Guin-Dar Lin, Luming DuanUniversity of Michigan

2009 March Meeting

G.-D. Lin, S.-L. Zhu, R. Islam, K. Kim, M.-S. Chang, S. Korenblit, C. Monroe, L.-M. Duan arXiv:0901.0579

Guin-Dar Lin, Luming DuanUniversity of Michigan

2009 March Meeting

Large Scale Quantum Computation in an Anharmonic Linear Ion Trap

Large Scale Quantum Computation in an Anharmonic Linear Ion Trap

Trapped ion quantum computation

- Monroe’s group

2S1/2

2P1/2

369 nm

|↓|↑

F,mF=0,0

F,mF=1,0

F,mF=0,0

Effective spin-1/2system in individual ion

transverseaxial

Unit:

Linear Paul trap

Motional modes modes ion

Raman Rabi freq.

laser detuning

Laser field

j n

Hamiltonian

gate time

ion controlled phaseion

phase space displacement

Quantum gate

Effective evolution

Controlled-phase flip (CPF)

Quantum control problem:

- Gate time, τ

- Laser detuning, μ

- Pulse shaping, Ω(t)

- Axial or transverse modes

~Ω(t)

1. Ion shuttling: 2. Quantum networks

BS

D1 D2

i 'i j 'j

pump pump

CNOT

pump pump

CNOT

Duan, Blinov, Moehring, Monroe, 2004

Kielpinksi, Monroe, Wineland, Nature 417, 709 (2002)

1. Ion shuttling:

Scaling it up !

- lack of translational symmetry

3. Linear chain? Adding more ions? Difficulties?

a. Geometrical issues

-- inhomogeneity:

N=20

N=60

N=120

Solution: build up a uniform ion trap Solution: build up a uniform ion trap

- structural instability

Scaling it up !

3. Linear chain? Adding more ions? Difficulties?

b. Cooling issues

c. Control issues

-- sideband cooling is difficult

-- sideband addressing is difficult

-- controlling complexityincreases with N (?)

Independent of N Independent of N

Axial Transverse

N=120

Solution: transverse modes Solution: transverse modes

Scaling it up !

Our proposalOur proposal

Box potential

finite gradient!V=0

uniform portion, F=0constant spacing=d

a real trap

+ Lowest order correction: quartic

inhomogeneity (std. deviation)

Design of a uniform ion crystal

N=120

Practical architecture

G.-D. Lin, S.-L. Zhu, R. Islam, K. Kim, M.-S. Chang, S. Korenblit, C. Monroe, L.-M. Duan arXiv:0901.0579

gate time

ion controlled phaseion

phase space displacement

Quantum gate (control scheme)

Effective evolution

Controlled-phase flip (CPF)

Quantum control problem:

- Gate time, τ

- Laser detuning, μ

- Pulse shaping, Ω(t)

- Axial or transverse modes

2N+1 constraints

(fixed)

(fixed)

chopped into segments# =2N+1 ?

N modes: real/imaginary

Segmental pulse shaping

Answer: We don’t need 2N+1, but a few!!

Pulse shape

Infidelity

Reason:Only local motion is significant.

G.-D. Lin, S.-L. Zhu, R. Islam, K. Kim, M.-S. Chang, S. Korenblit, C. Monroe, L.-M. Duan arXiv:0901.0579

TP

Temperature and imperfection1. Infidelity due to axial thermal motion (at Doppler temperature)

2. Infidelity due to anharmonicity of the ion vibration

3. Infidelity due to transverse thermal motion (out of LD-limit correction)

G.-D. Lin, S.-L. Zhu, R. Islam, K. Kim, M.-S. Chang, S. Korenblit, C. Monroe, L.-M. Duan arXiv:0901.0579

Ion spacing ~ 10 μmWidth of Gaussian beam ~ 4 μmCross-talk prob. ~ Doppler cooling is sufficient!Doppler cooling is sufficient!

G.-D. Lin, S.-L. Zhu, R. Islam, K. Kim, M.-S. Chang, S. Korenblit,

C. Monroe, L.-M. Duan arXiv:0901.0579

An an-harmonic axial ion trap leads to large uniform ion chains - with translational symmetry- structurally stable

Use of transverse phonon modes, eliminate the requirement of sideband cooling

Simple laser pulse control leads to high-fidelity gates in any large ion crystal

Complexity of quantum gate does NOT increase with the size of the system.

Multiple gates can be performed in parallel at different locations of the same ion chain.

Summary

Optimization of the quartic trap

purely harmonic

quartic (optimized)

inhomogeneity

spacing

Two central integrals

Gate fidelity

ideal gate

thermal field, T

Axial thermal fluctuation

Thank you.