quantum computing with entangled ions and photons

Quantum Computing with Quantum Computing with Entangled Ions and Entangled Ions and PhotonsPhotons Boris BlinovBoris Blinov

University of WashingtonUniversity of Washingtonhttp://http://

depts.washington.edu/depts.washington.edu/qcomp/qcomp/

28 June 201028 June 2010SeattleSeattle

OutlineOutline

• 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

What is a qubit (Qbit, q-What is a qubit (Qbit, q-bit)?bit)?

Quantum two-level system

| 1

|0

“Bloch sphere”

State of the qubit is described by its wavefunction | = |0 + |1

| 1

|0

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

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!

Quantum computing revealed• The power of quantum computing is twofold:

- parallelism and

- entanglement

• Example: Shor’s factoring algorithm

U(x)(axmodb)

H

H

H

H

...

input

ou

tput

|0

|0

|0

|0

|0

...|0

|0|0

...

...

QFT ...

evaluating f(x) for 2n inputs

massive entanglement

OutlineOutline

• 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

RF (Paul) ion trapRF (Paul) ion trap

Pote

nti

al

Position

Position

endcap

endcap

ring

3-d RF quadrupole

RF

The UW trap: linear RF The UW trap: linear RF quadrupolequadrupole

4 Ba ions

Chip-scale ion traps

NIST X-trapNIST X-trap

NIST racetrack trapNIST racetrack trap

European microtrapEuropean microtrap

137137BaBa++ qubit 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 Multi-qubit quantum logic gates via Coulomb gates via Coulomb interaction or via photon interaction or via photon couplingcoupling

|0

|1

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.

|

|

control

target

Cirac and Zoller, Phys. Rev. Lett. 74, 4091 (1995)

Raman beams

~4 microns

OutlineOutline

• 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

+ = H

S1/2

P1/2

= V

| mj=+1/2

||

| = |H| + |V|

Ion-photon entanglement via spontaneous Ion-photon entanglement via spontaneous emissionemission

| mj=-1/2

D

BS

DD1

D2

Remote Ion Entanglementusing entangled ion-photon pairs

2 distant ions

Coincidence only if photons in state:

| = |H1 |V2 - |V1 |H2

This projects the ions into …

|1 |2 - |1 |2 = | -ions

The ions are now entangled!|i = |H| + |V|

Simon and Irvine, PRL, 91, 110405 (2003)

OutlineOutline

• 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

“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

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).

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

Anharmonic Ring Ion Trap

OutlineOutline

• 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

Optical pumping: qubit initialization

493nm

650nm

1762nm

6S1/2

6P1/2

5D5/2

5D3/2

8.037 GHz

F=2

F=1

mF=0

mF=0

-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.

Rabi flops on the S – D transition

Hyperfine qubit Rabi flopping

Femtosecond optical Rabi flopping

Ion excitation with unit probability

““Integrated optics”: ion trap Integrated optics”: ion trap with a spherical mirrorwith a spherical mirror

N.A. = N.A. = 0.90.9

UW Physics

Putting things in Putting things in prospective…prospective…

UW Physics

Ion imaging using the mirror

– Resolve multiple (2) ions

• x`

infinity-corrected microscope lens spherical mirror

UW Physics

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

“Tack” Trap: Almost Zero Obstruction

UW Physics

“Tack” trap at work

Final remarks...

“Computers in the future may weigh no more than 1.5 tons.”

- Popular Mechanics (1949)

“I think there is a world market for maybe five computers.”

- Thomas Watson, chairman of IBM (1943)

UW ion trappers