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

The he fut uture ure of of comput omputing: ng: Quant uantum um Andrá ndrás s Gil Gilyén yén PhD PhD: Postdoc: Postdoc:

The he fut uture ure of of comput omputing: ng: Quant uantum um -Our -Our wor orld 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 ompu putat tations. ions.

Quant uantum um ef effect ects for or com omput 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 ously (with sly (with some some ampl amplitud itudes) es) -Int -Interferen rference: ce: co computatio mputations ns in in sup superp erpositio osition n can can co coll llect ectivel vely y co contrib ntribut ute to to the fin the final resu al result lt -Entangle -Entan glemen ment: : qu qubi bits s can can ha have ve st strong onger er than an cl classica assical corre l correlatio lations ns

Quant uantum um supr suprema emacy Quantum supremacy -Qua -Quantum ntum compute puters rs hav ave th the e pote otenti ntial al to to solve olve -Quantum computers have the potential to solve some me pr probl oblem ems ex expo pone nentia ntially lly more ore effic ficient ently ly tha han n some problems exponentially more efficiently than clas assical com al compu puters. ters. classical computers. -Google -Goo gle jus just rep report orted ed pas passing sing th the e cros cross-ov over r -Google just reported passing the cross-over po poin int, t, wher where e a qu quant antum um chip ip can can be be muc uch fa faste ter r point, where a quantum chip can be much faster 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. in practice than the best available supercomputer.

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Boaz B Boa Barak’ rak’s a anal nalog ogy (qu (quote oted b d by Sc Scott ott Aaron ronson on) Boaz Barak’s analogy (quoted by Scott Aaronson) vs. vs. “Deep Blue vs. Deep Deep B Blue vs ue vs. . Kasparov” Kas Kasparo arov” “

Mai ain n tec echni hniques ques for or quant quantum um al algori gorithm hms -Quant uantum um Fo Four urier trans nsfor orm: Shor hor’s s al algor gorithm for or fact ctor oring, ng, br breaki aking ng RSA cr crypt ypto- o-sys system em, etc. -Ham amiltoni onian an si simul ulation: on: dynam dynamical al si simulat ation on of of quan antum um syst ystems for or chem hemist stry, mater erial sc scienc ence, e, etc. c. -Grover over 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 onal regr gres essi sion on (HHL al algo gorithm): speeding- speedi ng-up up var various ous machi hine ne lear earni ning ng appl applicat ations ons

Qua uantum um Si Singul ngular ar Val alue ue transf ansfor ormat ation on -A common on uni unificat cation on / gener general alizat ation on of of Ham amiltoni onian an si simul ulat ation, on, Grov over er sear earch and and regr egress ession on (HHL) L). -Block ock-enc encodi odings: ngs: exponent exponential ally fast aster er mat atrix oper operat ations ons -Efficient ent ci circui uits & ne near-ter erm appl applicabi cability

Some e appl applicat cations ons / ot other 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 ons / ot other 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 ons / ot other 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 ons / ot other 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 ould d like e to o thank hank my my wonderf onderful ul co-aut o-author hors. s. Especi pecial ally, my my PhD hD adv advisor or Rona nald d de de Wolf, for or int ntroduc roducing ng me me to o thes hese e fasc ascina nating ng topi opics cs and and gui guidi ding ng me me throughout hroughout my my PhD PhD years ears.

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