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

«Demonstration of a small programmable quantum computer» Philip Rhyner, Colin Kälin 14.05.2018

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

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

Source: Jonathan Home, ETH Zürich 4

<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

Initialization e, 0i <latexit sha1_base64="btrayavfvdxzezdwdipovyudldi=">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</latexit> e, 1i <latexit sha1_base64="/nozfh/ki+mtrk0j8h/tahofv7c=">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</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=">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</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=">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</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

<latexit sha1_base64="fimujy6qkhbxcfopc9gxr0+wipe=">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</latexit> <latexit sha1_base64="qo/ndqjxa+xbqk0vi7baeotuieq=">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</latexit> <latexit sha1_base64="qo/ndqjxa+xbqk0vi7baeotuieq=">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</latexit> <latexit sha1_base64="bept0lii4mmr9zbr6w1/s34z8p8=">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</latexit> <latexit sha1_base64="fimujy6qkhbxcfopc9gxr0+wipe=">aaadlnicjvllssraekyn7/wnry9betwtirc9ii8euvzwvvcrji7rsnkkjlocij/g1e/xqzx7ez/bgzw9uvdxmctsd9d0v9dmosxixrjpe6w4pb19/qodq9xhkero2pjeyh6rdvjinai0tvpdmchurbpvmnre6jdlvdaoy3uqtlbt+cglygudjnvmklmn7acz6hmdbyzq/xri1qt5stzvjl86syhxolmzwjhokcjcb20ojdd0ywqo+ducdw8zsrpcemvpatlxuewvtr1mkwyerfv8bzi6ktgeseuspdpil5g7z6wloe4nyqyzbbsq+gxtk/e1ym0fo9wis1v4rruscugyt4kbxddjr8p2mfmu5t+virugjbuzu3urgmwj4mkhtzpco+klv76pwtmw5f00mznb7itfh4rwejita8mji3xjbjijlphserho8c72e70zupj2z7sbwcussclo9ee0vqpv88/bcrd8r2p03dlfqplezd/1mihpzgce47oizwyitpkrxdzh3nlwnpzn7ga6lxisj/fpos9vvu6jmw==</latexit> <latexit sha1_base64="yv9cgkjcbfsvjf22phxymknhyw4=">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</latexit> <latexit sha1_base64="yv9cgkjcbfsvjf22phxymknhyw4=">aaadohicjvjnt9taeh0xtcray0epxcwquk+r3us5ohyqjeqvjekqakk22asr+ev2bgkifksv8hv4efwgblwphhg7muiawthomznvzt7mjifmy10az7uporot795p1rvtm7mfps7nl8zul9mwifq7yuksoaidusu6vw2jtawo8kifsrirtjj4bv2du1wuokv3zfmujpkgn+qejgjdqhm4ugbkxxzpr3hnt477uverzqxvawultu84xakyrbgiguikqz1ggjk/lnx4yikdyussokbfr3cbaeyogauyerad8l9pq1uhkw3lwup2xcoxb8fmf6u8p4qxzlstqqixlhe854l1/1lhjmy2wzpkkiwnydwhbvclea9ljlxkqy9vyqzzyubbmxkc902qbufc/otrjpboaul/52pqw5rmrtmyf8rolhrsaioegthapc42jbjpjldsu6nhos232o/1wodk7e4oa5fkwnkk0fzfunoebt9vfc03y3++ry+v/s9n32v6ux7qwmiypnn9vmidw2ixtuv+g5e4cq6dw+fpeaedwrwmi3hynl/3obknkw==</latexit> <latexit sha1_base64="ab+3gozwpbt4ehrjt1hry32/k0e=">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</latexit> <latexit sha1_base64="fimujy6qkhbxcfopc9gxr0+wipe=">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</latexit> <latexit sha1_base64="yv9cgkjcbfsvjf22phxymknhyw4=">aaadohicjvjnt9taeh0xtcray0epxcwquk+r3us5ohyqjeqvjekqakk22asr+ev2bgkifksv8hv4efwgblwphhg7muiawthomznvzt7mjifmy10az7uporot795p1rvtm7mfps7nl8zul9mwifq7yuksoaidusu6vw2jtawo8kifsrirtjj4bv2du1wuokv3zfmujpkgn+qejgjdqhm4ugbkxxzpr3hnt477uverzqxvawultu84xakyrbgiguikqz1ggjk/lnx4yikdyussokbfr3cbaeyogauyerad8l9pq1uhkw3lwup2xcoxb8fmf6u8p4qxzlstqqixlhe854l1/1lhjmy2wzpkkiwnydwhbvclea9ljlxkqy9vyqzzyubbmxkc902qbufc/otrjpboaul/52pqw5rmrtmyf8rolhrsaioegthapc42jbjpjldsu6nhos232o/1wodk7e4oa5fkwnkk0fzfunoebt9vfc03y3++ry+v/s9n32v6ux7qwmiypnn9vmidw2ixtuv+g5e4cq6dw+fpeaedwrwmi3hynl/3obknkw==</latexit> <latexit sha1_base64="yv9cgkjcbfsvjf22phxymknhyw4=">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</latexit> <latexit sha1_base64="ab+3gozwpbt4ehrjt1hry32/k0e=">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</latexit> <latexit sha1_base64="mgpou/vq1lftgtvgs0ydxngi6gy=">aaadq3icjvjdsxtbfd3zwmtiq6y+9muxcd6f3sloo9gpcqulgkkelbk7jnhizneznqg25ef0tf09/gh/q99kh1vomeum0izwj0zuvwfopffo3ymlvjc2cg5q3oofh4upluqn5cdpvlbxmk97zt42ieomezqbozgqvaoz1bxapuqomcoaxanqx8mx7rx/quyp8+zqxhxqdbqnmn2uk8gs6p8mlz2y6ye1vtaozpnztlg5lvsrkzdr6zjbgxikggmehqywfooijx/hcbggihakctfdt8u5whqn5o7jumrerif8hza6rtcmsdmsjtthlztbmnphjvdruyzjdluv/zl2b/dhwqb/rdarzdfhfw1mxboovinucuhgxzmjijnr5t6zmtumgcsyb/p2bxkrii/3vj0vhu0v++98lm6xk3przbacuiklvzt6yrndbcgnpl4jc0cnwojlqegjy7u47zvt8gv2z7srwcuqwaxo+je0rkfxzz1vy5cv/v2o5p3e83yytmod7dbefvxglvamg9jio9rbht6gw35dlu/4jc/etffv++z9v6v6tspnhx8s7+cvokwpgw==</latexit> <latexit sha1_base64="mgpou/vq1lftgtvgs0ydxngi6gy=">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</latexit> <latexit sha1_base64="mgpou/vq1lftgtvgs0ydxngi6gy=">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</latexit> <latexit sha1_base64="mgpou/vq1lftgtvgs0ydxngi6gy=">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</latexit> <latexit sha1_base64="49ywbgrlvnbmcwzazrksexogqq4=">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</latexit> <latexit sha1_base64="49ywbgrlvnbmcwzazrksexogqq4=">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</latexit> <latexit sha1_base64="49ywbgrlvnbmcwzazrksexogqq4=">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</latexit> <latexit sha1_base64="fimujy6qkhbxcfopc9gxr0+wipe=">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</latexit> <latexit sha1_base64="i92sxl4gafb3grhsuyiizfpzwec=">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</latexit> <latexit sha1_base64="i92sxl4gafb3grhsuyiizfpzwec=">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</latexit> <latexit sha1_base64="joeef1dgptm9xw5zfwqbo6u6sqs=">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</latexit> <latexit sha1_base64="49ywbgrlvnbmcwzazrksexogqq4=">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</latexit> <latexit sha1_base64="49ywbgrlvnbmcwzazrksexogqq4=">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</latexit> <latexit sha1_base64="49ywbgrlvnbmcwzazrksexogqq4=">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</latexit> <latexit sha1_base64="49ywbgrlvnbmcwzazrksexogqq4=">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</latexit> <latexit sha1_base64="49ywbgrlvnbmcwzazrksexogqq4=">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</latexit> <latexit sha1_base64="49ywbgrlvnbmcwzazrksexogqq4=">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</latexit> Measurement Use optical shelving technique ri <latexit sha1_base64="mgpou/vq1lftgtvgs0ydxngi6gy=">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</latexit> <latexit sha1_base64="mgpou/vq1lftgtvgs0ydxngi6gy=">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</latexit> <latexit sha1_base64="mgpou/vq1lftgtvgs0ydxngi6gy=">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</latexit> <latexit 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

Readout/Rabi oscillations 9

<latexit sha1_base64="7ahu2awpnov50pbg3yuelst81xk=">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</latexit> <latexit sha1_base64="7ahu2awpnov50pbg3yuelst81xk=">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</latexit> <latexit sha1_base64="7ahu2awpnov50pbg3yuelst81xk=">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</latexit> <latexit sha1_base64="7ahu2awpnov50pbg3yuelst81xk=">aaael3icjvjltxrbek5hfaa+wotopepgzng4msekciehigytutfxwrigjj2zvunnnunphebkrvp7/dxgi/hq0bshq4tzdmuhvemtqq+/7+vqng6krjbact5zm/avq9euz87n37h56/zca/hobpmpvsj6yz7kai/gpuhkjvpa6ktsfurwnejeiiifmpxbsvclzlm3+rqqbympmjmsidci+a1vpb+sma7zovo2rki580rrygtxkm+yn2rcqfykzl4s9k+afyg+rxj4b/24amgkpq9ioqmmmbej3ffgioev9yovefdd1iqrhw/qarxxnrqx7fszcxfyyu7sb6th3tdw/w2ml80ovw7yzz6s0zfe9lttp+vqybctt0na0iydfnfaag+gkemiy0hbqaya8wq4lpjbbxcckba7gaoxhzmkdqe1zkn2jcybdi5ojp8rvvsnmmftpetsh7hlglohksf9nm/imuc22vvgxml8jvmtydffd6ji2xr4ijfaxzlyfig4hink/e+znsxjl5drbtghx1og80y3schzqhi8xnnp8pgyzf+8hw0jwkn7kcgscde3fp53tiurcrgyvhg8jwaehghvx7qhgz6exxyviqojuxti5bqfuwsno+lfytq9mn4uevp8we7v7+hisrvsdz2u+3q1vbhzvlfzuav3oipv6dfsqa92sn/qgli19c56b3+wp9qf7s9n1bmr0szb1lc//gb7xai4</latexit> <latexit sha1_base64="tlwwlwahiling5jwi15hmfvwid0=">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</latexit> <latexit sha1_base64="tlwwlwahiling5jwi15hmfvwid0=">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</latexit> <latexit sha1_base64="tlwwlwahiling5jwi15hmfvwid0=">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</latexit> <latexit sha1_base64="tlwwlwahiling5jwi15hmfvwid0=">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</latexit> <latexit sha1_base64="hhk6molkcgnw6cgnm2bto4fea0e=">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</latexit> <latexit sha1_base64="hhk6molkcgnw6cgnm2bto4fea0e=">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</latexit> <latexit sha1_base64="hhk6molkcgnw6cgnm2bto4fea0e=">aaadrhicjvjdsxtbfd3z2qrr1lgf+7iybj/cbim0j5j+ighfwwharwy3yzpks7vstgqr/ro+6u/xp/gffjo+ffhmzsq00tyjk3vvmxppvtn7ozwxpq2cq5r3bol5i8mp6frm7mtxc4351ztlnipi3ymzjcu6ksp1ylldscymupsxwg2jro9gg4/ufpdyf6xj0m17kuudoeqn5sjeyhlq7vd0ytxh+mgjgbqcwf5jj6ycjqq1mc3xfrcphjleggeijrswfgkfkr89haiqezvakbgcnpfzjr+om3delizder3wv89or0jtxk6zloyyvrlugpk+lri/igjetquq6ze0v7i/c9b/a4vtuxydntbgvjwwxa/elb6r8b/mycw87+upmre7viw1meo8tibrgvjy4o2s6bh66t/fx+iih+rddjm5io7f4oeopvgkidaqex+fhdmnritxsdtw0efd3pe6v/dl7xq0sqwwlbrsdp0xtk5h188tb8vjcv+co8fozttwgltcrxfnlxy1y1n4g0usc47eywwr2gs/bn7oci4l79k79m68n2oqv6tyfvdb8m7van7kqsw=</latexit> <latexit sha1_base64="hhk6molkcgnw6cgnm2bto4fea0e=">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</latexit> <latexit sha1_base64="nqq7cb7apn1skzpkwntzrexbn7u=">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</latexit> <latexit sha1_base64="nqq7cb7apn1skzpkwntzrexbn7u=">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</latexit> <latexit 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

<latexit sha1_base64="6znxng4c9v2ivqm8+y0agyzhoso=">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</latexit> <latexit sha1_base64="6znxng4c9v2ivqm8+y0agyzhoso=">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</latexit> <latexit sha1_base64="6znxng4c9v2ivqm8+y0agyzhoso=">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</latexit> <latexit sha1_base64="6znxng4c9v2ivqm8+y0agyzhoso=">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</latexit> <latexit sha1_base64="lcfidcj3kwuqhuinif6t2y1lpki=">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</latexit> <latexit sha1_base64="lcfidcj3kwuqhuinif6t2y1lpki=">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</latexit> <latexit sha1_base64="lcfidcj3kwuqhuinif6t2y1lpki=">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</latexit> <latexit sha1_base64="lcfidcj3kwuqhuinif6t2y1lpki=">aaadgxicjvjntxrbeh3lykecixy9tnyywguzq0w04ujajynrymiccutiz2wzdhz2ztltc8enp8hf41x+iwdff4ngcujveqv61atx1t2vvlmpxrrdtaacr9mzs3pzc4+flc49bs8/26vlsu11ly3z0h4kqta5kxtpgzfrg8pqnupyvz8mt318/0zb2ptfrruo9nfizyu5malyhi7b2/2hdpp+odwvllxlefjhvqz71msnrshv5h23o1e3khxedulg6abzo+vyawv9dfaixrgjabrw9hmo1pwdikaeitgrjsqspsnxjussmhdmlizder3yp+ppseelnr1mldkpq+tclpkhxnk/f8webf9v069pf3j/fsy7s8jelh2hf7qjfedf8rnxh1my7sscncybxh6smbbdxbmm8zpvs5cpgot4zns50th0iv++j8mj3si7gdirqfylpb87esuijtausih3wsyokcj5tgqe6peu/nvdkitydgnajvalsteo+v4tre/r9/pa23ky4n/n6lazt96no2785vvnc6uzstk8xwusco5eyxmfsmn+u3zdd/zavraea0eurf9tp1pnzgr+wshgl16nvva=</latexit> <latexit sha1_base64="syagluwjszot9yr9cyn1d54sqlw=">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</latexit> <latexit sha1_base64="syagluwjszot9yr9cyn1d54sqlw=">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</latexit> <latexit sha1_base64="syagluwjszot9yr9cyn1d54sqlw=">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</latexit> <latexit sha1_base64="syagluwjszot9yr9cyn1d54sqlw=">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</latexit> <latexit sha1_base64="1hmmz8w3oadnpxkkzy9zo0f2mas=">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</latexit> <latexit sha1_base64="1hmmz8w3oadnpxkkzy9zo0f2mas=">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</latexit> <latexit sha1_base64="1hmmz8w3oadnpxkkzy9zo0f2mas=">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</latexit> <latexit sha1_base64="1hmmz8w3oadnpxkkzy9zo0f2mas=">aaadi3icjvjdt9rafd1l/qauxetrl8anis9uwjhrgb8icdexgexcikfipt2ho9lu20xnl8cgx+wv4rx/hg+e3i0mslbmm3vvpffcc+9mjy4zu7kgugjnexfu3rs/v7d44ohso8ft5se7vtg2ie4lrvby/vhvojo57jnjmr1fwq1gcab34ufgnd+bafuziv/qtkt9ofjpbo5nohyho/z2nnrugo1lzw1x4kf94iqx99yprekhbobrb9oxjpooww4mmzfvhlu7qteq5v93wsbpofk7xxjrbrh6kjbgjbe0cjj6grqq/g4qikbj7bbtypaekbzgorzzoyzlk6gidvmfmjpo0jxxrvljdciugbdlpy/n3fuigjndd9x0k9qf3gecptd2mipypeepbuzfbvhcju4wion/laogetxlbspjtqgyazjndeucfblex2eezomoozf/834cjvfw7swqwqps31jye6ipzfhiq8n42brmso1y4on08nhjwervdaxgy931azvylsp5o1jpb2nrget5bnlavqzw73d03dl91q2dbvjldwdtvxlj83ikz3jbd/qga/iihc6b4dsucikf3pk36r3z3s+oc62mzgv/lg/zf3xewwu=</latexit> <latexit sha1_base64="oh2p5v8pay7hqnqwr1j1aknsfew=">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</latexit> <latexit sha1_base64="oh2p5v8pay7hqnqwr1j1aknsfew=">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</latexit> <latexit sha1_base64="oh2p5v8pay7hqnqwr1j1aknsfew=">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</latexit> <latexit sha1_base64="oh2p5v8pay7hqnqwr1j1aknsfew=">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</latexit> Two qubit gates E = e 2 e 2 p r2 + 2 ' = Et ~ r = e2 2 t 2~r 3 (e )2 2r 3 Optical dipole forces ##i! ##i Resulting displacement #"i! e i' #"i "#i! e i' "#i ""i! ""i 11

<latexit sha1_base64="gzwjb5ynggzbxowpur1z75tqxzg=">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</latexit> <latexit sha1_base64="gzwjb5ynggzbxowpur1z75tqxzg=">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</latexit> <latexit sha1_base64="gzwjb5ynggzbxowpur1z75tqxzg=">aaaelhicjvjnb9naeb3xflthk6vhlhyrqbyi7aojlkhvcwgjfrwpaspvver1tu4se23zm6ptlbp8hn4nf4s4cuwv4mdbqruvjka32szsm/fezq5xfkmqjo9/c+bca9dv3jxfany6fefuvebi/e0qh5ax7mr5mpddevuyvvp2jdkp7baljdkryh0xwlf1nunzvirxw+a4khtzlgi1r+liaoo1t7vd5ta+ul2r+jh+8jiumlf6jllilopo3ajjvlpq9x57fj2fqrbs+mitdbu+h8plzuyynzkozpvnuphwmm2dndvdbueodx9yof6z5bd9ht50etrji+qxms86sxrsn3kkaugzsdjkkkcuuyxflgxkuwfsj0basmsk65lg1ib2cjyeiwi6wh+c1w6naqytz8xqglukmcwuhj3cfmooamy7q0reif7cpges+esoi3a2hr4jcjgusomgcemhypxpmdxm816uohtommjagnmmw2pkhsmevcfpdpsozpqf92non17wvsgwc0bsjcwtjl6hugibcmwj18xm4cf4fch7entbwez3onfw+o76ibfhys66drt9l4i2r9vpfu+llxvcfkftyfzko/dbwydnrdw1+o3n0wn6smt4r89pld7sjvqnns3nxpnkfha/uf/d7+6pm+qcu2uw6i/h/vwnkbxxoq==</latexit> <latexit sha1_base64="gzwjb5ynggzbxowpur1z75tqxzg=">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</latexit> <latexit sha1_base64="wmpj0oyqlti7i9vdu/s+6deybxa=">aaadd3icjvjdaxnbfd3j+thwr9q++ubiunihw24rbb+euj8qrklg2kcshtntddtkv9jdbgvib/hx+krp/htbb8/cbkutaidm7r1nzj33zt0j8tiuled9btsds5evxf1axrl2/cbnw63v23tlni1c3quzocv6gsp1bfldq0wv635eajuesd4pjk/t+f5mf6xj0nfvsa5hiypsc2rcvreat7b6/cfwpor82izcj64+md807ra0ualg7w/mhx998wu4sb6o2ytxq+11pvnuecevntbqtzutntywxceyhjgiguakin4mhzk/axx4yimnmcdw0dnyrrhacnonzgkyfnej/ynggxpngvvnurjdvom5c2a6um/9qhqdsm1vtb+k/c79qbdorxxmomw7pkenqlgsiq+jvzgm43+zsc086+uimqe7viw1mad5o4k8estfg96ueh1dl/3nfcocyvpmysjmbbetc3929iwnbbgjnlh4lsyigohem6nhose72o91pudk7a5plvgtkmmtapsvag2ptp8l3pyvy//zhz139ja6vtf13z5qb+/ub2wjd3aphb6jx9jgs+yy3xaf8qmf8ax5zbnrpha6p9rmo85zw2/l8x8aoca4tq==</latexit> <latexit sha1_base64="wmpj0oyqlti7i9vdu/s+6deybxa=">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</latexit> <latexit sha1_base64="wmpj0oyqlti7i9vdu/s+6deybxa=">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</latexit> <latexit sha1_base64="fimujy6qkhbxcfopc9gxr0+wipe=">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</latexit> <latexit sha1_base64="6+h/avhouhh0hme5aubkcpthrcs=">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</latexit> <latexit sha1_base64="6+h/avhouhh0hme5aubkcpthrcs=">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</latexit> <latexit sha1_base64="of3/1t8frjhvo7h9h2dty7v69iy=">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</latexit> <latexit sha1_base64="wmpj0oyqlti7i9vdu/s+6deybxa=">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</latexit> <latexit sha1_base64="wmpj0oyqlti7i9vdu/s+6deybxa=">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</latexit> <latexit sha1_base64="wmpj0oyqlti7i9vdu/s+6deybxa=">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</latexit> <latexit sha1_base64="wmpj0oyqlti7i9vdu/s+6deybxa=">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</latexit> <latexit sha1_base64="wmpj0oyqlti7i9vdu/s+6deybxa=">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</latexit> <latexit sha1_base64="wmpj0oyqlti7i9vdu/s+6deybxa=">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</latexit> Two qubit gates Ising (XX) gate XX( ij )= 2 6 4 3 cos( ij ) 0 0 i sin( ij ) 0 cos( ij ) i sin( ij ) 0 7 0 i sin( ij ) cos( ij ) 0 5 i sin( ij ) 0 0 cos( ij ) XX['] =e i (1) x (2) x ' 12

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

Hardware Setup 14

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

Deutsch-Jozsa Algorithm 16

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) 250 450 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

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

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

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