Quantum Computing with Entangled Ions and Photons

1. Quantum Computing with Entangled Ions and Photons Boris Blinov University of Washington http://depts.washington.edu/qcomp/ 28 June 2010Seattle

2. Outline • Quantum computing • Ion traps and trapped ion qubits • Ion-photon entangled system • Putting 2 and 2 together: a hybrid system • Trapped ion QC at Washington

3. What is a qubit (Qbit, q-bit)? Quantum two-level system State of the qubit is described by its wavefunction | = |0 + |1 | 1  |0 | 1  “Bloch sphere” |0

4. Classical vs. Quantum • In a classical computer, the data is represented in series of bits, each taking a value of either 0 or 1. • Classical computation consists of operations on single bits (NOT) and multiple bits (e.g. NAND). • In a quantum computer, the data is represented in series of quantum bits, or qubits, each taking a value of |0, |1or any superposition of |0 and |1. • Quantum computation consists of operations on single qubits (called rotations) and multiple bits (e.g. CNOT - the Controlled-NOT gate). 0 1 1 0 0 1 0 0 1 1 1 0 …. |0 + |1

5. Quantum CNOT gate control qubit target qubit result |0 |0 |0 |0 |0 |1 |0 |1 |1 |0 |1 |1 |1 |1 |1 |0 |0 + |1 |0|0|0 + |1|1 Entangled state!

6. Quantum computing revealed • The power of quantum computing is twofold: • - parallelism and • - entanglement • Example: Shor’s factoring algorithm massive entanglement |0 H |0 H ... ... QFT ... input |0 H U(x) (axmodb) |0 H |0 |0 ... ... output |0 evaluating f(x) for 2n inputs |0

7. Outline • Quantum computing • Ion traps and trapped ion qubits • Ion-photon entangled system • Putting 2 and 2 together: a hybrid system • Trapped ion QC at Washington

8. Potential Position Position RF (Paul) ion trap endcap ring RF endcap 3-d RF quadrupole

10. The UW trap: linear RF quadrupole 4 Ba ions

11. Chip-scale ion traps NIST racetrack trap European microtrap NIST X-trap

12. 137Ba+ qubit • Qubit: the hyperfine levels of the ground state • Initialization by optical pumping • Detection by state-selective shelving and resonance fluorescence • Single-qubit operations with microwaves or optical Raman transitions • Multi-qubit quantum logic gates via Coulomb interaction or via photon coupling |1 |0

13. control target Raman beams Cirac-Zoller CNOT gate – the classic trapped ion gate Ions are too far apart, so their spins do not talk to each other directly. To create an effective spin-spin coupling, “control” spin state is mapped on to the motional “bus” state, the target spin is flipped according to its motion state, then motion is remapped onto the control qubit. ~4 microns | | Cirac and Zoller, Phys. Rev. Lett. 74, 4091 (1995)

14. Outline • Quantum computing • Ion traps and trapped ion qubits • Ion-photon entangled system • Putting 2 and 2 together: a hybrid system • Trapped ion QC at Washington

15. Ion-photon entanglement via spontaneous emission | = |H|+ |V| | mj=+1/2  P1/2 | mj=-1/2  s+ = H p = V S1/2 | |

16. Remote Ion Entanglementusing entangled ion-photon pairs Coincidence only if photons in state: |Y - = |H1 |V2 - |V1 |H2 This projects the ions into … |1 |2 - |1 |2= |Y -ions The ions are now entangled! D2 D1 D D BS |i = |H|+ |V| Simon and Irvine, PRL, 91, 110405 (2003) 2 distant ions

18. Outline • Quantum computing • Ion traps and trapped ion qubits • Ion-photon entangled system • Putting 2 and 2 together: a hybrid system • Trapped ion QC at Washington

19. “Hybrid” System: Small(ish) Ion Trap and Optical Interconnects We want to combine a number of “small” (10 – 100 qubits) ion traps in a network trough ion-photon entanglement interface. • novel trap designs (anharmonic, ring, …) • use of multiple vibrational modes and ultrafast pulses • fast optical switching

20. Anharmonic Linear Ion Trap By using a combination of electrodes make a “flat-bottom” axial trap; transverse trapping still harmonic. • ion-ion spacing nearly uniform even for large ion crystals • transverse vibrational modes tightly bunched (“band”) • sympathetic cooling on the fringes of the trap "Large Scale Quantum Computation in an Anharmonic Linear Ion Trap," G.-D. Lin, S.-L. Zhu, R. Islam, K. Kim, M.-S. Chang, S. Korenblit, C. Monroe, and L.-M. Duan, Europhys. Lett. 86, 60004 (2009).

21. Anharmonic Ring Ion Trap Removing the end cap electrodes of a linear trap and connecting the quadrupole rods onto themselves makes a (storage) ring ion trap • ion-ion spacing perfectly uniform • transverse vibrational modes tightly bunched (“band”) • sympathetic cooling on one side of the ring

22. Anharmonic Ring Ion Trap

23. Outline • Quantum computing • Ion traps and trapped ion qubits • Ion-photon entangled system • Putting 2 and 2 together: a hybrid system • Trapped ion QC at Washington

25. 6P1/2 650nm 5D5/2 493nm 5D3/2 1762nm F=2 mF=0 6S1/2 8.037 GHz F=1 mF=0 Optical pumping: qubit initialization -polarized light pumps the population into the F=2, mf=0 state. When pumped, ion stops fluorescing. We adjust the pump light polarization by tuning the magnetic field direction instead.

26. Rabi flops on the S – D transition

27. Hyperfine qubit Rabi flopping

28. Femtosecond optical Rabi flopping Ion excitation with unit probability

29. “Integrated optics”: ion trap with a spherical mirror N.A. = 0.9

30. Putting things in prospective… UW Physics

31. Ion imaging using the mirror • Resolve multiple (2) ions • x` spherical mirror infinity-corrected microscope lens UW Physics

32. Aspherical Schmidt-type correctorfixes aberration (somewhat) • Made from acrylic, in the machine shop • Cut the to precision of 25 μm • Hand-polish to ~0.1μm • Results: • Far from ideal due to misalignment and mirror imperfection, but… UW Physics

33. “Tack” Trap: Almost Zero Obstruction UW Physics

34. “Tack” trap at work UW Physics

35. Final remarks... Quantum “Computers in the future may weigh no more than 1.5 tons.” - Popular Mechanics (1949) Quantum “I think there is a world market for maybe five computers.” - Thomas Watson, chairman of IBM (1943)

36. UW ion trappers