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Ion Trap Quantum Computer Selected Topics

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Ion Trap Quantum Computer Selected Topics Ion Trap Quantum Computer Selected Topics Ruben Andrist & Thomas Uehlinger 1 Outline Ion Traps Part I Deutsch-Josza Deutsch-Josza algorithm Problem Algorithm Implementation Part II Scalability Scalability of ion trap Problem Move ions quantum computers Microtraps Photons Charges Part III Roundup Roundup & Outlook Ruben Andrist Thomas Uehlinger 2 0:98.')4Part+8, 6: ,I39:2 .07.:09 $ " % H " !1 1# %1#% Quantum Algorithms H !1 1# %! 1#% 0"0.9743(.6:-(9 ( 5 ! ! 5 &1 ( 5 " "$1&!' 5 249(43,"6:-(9 # H !1 1# %1#%!4389,39( H !1 1# %! 1#% !,$,3.0/) ":,39:2,3,()8+8 ,+;08 9/0 7+,/9,38107 ,1907 ,8+3,(0 20,8:702039 3 W 0:98.)*# ,48.,*!74. # $4. 343/439*;99> W A0B803*C ):,3E*",3/"C*,2-7A/E0; > Implementation of the Deutsch-Josza Ion Traps algorithm using trapped ions Deutsch-Josza Problem ! show suitability of ion traps Algorithm Implementation ! relatively simple algorithm Scalability Problem ! using only one trapped ion Move ions Microtraps Photons Charges Paper: Nature 421, 48-50 (2 January 2003), doi:10.1038/nature01336; Institut für Experimentalphysik, Universität Innsbruck ! Roundup ! MIT Media Laboratory, Cambridge, Massachusetts Ruben Andrist Thomas Uehlinger 4 The two problems Ion Traps The Deutsch-Josza Problem: Deutsch-Josza ! Bob uses constant or balanced function Problem Alice has to determine which kind Algorithm ! Implementation Scalability Problem The Deutsch Problem: Move ions Bob uses a fair or forged coin Microtraps ! Photons ! Alice has to determine which kind Charges Roundup Ruben Andrist Thomas Uehlinger 5 Four different types of coins Ion Traps Deutsch-Josza Problem Algorithm Implementation Scalability Problem Move ions Microtraps Photons The third line shows addition modulo 2: Charges Roundup Ruben Andrist Thomas Uehlinger 6 Deutsch-Jozsa Algorithm I Ion Traps Deutsch-Josza Problem Algorithm Implementation Scalability Problem Move ions Microtraps Photons Charges Roundup Ruben Andrist Thomas Uehlinger 7 Deutsch-Josza Algoritm II Ion Traps Deutsch-Josza Problem Algorithm Implementation Scalability Problem Move ions Microtraps Photons Charges Roundup Ruben Andrist Thomas Uehlinger 8 Implementation using trapped ions Ion Traps Deutsch-Josza Problem Algorithm Implementation ! ion in a Linear Paul Trap Scalability ! Relabel the states of the motional degree of freedom Problem Move ions ! Doppler / Sideband cooling prepares groundstate Microtraps Photons Charges Roundup Ruben Andrist Thomas Uehlinger 9 Qubits Ion Traps Deutsch-Josza Two qubits are involved: Problem Algorithm ! electronic quantum state of the ion Implementation ! phonon number of the axial vibrational mode Scalability Problem ! states can be swapped (by a pulse sequence) Move ions Microtraps Photons Charges Roundup Ruben Andrist Thomas Uehlinger 10 Manipulation of the trapped ion Ion Traps Deutsch-Josza Problem Algorithm Implementation Resonant pulses perform single-qubit rotations Scalability ! Problem Detuned pulses perform two-qubit rotations Move ions ! Microtraps Manipulation by a sequence of pulses Photons ! Charges Roundup Ruben Andrist Thomas Uehlinger 11 Main sources of errors Ion Traps Deutsch-Josza Problem Algorithm ! phases introduced by light shifts of the Implementation Scalability lasers Problem Move ions ! system may leave the computational Microtraps Photons subspace Charges Roundup Ruben Andrist Thomas Uehlinger 12 Time evolution of the qubit Ion Traps Deutsch-Josza Problem Algorithm Implementation Scalability Problem Move ions Microtraps Photons Charges Roundup Ruben Andrist Thomas Uehlinger 13 Part II Scalability 14 Introduction Ion Traps currently: Ion Trap Quantum Computer with ~10 ions. Deutsch-Josza Problem Algorithm Implementation useful application: Scalability Problem factorization of a 200-digit numer: Move ions requires 3’500 qubits (100’000 with the Microtraps Photons implementation of error correction) Charges from I. Cirac and P. Zoller, Nature 404, 579 (2000) Roundup a) are the current approaches scalable? b)what other approaches do we need? Ruben Andrist Thomas Uehlinger 15 Scalability of linear ion traps Ion Traps elementary requirements for quantum computation have been demonstrated, Deutsch-Josza but... Problem experimental and theoretical problems limit Algorithm the scalability Implementation Scalability " ! Problem (should be o.k.) (problem) Move ions ! addressing ! control over the Microtraps interaction of the Photons ! generation of qubits Charges entangled states with many ions Roundup (H. Häffner et al., Nature 438, 639 (2005) ! error correction (J. Chiaverini et al., Nature 432, 602 (2004) Ruben Andrist Thomas Uehlinger 16 Problem Ion Traps ! with adding more and more ions the chain gets heavier but on the other hand the coupling strength Deutsch-Josza decreases as Problem Algorithm need more time for gate operations Implementation ! harder to cool all ions to the ground state Scalability Problem Move ions ions get closer to each other ! Microtraps addressing more difficult Photons Charges ! driving transitions between single modes gets more difficult (more stray excitations) Roundup ~ some 10 ions at a maximum Ruben Andrist Thomas Uehlinger ! harder to cool all ions to the ground state 17 Solutions Ion Traps General idea: use multiple ion traps with few ions Deutsch-Josza Problem + couple these traps together Algorithm Implementation Implementations: Scalability Problem " Move the atoms between traps Move ions Microtraps # Array of microtraps Photons Charges $ Coupling via photons Roundup % Coupling via image charges Ruben Andrist Thomas Uehlinger 18 progress Architecture for a large-scale ion-trap quantum computer D. Kielpinski*, C. Monroe† & D. J. Wineland‡ * Research Laboratory of Electronics and Center for Ultracold Atoms, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA † FOCUS Center and Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1120, USA ‡ Time and Frequency Division, National Institute of Standards and Technology, Boulder, Colorado 80305, USA ........................................................................................................................................................................................................................... Among the numerous types of architecture being explored for quantum computers are systems utilizing ion traps, in which quantum bits (qubits) are formed from the electronic states of trapped ions and coupled through the Coulomb interaction. Although the elementary requirements for quantum computation have been demonstrated in this system, there exist theoretical and technical obstacles to scaling up the approach to large numbers of qubits. Therefore, recent efforts have been concentrated on using quantum communication to link a number of small ion-trap quantum systems. Developing the array-based approach, we show how to achieve massively parallel gate operation in a large-scale quantum computer, based on techniques already demonstrated for manipulating small quantum registers. The use of decoherence-free subspaces significantly reduces decoherence during ion transport, and removes the requirement of clock synchronization between the interaction regions. quantum computer is a device that prepares and the Coulomb coupling necessary for entangling gates3,21. Lasers are manipulates quantum states in a controlled way, offering focused through the interaction region to drive gates. We then move significant advantages over classical computers in tasks the ions again to prepare for the next operation. such as factoring large numbers1 and searching large We can realize the trapping and transport potentials needed for databases2. The power of quantum computing derives the QCCD using a combination of radio-frequency (r.f.) and Afrom its scaling properties: as the size of these problems grows, the quasistatic electric fields. Figure 1 shows only the electrodes that resources required to solve them grow in a manageable way. Hence a support the quasistatic fields. By varying the voltages on these useful quantum computing technology must allow control of large electrodes, we confine the ions in a particular region or transport quantum systems, composed of thousands or millions of qubits. them along the local trap axis, which lies along the thin arrows in Fig. Ion Traps The first proposal for ion-trap quantum computation involved 1. Two" more Move layers of electrodes the lie aboveions and belowaround the static confining a string of ions in a single trap, using their electronic states electrodes,D. Kielpinksi, as shown C. Monroe in Fig.& D. 2.J. Wineland, Applying Nature r.f. voltage417, 709 (2002) to the outer layers as qubit logic levels, and transferring quantum information between createsthree a layer quadrupole T-junction trap: field W. thatK. Hensinger confines et al., the Appl. ions Phys. transverseLett. 88, 034101 to (2006) the ions through their mutual Coulomb interaction3. All the elementary local trap axis by means of the ponderomotive force22. This geometry requirements for quantum computation4—including efficient quan- allowsproposal: stable transport quantum-charge-coupled-deivce of the ions around ‘T’ and ‘X’ junctions, so we (QCCD) tum state preparation5–7, manipulation7–10 and read-out7,11,12—have can build complex, multiply connected trap structures. been demonstrated in this system. But manipulating a large number = ion chip Deutsch-Josza of ions in a single trap presents immense technical difficulties, and Problem scaling arguments suggest that this scheme is limited to compu-
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