Memristors go quantum

This is an accepted manuscript. ! Cite this article:! Lamata,!L.!Memristors!go!quantum.!Nat.!Photon.!(2022).!https://doi.org/10.1038/s41566-022-00975-3! INTEGRATED)OPTICS) Memristors)go)quantum) Lucas&Lamata&& A) photonic) quantum) memristor) is)experimentally) demonstrated,) paving) the) way) to) neuromorphic)quantum)computing.) Every!undergraduate!student!in!electronic!engineering!learns!about!the!basic!building!blocks! of!electric!circuits,!namely,!the!inductor,!capacitor,!and!resistor.!In!1971,!Leon!Chua!proposed! a!new!circuit!element,!complementary!to!the!previous!three:!the!memristor![1].!A!memristor! is!a!device!whose!resistance!has!memory,!i.e.!it!stores!information!about!its!past!states,!and! thus! the! name! “memristor”,! or! memory-resistor.! The! concept! of! memristor! devices! has! evolved! in! the! past! few! decades! and! has! been! extensively! studied! both! in! theory! and! experiments![2].!Memristors!are!expected!to!provide!a!new!paradigm!for!computing,!in!terms! of!physical!neural!networks!and!neuromorphic!computing.!Being!this!concept!basically!from! classical!physics,!it!was!not!until!very!recently!that!a!quantum!version!was! proposed! and! analysed.!A!quantum!memristor!is!a!device!that!exhibits!both!quantum!coherence!and,!in!its! classical!limit,!memristive!behaviour.!This!concept!was!introduced!by!Pfeiffer!et&al.![3]!and! proposals! for! implementations! with! quantum! platforms! were! subsequently! analysed,! leveraging!on!quantum!photonics![4]!and!superconducting!circuits![5].! ! Now,! writing! in! Nature& Photonics,! M.! Spagnolo! et& al.! [6]! have! experimentally! realized! a! photonic!quantum!memristor,!showing!both!its!coherent!and!memristive!behaviour.! ! The!motivation!to!introduce!this!element!is!to!elucidate!whether!one!may!harness!both!the! advantages! of! quantum! computing! and! the! memory! characteristics! of! the! memristor.! Quantum!benefits!include!much!faster!computation!via! quantum! parallelism! and! genuine! quantum! properties! such! as! entanglement,! while! the! memory! behaviour! is! a! nonlinear! feature!enabling!quantum!neuromorphic!computing!beyond!purely!unitary!evolution,!which! is! linear.! Pfeiffer! et& al.! [3]! suggested! to! attain! the! two! functions! via! a! combination! of! a! quantum! two-level! system,! weak! measurements,! and! feedback.! The! two-level! system! provides!the!quantum!behaviour,!while!the!measurement!and!feedback,!in!turn,!enable!the! nonlinear! memristive! behaviour.! Two! different! quantum! platforms! were! later! studied! for! implementing!this!idea,!namely,!superconducting!circuits![5]!and!quantum!photonics![4].!In! the! latter! case,! the! quantum! memristor! is! based! on! a! tuneable! beam! splitter,! where! the! outcome!of!one!of!the!output!ports!determines!the!reflectivity!of!the!beam!splitter!itself.!This! feedback! mechanism! provides! the! memory! and! nonlinear! behaviour,! while! the! photonic! degrees! of! freedom! provide! the! quantum! coherence.! Spagnolo! et& al.! [6]! now! implement! experimentally!an!enhanced!version!of!this!proposal!in!an!integrated!photonic!chip.! ! Quantum! photonics! is! a! widely! studied! quantum! platform,! both! theoretically! and! experimentally! [7].! Employing! photons! for! encoding! quantum! information! is! appealing! because!photons!can!propagate!to!long!distances!with!no!decoherence,!which!makes!them! well!suited!for!communication!networks.!However,!current!drawbacks!of!photonic!quantum! computing!include!difficulty!in!producing!single!photons!on!demand,!detectors!with!far!from! ideal! fidelities! and! limitations! in! achieving! nonlinear! behaviour,! as! quantum! photonics! behaves!mostly!linearly.!!The!first!two!aspects,!the!single-photon!sources!and!detectors,!are! constantly! improving,! e.g.,! with! quantum! dot! single-photon! sources! and! superconducting! detectors.! The! third! aspect,! the! nonlinear! behaviour,! united! to! coherent! properties! and! network!structure,!is!what!a!quantum!memristor!based!on!quantum!photonics!could!enable.! The!demonstration!of!a!photonic!quantum!memristor!by!Spagnolo!et&al.![6]!may!represent!a! basic! building! block! for! neuromorphic! quantum! computing.! This! may! evolve! into! a! novel! quantum! computing! paradigm,! largely! unexplored,! that! could! share! connections! and! common!speedups!with!the!field!of!quantum!machine!learning,!when!compared!to!classical! machine!learning![8,9].! ! The!authors!adapted!the!proposal!of![4]to!make!it!more!suitable!for!a!real!experiment,!and! implemented!it!on!an!integrated!quantum!photonics!chip.!The!device!consists!of!a!dual!rail! encoding! with! an! integrated! waveguide! system! connected! to! a! single! photon! source! and! detector.!The!memristive!behaviour!is!implemented,!as!envisioned!in![4],!via!a!tuneable!beam! splitter,!where!the!outcome!of!one!of!the!output!ports!is!fed!onto!the!reflectivity!of!the!beam! splitter! itself! (pictured! in! figure! 1(a)).! This! feedback! mechanism! produces! the! nonlinear! behaviour!that!may!be!employed!as!a!useful!resource!for!neuromorphic!quantum!computing.! The!tuneable!beam!splitter!is!created,!as!customary!in!integrated!waveguide!photonics,!via!a! Mach-Zehnder! interferometer! whose! arms! come! very! near! to! each! other! at! two! nearby! points,!allowing!tunnelling!and!therefore!quantum!superposition!of!the!two!paths,!as!shown! in!figure!1(b).!The!reflectivity!of!the!beam!splitter,!represented!by!the!probability!of!photon! crossing! between! different! modes,! is! tuned! by! a! thermal! phase! shifter.! The! shifter! is! controlled!externally!by!connecting!one!of!the!output!waveguides!via!an!optical!fibre!to!a! microcontroller,! which! directly! handles! the! phase! shifter,! as! shown! in! figure! 1(b).! State! preparation!and!state!tomography!are!also!included!in!the!chip,!before!and!after!the!quantum! memristor!section,!respectively.!This!allows!for!a!detailed!analysis!of!the!performance!of!the! device.!All!the!waveguides!are!fabricated!via!laser!writing!on!a!glass!substrate.! ! The! authors! also! speculate! on! possible! performance! improvement! brought! about! by! a! network!of!quantum!memristors!for!machine!learning!tasks,!such!as!an!image!classification! problem.! They! carry! out! numerical! simulations! of! a! neural! network! that! employs! purely! classical!resources,!and!compare!it!to!a!network!that!uses!just!three!quantum!memristors.! The!numerical!results!show!that!with!only!this! limited!amount!of!quantum! memristors,!a! significant!gain!in!resources!can!be!achieved.!Indeed,!about!1000!images!would!be!needed! for!training!the!network!with!the!quantum!memristors,!as!opposed!to!the!classical!case,!which! would!require!more!than!one!order!of!magnitude!more!images.!In!addition,!the!quantumbased!network!could!classify!images!with!an!accuracy!of!95%,!while!the!classical!counterpart! would!only!achieve!71%!accuracy.!Even!though!it!is!hard!to!compare!neural!networks!to!each! other,!be!it!classical!or!quantum,!these!results!point!to!a!possible!quantum!advantage!by! employing!quantum!memristors!in!machine!learning.! ! Finally,!the!authors!also!numerically!analyse!the!performance!of!a!network!involving!quantum! memristors! for! tasks! such! as! entanglement! detection.! They! show! that! the! nonlinear! behaviour!of!the!quantum!memristors!allows!one!to!detect!entanglement!with!no!human! intervention!and!in!a!highly!efficient!way.! ! The!implementation!of!a!quantum!memristor!in!a!quantum!photonics!system!opens!up!an! avenue! for! neuromorphic! quantum! computing! by! quantum! photonics! networks.! The! combination! of! quantum! coherence! (and,! therefore,! quantum! parallelism)! with! nonlinear! behaviour! provided! by! this! basic! building! block,! may! enable! a! plethora! of! applications! in! machine! learning! calculations! and! possibly! other! fields.! Even! though! it! is! usually! hard! to! rigorously!prove!a!speedup!of!a!quantum!machine!learning!device!with!respect!to!a!classical! one!(just!as!it!is!hard!to!prove!a!speedup!of!a!classical!machine!learning!system!with!respect! to!another!one),!the!field!is!worth!studying,!both!from!a!purely!fundamental!side,!and!for!the! promising!applications!in!computing!that!it!could!enable.!Challenges!for!the!future!involve,! Figure&1.& (a)& Basic& concept&of&a&quantum&memristor.&A&is&the&input& port,&while& C&and& D&are&output&ports.&The& measurement&at&port&D&is&used&to&update&the&reflectivity&R(t).&(b)&Scheme&of&the&integrated&quantum&photonic& chip&consisting&of&a&state&preparation,&a&memristor&and&a&state&tomography§ion.&The&tuneable&beamsplitter& is&implemented&in&the¢ral§ion&as&a&Mach-Zehnder&interferometer&whose&phase&in&one&arm&is&updated&by& aµcontroller&that&drives&a&thermal&phase&shifter. & from!the!theoretical!side,!to!prove!via!complexity!class!techniques!that!the!neuromorphic! quantum!computing!paradigm!indeed!outperforms!classical!machine!learning!protocols!when! scaling!the!system!up.!From!the!experimental!side,!further!improvements!in!efficiencies!of! on-demand!deterministic!single-photon!sources,!as!well!as!single-photon!detectors,!will!be! required!to!enable!the!extension!of!this!technology!to!a!network!of!many!photonic!quantum! memristors.!Should!these!challenges!be!solved,!among!the!prospects!one!may!expect!are! more! efficient! machine! learning! calculations,! as! well! as! quantum! simulations! of! open! quantum!systems.! ! References) [1]!Chua,!L.!IEEE&Transactions&on&circuit&theory!18,!507–519!(1971).! [2]!Di!Ventra,!M.,!Y.!V.!Pershin,!Y.!V.,!&!!Chua,!L.O.!Proceedings&of&the&IEEE!97,!1717!–!1724! (2009).! [3]!P.!Pfeiffer,!P.,!Egusquiza,!I.!L.,!Di!Ventra,!M.,!Sanz,!M.,!&!Solano,!E.,!Sci.&Rep.!6,!29507! (2016).! [4]!M.!Sanz,!Lamata,!L.!!&!Solano,!E.!APL&Photonics!3,!080801!(2018).! [5]!Salmilehto,!J.,!!F.!Deppe,!F.,!Di!Ventra,!M.,!Sanz,!M.,!&!Solano,!E.!Sci.&Rep.!7,!42044!(2017).! [6]!Spagnolo,!M.!et&al.,!!Nat.&Photon.,!xxx,!xxx!(2022).! [7]!O'Brien,!J.!L.,!Furusawa,!A.!&!Vučković,!J.,!Nat&Photon.!3,!687!(2009).! [8]!Lamata,!L.!Mach.&Learn.:&Sci.&Technol.!1,!033002!(2020).! [9]!Biamonte,!J.,!et&al.,!Nature!549,!195–202!(2017).! ! Author)information) Affiliations! Departamento&de&Física&Atómica,&Molecular&y&Nuclear,&Facultad&de&Física,&Universidad&de& Sevilla,&Apartado&1065,&41080&Sevilla,&Spain& Lucas!Lamata! [email protected]& ! Ethics)declarations) Competing!interests! The!author!declares!no!competing!interests.!