1. Quantum Computation With Trapped Ions Brian Fields

2. Overview • Intro to Quantum Computation • Trapping Ions • Ytterbium as a qubit • Quantum Gates • Future Brian Fields

3. What does a Quantum Computer Do? • Shor’s Algorithm • Factoring products of prime numbers • Deutche Jose Algorithm • Quantum Simulation • Magnetism, Ising model, with more qubits possible particle scattering Brian Fields

4. What Is a Quantum Computer? Divincenzo’sPostulates • Scalable, well defined Qubits • State initialization • Long Coherence Times compared to Gate Speed • Universal Set of Quantum Gates • Efficient State Read Out Brian Fields

5. History Mass Spec, Atomic Clocks, systems developed • Penning Trap • RF-Paul Trap • Surface Ion Traps Brian Fields

6. Brian Fields

7. In order to confine particles, seek linear restoring force F=-kr, Quadrupolar potential gives linear electric field Unfortunately Earnshaw’s theorem proves it is impossible to confine in all directions at once with static fields alone () add an oscillating RF field , Brian Fields

8. Matheiu Equation Brian Fields

9. Brian Fields

10. Desire a closed cycling transition • Detune Doppler cooling laser red of this transition. • Due to Doppler shifts arising from atoms thermal motion laser appears resonant when atom is moving towards beam and further red detuned when moving away • Loses momentum upon absorption moving towards beam, gains momentum upon spontaneous emission but emission is in random direction averages to zero Doppler Cooling Brian Fields

11. Ytterbium 171+ Hyperfine State Qubit Long Coherence Times~10s Insensitive external B-Field Cooling Closed (with repump beams) Optical Pumping Min error ~ 10^-6 Detection Typical accuracy ~ 98 % Brian Fields

12. Sideband Cooling Brian Fields

13. ()()} Brian Fields

14. Single Qubit Rotations Brian Fields

15. Single Qubit Rotations • Two Qubit Entangling Gates • CNOT • CiracZoller • Molmer Sorenson Quantum Gates Brian Fields

16. The previous Hamiltonian's can be applied to generate the following Single Qubit Rotations Quantum Gates Brian Fields

17. Cirac-Zoller CNOT • The internal state of a control ion is mapped onto the motion of an ion string • The state of the target ion is flipped conditioned on the motional state of the string • Motion of ion string is mapped back to control ion state Result – Flips T if C is Brian Fields

18. Possible Pulse Sequence for a CNOT gate Brian Fields

19. More Qubits • Higher Fidelities, better state detection • Motional Decoherence • Modular Trap arrays for Scaling • Photon Ion Flying Qubitentanglement Future Brian Fields

20. References • Steven Olmschenk.. “QUANTUM TELEPORTATION BETWEEN DISTANT MATTER QUBITS” Doctoral Thesis. University of Maryland. (2009) • David Hayes. “Remote and Local Entanglement of Ions using Photons and Phonons”. Doctoral Thesis. University of Maryland. (2012) • Johnathan Mizrahi. “ULTRAFAST CONTROL OF SPIN AND MOTION IN TRAPPED IONS”. Doctoral Thesis. University of Maryland. (2013) • Timothy Andrew Manning, “QUANTUM INFORMATION PROCESSING WITH TRAPPED ION CHAINS”. Doctoral Thesis. University of Maryland. (2014) • Chris Monroe, et all. “Large-scale modular quantum-computer architecture with atomic memory and photonic interconnects”. PHYSICAL REVIEW A 89, 022317 (2014) • DiVincenzo, David “The Physical Implementation of Quantum Computation”. ARXIV.arXiv:quant-ph/0002077v3 13 Apr 2000 (2008) • J I Cirac, P. Zoller. “Quantum Computations with Cold Trapped Ions”. Physics Review Letters. Volume 74 . Issue 20. May 15 (1994) • H. H¨affner, C. F. Roos, R. Blatt, “Quantum computing with trapped ions”. ARXIV.arXiv:0809.4368v1 [quant-ph] 25 Sep 2008 (2008) Brian Fields