Lab · Introduction to Quantum Computing Stephen Casey –NASA Langley Research Center Slide template creator –Krysta Svore Langley

Langley Research Center

Spectroscopy Quantum mechanicsVideo compression Signal processingAcoustics

Classical FFT:1GB → 10 billion operations

Quantum FFT:1GB → 27 operations

Page 14: Introduction to Quantum Computing - Jefferson Lab · Introduction to Quantum Computing Stephen Casey –NASA Langley Research Center Slide template creator –Krysta Svore Langley

?

1807082088687404805951656164405905566278102516769401349170127021450056662540244048387341127590812303371781887966563182013214880557

?= ×

Langley Research CenterSlide credit: John Preskill

Page 15: Introduction to Quantum Computing - Jefferson Lab · Introduction to Quantum Computing Stephen Casey –NASA Langley Research Center Slide template creator –Krysta Svore Langley

39685999459597454290161126162883786067576449112810064832555157243

1807082088687404805951656164405905566278102516769401349170127021450056662540244048387341127590812303371781887966563182013214880557

45534498646735972188403686897274408864356301263205069600999044599

= ×

Langley Research Center

Peter Shor

Slide credit: John Preskill

Page 16: Introduction to Quantum Computing - Jefferson Lab · Introduction to Quantum Computing Stephen Casey –NASA Langley Research Center Slide template creator –Krysta Svore Langley

Langley Research Center

Quantum ComputerClassical Computer

193 digits:30 CPU-years (2.2 GHz)

193 digits:0.1 seconds

500 digits:1012 CPU-years

500 digits:2 seconds

Page 17: Introduction to Quantum Computing - Jefferson Lab · Introduction to Quantum Computing Stephen Casey –NASA Langley Research Center Slide template creator –Krysta Svore Langley

Langley Research Center

import Quipper

w :: (Qubit,Qubit) -> Circ (Qubit,Qubit)

w = named_gate "W"

toffoli :: Qubit -> (Qubit,Qubit) -> Circ Qubit

toffoli d (x,y) =

qnot d 'controlled' x .==. 1 .&&. y .==. 0

eiz_at :: Qubit -> Qubit -> Circ ()

eiz_at d r =

named_gate_at "eiZ" d 'controlled' r .==. 0

circ :: [ (Qubit,Qubit) ] -> Qubit -> Circ ()

circ ws r = do

label (unzip ws,r) (("a","b","r")

with_ancilla $ \d -> do

mapM_ w ws

mapM_ (toffoli d) ws

eiz_at d r

mapM_ (toffoli d) (reverse ws)

mapM_ (reverse_generic w) (reverse ws)

return ()

main = print_generic EPS circ (replicate 3 (qubit,qubit)) qubit

Programming languagesLiqui|>Quipper

QCL, Q, qGCL, QFC, QPL, QML, and others!

CCAdd a cbs // Perform the initial Add

AddA' N bs // Invert the add

QFT' bs // Convert out of Fourier space

CNOT [bMx ; anc] // Remember the overflow bit

QFT bs // Return to Fourier space

CAddA N (anc :: bs) // Do the add based on overflow

ccAdd' a cbs // Undo the add

QFT' bs // Get out of Fourier space

X [bMx] // Use the top bit as a flag

CNOT [bMx ; anc] // Clean up the Ancilla

X [bMx] // Reverse use of the top bit

QFT bs // Return to Fourier space

CCAdd a cbs // Do the final version of the add

Page 18: Introduction to Quantum Computing - Jefferson Lab · Introduction to Quantum Computing Stephen Casey –NASA Langley Research Center Slide template creator –Krysta Svore Langley

Image credit: D-Wave Systems, Inc.

D-Wave Two

4K

1K

300mK

20mK

77K

Page 19: Introduction to Quantum Computing - Jefferson Lab · Introduction to Quantum Computing Stephen Casey –NASA Langley Research Center Slide template creator –Krysta Svore Langley

Langley Research Center

Chimera structure

Superconducting flux qubits

Processor Architecture

Ising model

Page 20: Introduction to Quantum Computing - Jefferson Lab · Introduction to Quantum Computing Stephen Casey –NASA Langley Research Center Slide template creator –Krysta Svore Langley
Page 21: Introduction to Quantum Computing - Jefferson Lab · Introduction to Quantum Computing Stephen Casey –NASA Langley Research Center Slide template creator –Krysta Svore Langley

Langley Research Center

s=+1

s=+1

s=-1

s=-1

h1 h2

h3 h4

J34

J12

J13 J24

Find optimum s to minimize H(s)

Page 22: Introduction to Quantum Computing - Jefferson Lab · Introduction to Quantum Computing Stephen Casey –NASA Langley Research Center Slide template creator –Krysta Svore Langley

Langley Research Center

Graph embedding

Image credit: Dridi and Alghassi, 2015

Page 23: Introduction to Quantum Computing - Jefferson Lab · Introduction to Quantum Computing Stephen Casey –NASA Langley Research Center Slide template creator –Krysta Svore Langley

Langley Research Center

Uf

Gate model

H

H

H

Adiabatic model

Page 24: Introduction to Quantum Computing - Jefferson Lab · Introduction to Quantum Computing Stephen Casey –NASA Langley Research Center Slide template creator –Krysta Svore Langley

Optimized solution = global minimum energyLangley Research Center

Quantum annealing

Thermal annealing

Page 25: Introduction to Quantum Computing - Jefferson Lab · Introduction to Quantum Computing Stephen Casey –NASA Langley Research Center Slide template creator –Krysta Svore Langley

Optimization equals …

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Page 26: Introduction to Quantum Computing - Jefferson Lab · Introduction to Quantum Computing Stephen Casey –NASA Langley Research Center Slide template creator –Krysta Svore Langley

Machine Learning

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Page 27: Introduction to Quantum Computing - Jefferson Lab · Introduction to Quantum Computing Stephen Casey –NASA Langley Research Center Slide template creator –Krysta Svore Langley

Langley Research Center

Large Hadron Collider

NASA Quantum Artificial Intelligence Lab (QuAIL)

Searching for Exotic Particles in High-Energy Physics with Deep Learning

Baldi et al., 2014

Deep Neural Networks

Shallow Neural Networks

Boosted Decision Trees

Bayesian Network Structure Learning Using Quantum Annealing

O'Gorman et al., 2014

NASA Kepler mission’s search for habitable, Earth-sized planets

Page 28: Introduction to Quantum Computing - Jefferson Lab · Introduction to Quantum Computing Stephen Casey –NASA Langley Research Center Slide template creator –Krysta Svore Langley

Other Applications

Langley Research Center

Page 29: Introduction to Quantum Computing - Jefferson Lab · Introduction to Quantum Computing Stephen Casey –NASA Langley Research Center Slide template creator –Krysta Svore Langley

Langley Research Center

Searching large

databases

Quantum field theory

Quantum simulation

• Relativistic scattering amplitudes in four-dimensional spacetime • Jordan et at. (2012)• Exponential speedups

Grover’s algorithm •Grover (1996) •

Quadratic speedups •

• Quantum chemistry, materials science, large physical systems• Feynman (1982); Lanyon et al. (2009) • Exponential speedups

EncryptionBreaks RSA, DSA, ElGamal, and elliptic curve signature protocols •Unbreakable encryption – BB84, E91, Lo-Chau, KMB09 protocols •

Shor (1994), Bennett and Brassard (1984), Ekert (1991) •Quantum key networks exist in Boston, LANL, Vienna, Geneva, and Tokyo •

Page 30: Introduction to Quantum Computing - Jefferson Lab · Introduction to Quantum Computing Stephen Casey –NASA Langley Research Center Slide template creator –Krysta Svore Langley

Thanks to Markus DiefenthalerLangley Research Center

What happens next?