Physical implementations of quantum computing Andrew Daley Department of Physics and Astronomy University of Pittsburgh Overview (Review) Introduction • DiVincenzo Criteria • Characterising coherence times Survey of possible qubits and implementations • Neutral atoms • Trapped ions • Colour centres (e.g., NV-centers in diamond) • Electron spins (e.g,. quantum dots) • Superconducting qubits (charge, phase, flux) • NMR • Optical qubits • Topological qubits Back to the DiVincenzo Criteria: Requirements for the implementation of quantum computation 1. A scalable physical system with well characterized qubits 1 | i 0 | i 2. The ability to initialize the state of the qubits to a simple fiducial state, such as |000...⟩ 1 | i 0 | i 3. Long relevant decoherence times, much longer than the gate operation time 4. A “universal” set of quantum gates control target (single qubit rotations + C-Not / C-Phase / .... ) U U 5. A qubit-specific measurement capability D. P. DiVincenzo “The Physical Implementation of Quantum Computation”, Fortschritte der Physik 48, p. 771 (2000) arXiv:quant-ph/0002077 Neutral atoms Advantages: • Production of large quantum registers • Massive parallelism in gate operations • Long coherence times (>20s) Difficulties: • Gates typically slower than other implementations (~ms for collisional gates) (Rydberg gates can be somewhat faster) • Individual addressing (but recently achieved) Quantum Register with neutral atoms in an optical lattice 0 1 | | Requirements: • Long lived storage of qubits • Addressing of individual qubits • Single and two-qubit gate operations • Array of singly occupied sites • Qubits encoded in long-lived internal states (alkali atoms - electronic states, e.g., hyperfine) • Single-qubit via laser/RF field coupling • Entanglement via Rydberg gates or via controlled collisions in a spin-dependent lattice Rb: Group II Atoms 87Sr (I=9/2): Extensively developed, 1 • P1 e.g., optical clocks 3 • Degenerate gases of Yb, Ca,... P2 3 • Stable lasers, especially for clock P1 transition frequency 3 P0 689nm 1 Key properties S0 • Metastable triplet states: 3 - P0 Lifetimes >150s (Fermions) 3 - P1 linewidth ~ kHz 3 - P2 lifetime >>150s • Many nuclear spin levels for fermionic isotopes • Nuclear spin states decoupled from electronic state on clock transition Quantum Computing with Alkaline Earth Atoms 87Sr (I=9/2): 1 Implementation of Quantum Computing: P1 • Nuclear spin states for qubit storage 3 P2 (insensitive to magnetic field fluctuations) 3 P1 D. Hayes, P. S. Julienne, and I. H. Deutsch, 3 PRL 98, 070501 (2007) P0 I. Reichenbach and I. H. Deutsch, PRL 99, 123001 (2007). 689nm • Electronic state for: - Access to qubits 1 S0 - Gate operations HERE: Via state-dependent lattices A. J. Daley, M. M. Boyd, J. Ye, and P. Zoller, Phys. Rev. Lett. 101, 170504 (2008) AC Polarisability (AC-Stark Shift per intensity) for 87Sr Ye, Kimble, & Katori, Science 320, 1734 (2008). 0.2 0.4 0.6 0.8 2 3 4 2 3 to states in the long-lived P2 manifold. As shown schematically in Fig. 1, we would transfer qubit states 3 |0" and |1" to the P0 level (which can be done state- selectively in a large magnetic field due to the differ- 1 3 ential Zeeman shift of 109Hz/G between S0 and P0), and2 then selectively transfer them to additional readout 3 87 Polarizability and State-dependent lattices: levels |0x" and |1x" in the P2 level (e.g., for Sr we 3 3 to states in the long-lived P2 manifold. As showncould choose |0x"≡| P2,F =13/2,mF = −13/2" and 3 schematically in Fig. 1, we would transfer qubit states|1x"≡| P2,F =13/2,mF = −11/2", where F is the 3 total angular momentum and mF the magnetic sublevel, |0" and |1" to the P0 level (which can be done state- 3 and connect these states to the P0 level via off-resonant selectively in a large magnetic field due to the differ- 3 1 3 Raman coupling to a S1 level). The individual qubit se- ential Zeeman shift of 109Hz/G between S0 and P0), 3 lectivity can be based on a gradient magnetic field, as P2 and then selectively transfer them to additional readout 3 1 3 87 is much more sensitive to magnetic fields P0 or S0.A levels |0x" and |1x" in the P level (e.g., for Sr we2 2 gradient field of 100 G/cm will provide an energy gradient could choose |0x"≡|3P ,F =13/2,m = −13/2" and 2 3 F 3 to states in the long-lived P2 manifold. As shownof 410 MHz/cm for |0x" or an energy difference of about FIG.|1 2:x"≡ (a) Energy| P2,F level=13 diagram/2,mF showing= −11 how/2", independent where F is the schematically3P in Fig. 1, we would transfer qubit states 0 3 1 3 15kHz between atoms in neighbouring sites. In the same optical lattices can be|0 produced" and |1" to for the theP0 levelS0 (whichand canP0 belevels done state- total angular momentum and mF the magnetic sublevel,field the 3P level states will be shifted by −m × 1Hz in by finding wavelengthsselectively where the in polarisability a large3 magnetic of field each due of to th thee differ- 0 I and connect these states to the P0 level via o1ff-resonant3 ential Zeeman shift of 109Hz/G between S0 and P0neighbouring), sites, which again indicates the advantage levels is zero and the other1 non-zero.3 (b) AC Polarisability 1 Raman3 couplingand toS then a0 S selectively1 level). transfer The them individual to additional qubitreadout se- of S0 and P0 levels near 627nm. (c) AC polarisability3 of87 of storing qubits on the nuclear spin states. This selec- 1 3 levels |0x" and |1x" in the P2 level (e.g., for Sr3 we lectivity can be based on a gradient3 magnetic field, as P2 S0 and P0 levels nearcould 689nm. choose (d)|0x"≡ AC| P polarisability2,F =13/2,mF of= − dif-13/2" andtively can be used to transfer atoms site-dependently to 3 3 3 1 ferentism muchF sublevels more of sensitive| the1x"≡P| 2P, to2F,F magnetic=13=13//22,m hyperfineF fields= −11/2" levelP, where0 or forFSis0.A thethe transport lattice, or to read out qubits by transfer- π−polarisedgradient light field at of 627nm 100total G/cm angular and 689.2nm. momentum will provide and m anF the energy magnetic gradient sublevel, 3 3 ring only the |0" state to P2, then making fluorescence and connect these states to the P0 level via off-resonant 3 of 410 MHz/cmRaman for |0 couplingx" or an to a energyS1 level). di Thefference individual of qubit about se-measurements (e.g., using the cycling transition between FIG. 2: (a) Energy level diagram showing how independent lectivity can be based on a gradient magnetic field, as 3P 3 3 1 3 15kHz between atoms in neighbouring sites. In the samethe2 P2,F =13/2 and D3 manifold). optical lattices can be produced for the S0 and P0 levels 3 1 field the 3P levelis much states more will sensitive be shifted to magnetic by fields−mP30×or1HzS0.A in by finding wavelengths where the polarisability of each of thestorage lattice for0 qubits,gradient which field of 100 will G/cm not will a provideffect thean energyI P0 gradient A necessary requirement here is that our states |0x" 3 states.neighbouring Similarly, thesites,of 410polarizability which MHz/cm again for |0x of" indicatesor anP0 energyat 689.2nm the difference advantage of about levels is zero and the other non-zero.FIG. (b) 2: (a) AC Energy Polarisability level diagram showing how independent and |1x" are trapped in the combination of the storage 1 3 1 3 15kHz between atoms in neighbouring1 sites. In the same 0 0 optical lattices can be producedis for∼ theof1550a.u,S0 storingand P0 levels whereas qubits on the the3 polarisability nuclear spin of states.S0 is zero. This selec-and transport lattices (these will both provide AC-Stark of S and P levels near 627nm. (c) AC polarisability of field the P0 level states will be shifted by −mI × 1Hz in 1 3 by finding wavelengths where the polarisability of each of the 3 S0 and P0 levels near 689nm. (d) AClevels polarisability is zero and the other of non-zero. dif-This (b)tively is AC largely Polarisability can because be usedneighbouring of to the transfer near-resonant sites, which atoms again site-dependently indicates coupling the of advantageshifts to for the P2 level). In Fig. 2d we plot the polaris- 3 1 3 1 3 ferent mF sublevels of the P2, F =13of /S20 and hyperfineP0 levels level near 627nm. for (c) AC polarisability of of storing qubits on the nuclear spin states. This selec- 3 1 3 S0 totheP transport1, which is lattice, made or possible to read without out qubits large by spon- transfer-ability of all of the magnetic sublevels of P2, F =13/2 S0 and P0 levels near 689nm. (d) AC polarisability of dif- tively can be used to transfer atoms site-dependently to π−polarised light at 627nm and 689.2nm. 3 3 ferent mF sublevels of the P2, Ftaneous=13/ring2 hyperfine emission only level the for rates|0"thestate transportdue to to lattice, theP2, narrow then or to read making linewidth out qubits fluorescence by of transfer-at our lattice wavelengths, and the large tensor shifts π−polarised light at 627nm and 689.2nm.3 3 P1.measurements This lattice can (e.g.,ring be only using used the | for0 the" statetransport cycling to P2, then transition, and making atoms fluorescence betweenmake certain mF levels suitable for trapping at the same 3 measurements3 (e.g., using the cycling transition between in itthe willP not,F be=13 affected/2 and3 byD themanifold).