Generation of entanglement & suppression of decoherence in ENDOR-ba

sed quantum computing

Robabeh Rahimi1, Akira SaiToh2, and Mikio Nakakara1

1 Department of Physics, Kinki University2 Graduate School of Engineering Science, Osaka University

2007/9/? IICQI'07, Kish, IRAN 2

Liquid state NMR Quantum ComputingSeems working fine

Drawbacks of NMR quantum computing

• requires number of experiments, molecules

• weak signal intensity

Pseudo-pure states come with some costs!!

Exponential !!

!

Sates in the current NMR experiments separable (non-entangled)

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For NMR Quantum ComputingHigher nuclear spin polarizations are requires

• Directly:

lowering the temperature; mK required!

increasing the magnetic field; current technology• Indirectly:

parahydrogen molecule; a large number of qubits

dynamic nuclear polarization (DNP)

Spin polarization is transferred

from electron spins, with high spin polarization,

to the nuclear spins, with low spin polarizationlow spin polarization.

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Electron spin bus systems forquantum computing

Solid state quantum computingwith a bus spin, an electron spin, coupled to client qubits, many nuclear spins.*

* M. Mehring, J. Mende, Phys. Rev. A 73, 052303 (2006)

solid state

can be cooled to low temperaturewith an available high magnetic field

quantum limit can be achieved

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ENDOR; Electron Nuclear DOuble ResonanceNMR in paramagnetic entities

Pulsed ENDORelectron-nuclear spin manipulation technology

high sensitivity & high polarization from ESR high resolution & nuclear selectivity from NMR

Magnetic Resonasnce Technology: ENDOR = ESR ＋ NMR High sensitivity ( ～ 101-2 GHz) High resolution ( ～ 1 kHz)

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Block Diagram of Pulsed QC-ENDOR Setup

X-band ( 10 GHz) Version:

～ DetectorTWTAPulse Former

RF Generator Nd:YAG LaserRF Amplifier

8 channel

Two Direct Digital Synthesizers

1 kW

300 W, 0.25 150 MHz 500 W, 0.30 35 MHz1000 W, 0.01 250 MHz

50 Hz, 90 mJ (at 532 nm) 1064/532/355/266 nm

High-Speed Digital Oscilloscope

Pulse Programmer

Water-cooling Electromagnet (-1.5~1.5 T)

9.6 GHzMW OSC.

ENDOR Probehead(Dielectric Resonator with RF Coil)Operating at liq. He Temp.

Liq. He Cryostat with a Gas-Flow Controller

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Pulse Electron Multiple Resonance Spectrometers　

ESR/ENDOR/ELDOR

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Entanglement & ENDOR

• Pseudo-pure state entanglemententanglement*:

*Mehring et al., PRL. 90, 153001(2003)

(a) (b) (c)

neneP

neneP

neSI

2

1

2

1 )()2/( 2434 MWRF

(a) (b) (c)

1

2

4

3

w24

w12

w34

1

2

4

3

w24

w12

w34

1

2

4

3

w24

w12

w34

2007/9/? IICQI'07, Kish, IRAN 9

(Pseudo-)Entanglement

ENDOR quantum computing

MW RF1 RF2 Bell state nTPPI

w24 w12 w34 f1 − f2

w24 w34 w12 f1 + f2

w13 w12 w34 f1 + f2

w13 w34 w12 f1 − f2

2

1

2

1

2

1

2

1ESRENDOR

1

2

4

3

w24

w12

w34

w13

RF1 RF2 RF2

echo

MW MW MW

2

2

2

2

1f

2f109

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Malonyl Q-band

1.198898w24

1.198898w24

1.201028w13

B0/T

C

B

A

22.701w34

79.699w12

79.699w12

22.701w34

79.757w12

22.777w34

RF2/MHzRF1/MHz

0 2 4 6 8 10

TPPI Frequency / MHz

21

21

21

|1 − 2 ||1 + 2|

|1||2|1 = -5.2 MHz2 = 1.0 MHz

(Pseudo-)EntanglementENDOR quantum computing

ESRENDOR

1

2

4

3

w24

w12

w34

w13

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DPNO Q-band

11

11

21

21

0 2 4 6 8 10

TPPI Frequency/ MHz

0 2 4 6 8 10

TPPI Frequency/ MHz

1 − 2 ||1 + 2|

|1|

2|

1 = -5.2 MHz2 = 1.0 MHz

00

00

21

21

B0 = 1. 2044T

B0 = 1.2066T

HN IIS MMMS IN IH

21

21 ,1,

21

21 ,1,

21

21 ,1,

21

21 ,1,

21

21 ,0,

21

21 ,0,

21

21 ,0,

21

21 ,0,

(Pseudo-)EntanglementENDOR quantum computing

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Decoherenceelectron spin with very short decoherence time

Radical T1 /ms

DPNO-d10 42.5

Malonyl radical 91.5

DPNO 392.0

Spin-lattice relaxation time, T1@10K, saturation recovery

Radical T2 /μs

Malonyl radical 5.200 *

DPNO 0.777

DPNO-d10 0.489

Spin-spin relaxation time, T2@10 K , two pulse echo decay

* at 20 K

R. Rahimi, PhD thesis, quant-ph/0609063

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A conventional model of a spin-boson system

On-resonance bosons,if dissipation is ignored,oscillation is found rather than a decay

A dissipative model of a spin-boson system

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System study

CPS HHHH

n

kkk

n

jjjS SSASfH

100

0

bn

lkllP aaH

1

as

ssaasC aaSCH

a

ssaaC aaSCH~

Spin system Hamiltonian

Boson system Hamiltonian

Spin-boson coupling

For a bosonic mode in resonance with the spinaa aS

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Tk

H

Z BO exp

1 the original density operator

(b) With polarization transfer Tk

H

PO

B

P

eZ

1n

ele

1

(a) Without polarization transfer OO

is the reduced density operator of the electron spin of the original stateele O

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the total entangling operationentU

Q-band ENDOR; 35 GHz

IUIU O entent0

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A dissipative noise model

tiHTk

H

p

tttiH eetptpett B

P

uu

Tr111

t is a map

tiHt

tiH etett

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Decoherence control

LntxLnL

xLnLtnLVtH x 10 n

XVdtixLnL

nL

exp

xH a Hamiltonian of bang-bang pulses

10 x is a duty ratio

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tVHieU 1tiHeU 2

Time evolution

txLtLxL tΔt

//1

12

0ρtρ Lt

L

at time Lt

111 UUu 222 UUu

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Case without prior polarization transfer

10.0 GHz,1000.1 210 pcc

10.0 GHz,1000.1 610 pcc

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Case without prior polarization transfer

50.0 GHz,1000.1 610 pcc

99.0 GHz,1000.1 610 pcc

Wipe effect

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Case with prior polarization transfer

10.0 GHz,1000.1 210 pcc

10.0 GHz,1000.1 610 pcc

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Case with prior polarization transfer

50.0 GHz,1000.1 610 pcc

99.0 GHz,1000.1 610 pcc

Wipe effect

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Conclusion

-For an electron spin bus system, entanglement is achieved under milder experimental conditions.

-Decoherence control for an electron spin bus system is rather more challenging.

-If the number of qubits is small, we find some regions of parameters, not much far from the currently accessible region of magnetic spectroscopy technology, where the quantum state can be stable.

- A high probability of dissipation of bosons result in slow decoherence, quantum wipe effect.

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work done by

S. Nishida, K. Toyota, D. Shiomi, Y. Morita, A. Ueda, S. Suzuki, K. Nakasuji (Osaka City Univ.) K. Furukawa, T. Nakamura (IMS) H. Hara, P. Carl, P. Höfer (Bruker Biospin Co.)

Masahiro Kitagawa (Osaka Univ.)

Takeji Takui (Osaka City Univ.)

Kazunobu Sato (Osaka City Univ.) Akira SaiToh (Osaka Univ.)

Mikio Nakahara (Kinki Univ.)

RR is supported bySasakawa scientific research grant from the Japan Science Society