«Demonstration of a small programmable quantum computer with atomic qubits» Philip Rhyner, Colin Kälin

Transcription

1 «Demonstration of a small programmable quantum computer» Philip Rhyner, Colin Kälin

2 Introduction PART 1: Trapped ion quantum computers Ion trap States, Initialization and Measurement One- and Two-qubit gates PART 2: Deutsch Jozsa algorithm: Hardware setup Deutsch-Jozsa algorithm (Bernstein-Vazirani algorithm) Conclusions 2

3 Ion trap Paul trap invented by Wolfgang Paul (Nobel prize 1989) Earnshaw s theorem 4 blades for confinement, Lasers for interaction (reading qubits, cooling, gates) Source: Universität Innsbruck, Quantum Optics Theory Group Use e.g. a CCD camera to take an image 3

4 Source: Jonathan Home, ETH Zürich 4

5 <latexit sha1_base64="t705wrnd3q5xmlz/rxmqmqqtcqw=">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</latexit> <latexit sha1_base64="t705wrnd3q5xmlz/rxmqmqqtcqw=">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</latexit> <latexit sha1_base64="t705wrnd3q5xmlz/rxmqmqqtcqw=">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</latexit> <latexit sha1_base64="t705wrnd3q5xmlz/rxmqmqqtcqw=">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</latexit> States Hilbert space: Electronic states of the ion and normal modes of the chain First approximation: harmonic trap Long decoherence times possible (seconds) <latexit sha1_base64="asvdzadbbek1ekmvsevxkewyafo=">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</latexit> = Rabi frequency = decay rate Source: R. Blatt et al., Entangledstates oftrapped atomic ions 5

6 Initialization e, 0i <latexit sha1_base64="btrayavfvdxzezdwdipovyudldi=">aaadrxicjvjdsxtbfd3zfmjsl9hhviwnht6usfse+yh+iuhlbbntvmruzoxdnrvl7isgwv/rv/09/q39eb6vphx0zhvtqke2eyb3zplzz5yzvwew68j43o+k8+jxk6dz89wfz89fvhy1wftqf+kwj1qrsum074rbowkdqjbrjladlffbiizvqdjfspshi5uxok32zvmmjgdbl9enogomos9hfwxg6r138xwx7ju8ge504pdjhevoprxkmo7qryoiqwygkmawjxgg4o8qpjxkxi4xjpyz07kvcief1g7jumqerpv873f1wkij11azkoqip8scostdvoxcfswqbhuqyl4w/uy8f6z3zxpgomwdnjggvkyk4ifibqdk/k9yudinxmapdokw4fqreve3lsiuic4+83zgddsz5mh3mtjbr3kxtwymih2x6i+jte7kxpqy42jlmd1qhlieyrkuwryl/v4tbvferssysfsikpsk1n/oad1apzpelp3l3++j6at9oef7dx9vpb62xvbypf7jdd6xj1axhh006tei42+4xjxz3bl2fjq/7qhopaxzxl/dubkf1vkpfg==</latexit> e, 1i <latexit sha1_base64="/nozfh/ki+mtrk0j8h/tahofv7c=">aaadrxicjvjdsxtbfd1zrtw29am++riycn0oybci+ij2a6fyipjekosyu45xygz32z0invgrfk2/x9/gj+ib+ftqm9enykwteyb3zplzz5yzvwew68j43mxfmzp+nvn8tjr34uwr+yxfpdetih3lkwpgazzm+2fqqfgnqmm0idv+lqtggmaqhq4+2p32scolnsz75irtvwhqt/shjgjd6ft3omxyvfnpvy/wvlonw32c+gvsqzka6vjlgv0cieweeyzqsgcyxwhq8nebdw8zsr7gxhjmwvyvtjhh2hfzioya6id/fa46jzpwbtulqy54ssyzs9lfg87pohisbu9vzavg35w/bov/9ysxkfuhj4whfauiuepc4iim/1uos+bey1mqqzomufzk3tvtcfjfebdfetsjoppz8s/3mtjehryljjmtxl5ydo/oi3dyygpzcffjmh1qhli+ljncnhkx+70mcq683qfjifgjsliqwv85o/vo/tzxtuws/88+epy03td9r+7vrtu2t8oem8ukvvgwfbsotwyjqb8rhz/hj86dc+exc+vc31gdslmzjafdubkf2cypfw==</latexit> e, 2i <latexit sha1_base64="b/eycdeucaucge2uynaxjvdtrjw=">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</latexit> e, 3i e, 4i <latexit sha1_base64="nc9ono/yuskg06btysvwx94afuy=">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</latexit> <latexit sha1_base64="yd6jqfq5+14ojscuz3bl/truj+8=">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</latexit> Doppler cooling Using a slightly red-detuned laser Then use Doppler effect Sideband cooling E.g. laser with frequency s.t. 6 1i ) (here ei = <latexit sha1_base64="z6zaaockd9pl4tjiileoiaupok8=">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</latexit> g, 3i! e, 2i <latexit sha1_base64="ufzpgbqmmxkg5cueojnxgrc6at8=">aaadxxicjvjntxrbeh27awqismdbgwcmbkw8km0mmuir4edmjaytf0hyqnqgzujs7mykpxcdmz36a7zqj/hkh/hg62iwualsm96qfvxqvxvpjvvuahdf31rtygb21u25+yu7i3exljsrq7t1obap7qdlxtr9rnu6n4xuo+nyvv9zruzjrves4xmf3zvttjzl8cgdv/pwpllcnjhuoujhnfxbultjtvf4gg6syu6dsrb8gaqqnzanr51u1itkhdeduhg6anzoudjawwdhkjfijbe0cjj6orrq/g4qi0jf7batypaekbjgfavmhzolyvbeh/zpedpo0ijnr1lldsoqobdlzoih3k9emshbv9x0a9of3beczx+tmbfl3+e5bulfevf8s9zhliz/zy4a5luvn8lm2khiwzn5mbctybtbqrzj7zzoghrfp9/h4qtp5f0mmzug/sxsxx29ymqsg0okxethztri5hwmnul0erf/va4uqnm7y1olvotk0sj6/i2t79h3c8pbcrlip+fouro72yujxvz+sxdru5mxodzhazzihd3ffl5jh/2m+itp+ikv7e/bblaylf1s260mzw2/redet4ncrtq=</latexit> g, 3i g, 2i g, 1i <latexit sha1_base64="dwhhikeqs4mrm3w5svsevnrdrn8=">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</latexit> g, 0i <latexit sha1_base64="7j5zet+nhgg7cz7s/pqovg+ik9g=">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</latexit> <latexit sha1_base64="vp+zofywscjnrxxb3xwfoqlrna0=">aaadrxicjvjds9xafd0brz+trvros+gi+cblioi+il8irbhq9qovksqxdptnqjir6okv8lx9pf6g/gjfpe8fe+yabzvaz5m9d86ce+bm5iz5okvjeb9qtl//h4hboegr0y+fxsbre5o7zdytitwksiqr9sogvilovctok6j9vfbbj0zuxthetft756oodzz+mxe5ou4ecappdrqyqgdhbwv68dz81fd6w2t6mtzxiv8ldvrjj5uoteeij8gqoysoffiy5gkclpwdwoehnngxesqkzlr2fa4wwtouwyqmggib/zfxhxwacm01s6moeercwbdsxqznhiigznttffos8q/npwdxp0/oibj1emeyunfyfleig5yr8b/ktsv89pkeypaoa64vmq91k4j8ectfnm9nreczs998h4ntlmm7adjzqeylru+o1rhtegvljot1ycbucgv9lme4apeu9ns9krjydiemguqlkmmlap0xjnaj9fpo27kz/jd99drznw/6xtp/utbyxql6bajt+ixz9teilrgjhfqn6pgap/dtuxfuntvn9wpvqvu1u3g2npu/4l6pgg==</latexit> <latexit sha1_base64="6f9mpk6xfjsnpdivjcs9tkoc8ww=">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</latexit> Source: Nielsen, Chuang, Quantum Computation and Quantum Information g, 4i <latexit sha1_base64="pjcdsyaerbqz4brs2gfyvgfcm2u=">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</latexit> decays to g, 1i, g, 2i, g, 3i <latexit sha1_base64="s55hkxep8tgb3beyfopg4gfzvgc=">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</latexit> After some time in g, 0i <latexit sha1_base64="7j5zet+nhgg7cz7s/pqovg+ik9g=">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</latexit> 6

7 <latexit sha1_base64="fimujy6qkhbxcfopc9gxr0+wipe=">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</latexit> <latexit 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sha1_base64="qo/ndqjxa+xbqk0vi7baeotuieq=">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</latexit> <latexit 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sha1_base64="ufzpgbqmmxkg5cueojnxgrc6at8=">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</latexit> <latexit sha1_base64="ufzpgbqmmxkg5cueojnxgrc6at8=">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</latexit> <latexit sha1_base64="ufzpgbqmmxkg5cueojnxgrc6at8=">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</latexit> <latexit sha1_base64="ufzpgbqmmxkg5cueojnxgrc6at8=">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</latexit> Initialization Doppler cooling Using a slightly red-detuned laser Then use Doppler effect to loose momentum 171 Yb + Sideband cooling E.g. laser with frequency s.t. decays to g, 3i! e, 2i g, 1i, g, 2i, g, 3i After some time in g, 0i 7

8 <latexit sha1_base64="fimujy6qkhbxcfopc9gxr0+wipe=">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</latexit> <latexit 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sha1_base64="mgpou/vq1lftgtvgs0ydxngi6gy=">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</latexit> Lifetime of 1iand is much longer than for ri 0i 171 Yb + Many scattered photons if in state 1i Adapted from: Leibfried et al., Quantum dynamics of single trapped ions 8

9 Readout/Rabi oscillations 9

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sha1_base64="nqq7cb7apn1skzpkwntzrexbn7u=">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</latexit> <latexit sha1_base64="nqq7cb7apn1skzpkwntzrexbn7u=">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</latexit> Single qubit gates Use two far-detuned lasers Hamiltonian with Rabi frequencies 1, 2 and detuning L of the beatnote from the g! e transition: 1 2 H int = # #i h# + " "i h" + "i h# e i(k Lr 4 Lt) + H.c. Source: C. Monroe Rabi oscillation of the Raman transition 10

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13 Two qubit gates Adapted from: Debnath et al., Demonstration of a small programmable quantum computer 13

14 Hardware Setup 14

15 Deutsch-Jozsa Algorithm Determine if an oracle is balanced or constant 3 input qbits, 1 function register and 1 ancilla => 5 qubits Implement the oracle as a series of three CNOT gates acting on the function register 15

16 Deutsch-Jozsa Algorithm 16

17 17

18 18

19 Conclusions Superconducting Qubits Ion traps Readout fidelities 96 % 99 % (depends on state) Gate fidelities (single qubit, 2- qubit) 99.7 % and 96.5 % 99.1(5) % and 97(1) % Coherence times ~60 "# 0.5 s Gate times (single qubit) 130 ns 20 μs Gate times (2-qubit) ns 250 μs Industry Well-established Non-existing Scalability Better Worse Complexity Better Worse Source: Linke et al., Experimental comparison of two quantum computing architectures 19

20 Bernstein Vazirani Algorithm Evaluate the value of c with a single try: C is implemented as CNOTs acting on the ancilla qubit X 5 21

21 !! = 0! + 1! 2! 0! 1! 2!! = 0! + ( 1)!! 1! 2! 0! 1! 2!! = 0!!! + 1!!!!!! 0! =! 0! 22

22 The correct outcome c is obtained with a probability of 0.903(2) 23