The he fut uture ure of of comput omputing: ng: Quant uantum - - PowerPoint PPT Presentation

The he fut uture ure of

• f comput
• mputing:

ng: Quant uantum um

Andrá ndrás s Gil Gilyén yén PhD PhD: Postdoc: Postdoc:

The he fut uture ure of

• f comput
• mputing:

ng: Quant uantum um

• Our
• Our wor
• rld is qu

ld is quan antum tum m mec echani anical. al.

• Qua
• Quantum

ntum com compute puters rs e ena nable ble no novel el c com

• mpu

putat tations. ions.

Quant uantum um ef effect ects for

• r com
• mput

uting ng

• Sup
• Superpo

erpositio sition: n: a qu qubit bit can can be be both both 0 0 an and d 1 1 simu simultane ltaneou

• usly (with

sly (with some some ampl amplitud itudes) es)

• Int
• Interferen

rference: ce: co computatio mputations ns in in sup superp erpositio

• sition

n can can co coll llect ectivel vely y co contrib ntribut ute to to the fin the final resu al result lt

• Entan
• Entangle

glemen ment: : qu qubi bits s can can ha have ve st strong

• nger

er than an cl classica assical corre l correlatio lations ns

Quantum supremacy Quant uantum um supr suprema emacy

• Quantum computers have the potential to solve
• Qua
• Quantum

ntum compute puters rs hav ave th the e pote

• tenti

ntial al to to solve

• lve

some problems exponentially more efficiently than some me pr probl

• blem

ems ex expo pone nentia ntially lly more

• re effic

ficient ently ly tha han n classical computers. clas assical com al compu puters. ters.

• Google just reported passing the cross-over
• Goo
• Google

gle jus just rep report

• rted

ed pas passing sing th the e cros cross-ov

• ver

r point, where a quantum chip can be much faster po poin int, t, wher where e a qu quant antum um chip ip can can be be muc uch fa faste ter r in practice than the best available supercomputer. in in pr prac actice t tice than han the the b bes est t av avai ailab lable le sup uperc ercomp mpute uter.

Boaz Barak’s analogy (quoted by Scott Aaronson) Boa Boaz B Barak’ rak’s a anal nalog

• gy (qu

(quote

• ted b

d by Sc Scott

• tt Aaron

ronson

• n)

vs. vs.

Boaz Barak’s analogy (quoted by Scott Aaronson) Boa Boaz B Barak’ rak’s a anal nalog

• gy (qu

(quote

• ted b

d by Sc Scott

• tt Aaron

ronson

• n)

vs. vs. “ “Deep Blue vs. Deep Deep B Blue vs ue vs. . Kasparov” Kas Kasparo arov”

Mai ain n tec echni hniques ques for

• r quant

quantum um al algori gorithm hms

• Quant

uantum um Fo Four urier trans nsfor

• rm: Shor

hor’s s al algor gorithm for

• r

fact ctor

• ring,

ng, br breaki aking ng RSA cr crypt ypto-

• -sys

system em, etc.

• Ham

amiltoni

• nian

an si simul ulation:

• n: dynam

dynamical al si simulat ation

• n of
• f

quan antum um syst ystems for

• r chem

hemist stry, mater erial sc scienc ence, e, etc. c.

• Grover
• ver sear

search: ch: gene neric c quadr quadrat atic sp spee eed-up up for unst struct ctur ured ed sear search ch pr problem ems

• Lar

Large- ge-di dimen ensional

• nal

regr gres essi sion

• n

(HHL al algo gorithm): speedi speeding- ng-up up var various

• us machi

hine ne lear earni ning ng appl applicat ations

• ns

Qua uantum um Si Singul ngular ar Val alue ue transf ansfor

• rmat

ation

• n
• A common
• n uni

unificat cation

• n / gener

general alizat ation

• n of
• f Ham

amiltoni

• nian

an si simul ulat ation,

• n, Grov
• ver

er sear earch and and regr egress ession

• n (HHL)

L).

• Block
• ck-enc

encodi

• dings:

ngs: exponent exponential ally fast aster er mat atrix oper

• perat

ations

• ns
• Efficient

ent ci circui uits & ne near-ter erm appl applicabi cability

Some e appl applicat cations

• ns / ot
• ther

er res resul ults

• Speedin

ing up gradie ient t co computa tatio tion usin ing quantu tum compute ters with with applic icatio tions to to variatio tional cir ircuits its and quantu tum neural netw tworks.

Some e appl applicat cations

• ns / ot
• ther

er res resul ults

• Speedin

ing up gradie ient t co computa tatio tion usin ing quantu tum compute ters with with applic icatio tions to to variatio tional cir ircuits its and quantu tum neural netw tworks.

• Speedin

ing up Lin inear Programs, , Semidefin finite ite Programs, , and general l co convex opti timiz izatio tion problems s + fin findin ing lim limita itati tions s on quantu tum s speed-ups. s.

Some e appl applicat cations

• ns / ot
• ther

er res resul ults

• Speedin

ing up gradie ient t co computa tatio tion usin ing quantu tum compute ters with with applic icatio tions to to variatio tional cir ircuits its and quantu tum neural netw tworks.

• Speedin

ing up Lin inear Programs, , Semidefin finite ite Programs, , and general l co convex opti timiz izatio tion problems s + fin findin ing lim limita itati tions s on quantu tum s speed-ups. s.

• Effi

ficie iently tly wo working with th th the lo lowest- t-energy sta tate tes of f some str tructu tured H Hamil ilto tonia ians ( s (quantu tum m mechanical s l syste stems)

Some e appl applicat cations

• ns / ot
• ther

er res resul ults

• Speedin

ing up gradie ient t co computa tatio tion usin ing quantu tum compute ters with with applic icatio tions to to variatio tional cir ircuits its and quantu tum neural netw tworks.

• Speedin

ing up Lin inear Programs, , Semidefin finite ite Programs, , and general l co convex opti timiz izatio tion problems s + fin findin ing lim limita itati tions s on quantu tum s speed-ups. s.

• Effi

ficie iently tly wo working with th th the lo lowest- t-energy sta tate tes of f some str tructu tured H Hamil ilto tonia ians ( s (quantu tum m mechanical s l syste stems).

• Using quantu

tum machin ine le learning ideas s to to speed up classic ical machin ine le learnin ing ta tasks.

I woul

• uld

d like e to

• thank

hank my my wonderf

• nderful

ul co-aut

• -author

hors. s. Especi pecial ally, my my PhD hD adv advisor

• r Rona

nald d de de Wolf, for

• r int

ntroduc roducing ng me me to

• thes

hese e fasc ascina nating ng topi

• pics

cs and and gui guidi ding ng me me throughout hroughout my my PhD PhD years ears.

* sourc source e of

• f images

ages:

• Pi

Pint nter erest est

• Goo
• ogle
• IBM

BM / digi gital altrends. ends.com

• m
• Wikiped

edia