Quantum Computation With Trapped Ions

Brian Fields

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’s Postulates1. Scalable, well defined Qubits2. State initialization3. Long Coherence Times compared to Gate Speed4. Universal Set of Quantum Gates5. 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 fieldUnfortunately 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• Cirac Zoller• 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 CNOT1) The internal state of a

control ion is mapped onto the motion of an ion string

2) The state of the target ion is flipped conditioned on the motional state of the string

3) 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 Qubit entanglement

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)