A two-qubit conditional quantum gate
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A two-qubit conditional quantum gate with single spins. Univ. of Stuttgart. F.Jelezko , J. Wrachtrup I. Popa, T. Gaebel, M. Domhan, C. Wittmann. Outline. • Introduction • Single spin states: Read-out, manipulation, coherence time

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A two-qubit conditional quantum gate with single spins

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A two-qubit conditional quantum gate

with single spins

Univ. of Stuttgart

F.Jelezko, J. Wrachtrup

I. Popa, T. Gaebel,

M. Domhan, C.Wittmann


Outline

• Introduction

• Single spin states: Read-out, manipulation, coherence time

• CROT gate with single electron and nuclear spin in a solid

• Scaling up: Positioning of single N-V defects in diamond


History

Science 275 (1997) 350-365

A pure state (single spin EPR,NMR):

but see e.g. J. Wrachtrup, A. Gruber, L. Fleury, C. von Borczyskowski

„Magnetic Resonance on single nuclei“ CPL 267 (1997) 179


  • 1. Magnetic Resonance Force Microscopy

    • Rugar et al. Nature430, 329 (2004);

3.Optically detected ESR on single spin

See e.g. Jelezko et al. APL 81 (2002) 2160,

Jelezko & Wrachtrup Journal of Physics: Condensed Matter 16, R1089 (2004)

Single spin read-out

2. Electrical detection

Durkan, C. & Welland, M. E. Appl. Phys. Lett.80, 458-460 (2002) - STM

M. Xiao, I. Martin, E. Yablonovitch, H. W. Jiang Nature 430, 435 - 439 (2004) - FET

J. M. Elzerman, R. Hanson, L. H. Willems van Beveren, B. Witkamp, L. M. K. Vandersypen, L. P. Kouwenhoven Nature 430, 431 - 435 (2004)


Optical transition (2 eV)

ESR (10-5 eV)

Optical readout

Single defect detection:

Optical microscopy

m

n

300 nm

0

0

3

The number of scattered photons

depends on spin state

Brossel and Bitter (1952) Phys. Rev. 86 308 (mercury vapours)

Wrachtrup et al. Nature 363, 244–245 (1993) (single molecules)


Microwave resonator

(D. Suter Univ. Dortmund)

Typical value for ESR p-pulse - 10 ns

Superconducting

magnet

Optical microscope

MW and

RF loop

MO, N. A. 0.85

500 m

Set-up

Variable temperature microscope

Operating temperature – 1,6 – 300 K

Detection yield – 1 percent

Magnetic field – up to 5 T


3E

1A

DE=1.945eV

3A

3 GHz

Nitrogen Vacancy (NV) center in diamond

Diamond:

-bandgap 6 eV

-Tdebay: 2000K

Long T2 of defects at RT

Optical detection of single defects

Gruber A, Wrachtrup J et al, SCIENCE 276 2012 (1997)


10 µm

Single N-V centers implantation

App. 2 N iones/ N-V defect


t

Photon stream

2

1

Single center signature: photon antibunching

Single photon source:

Weinfurter et al. PRL 85 (2000)

Grangier et al. PRL 89 (2003)


40MHz

Fluorescence/a.u.

ms=0

ms=±1

ms=±1

ms=0

Relaxation time:

T1:1-2 s (2 K)

2 ms (300 K)

Observation of single electron spin quantum jump at T=2K

Low temperature optical spectroscopy, bulk:

D. Redman J. Opt. Soc. Am. B 9, No. 5, (1992).

Single defects:

Jelezko F et al. APL 81 , 2160 (2002)

3E

1A

E~3GHz


Spin system:

T1~ 2ms

T2: ?

probe

ms=±1

Laser

Laser

I

ms=0

MW

Switch off the Laser light

during manipulating the spin

Strong probe

time

Inhibition of coherent spin state evolution by measurement („ a watched pot never boils“)

T=300K

MW pulse

Weak probe


/2

/2

t1

 = 0.3 ms

How large is T2?Hahn Echo


Hahn echo decay

F. Jelezko et al PRL 92 (2004) 076401

Decoherence due to P1 centers ?

(P1 - single substitutional nitrogen,

100 ppm in HPHT Ib diamond)

„first data“: T2 0.3-0.5 s


/2

/2

1

t2

Hahn echo decay of single N-V center in IIa type diamond

  • pulse – 8 ns

    T2/Tgate = 105


Optical single nuclear spin read-out (13C diamond)

3

2

1

13C spins as qubits: Wrachtrup

Opt. Spectr. 91 429 (2001) – optical spectroscopy

Hyperfine splitting

A1,2,3 = 130 MHz

Fine Structure:

Splittting: 3 GHz

Experimental realization using ESR:

Jelezko et al. Phys. Rev. Lett. 93, 130501 (2004)   

Ab initio calculations:

M.Luszczek et al. Physica B 348, 292 (2004)


2

C

1

B

A

3

D

4

Gates: qubits

1st qubit: electron spin of N-V

2nd qubit: nuclear spin of 13C

C:130 MHz

D:10 MHz

A:2800 MHz

B:2940 MHz

ESR

NMR (ENDOR)


2

C

1

A

3

4

Rabi nutation of single electron and single 13C spin – single qubit operations

ESR (transition A)

C

ENDOR (transition C)

Averages over 105 Cycles


Input

Output

CROT-gatea two qubit gate

flips the nuclear spin dependent on the orientation of the electron spin

with π/2(z) equivalent to the CNOT-gate

Experimental: selective NMR π-pulse

2

π

1

3

4


2

1

3

ρ

ρ

4

state

state

state

state

Tomography of state after CROT

π

Ideal result:

Initial state:


CROT=

Tomography of state after CROT

Theory

Experiment

Parameters for calculation:

ESR: 15 ns; T2e=1.2 s;

NMR:400 ns; T2n=3.6 s;

Jelezko et al. quant-ph/0402087


3

2

1

Scaling up

13C spin cluster is scalable up to 3-12 qubits

Fully scalable architecture – coupled NV defects

Coupling: magnetic dipole (short range)

Optical dipole (long range)

N+

beam

5 nm

Diamond

NV defect


N+ ions, 2MeV

Positioning accuracy limitations

N+ ions

surface of sample

1,1µm

~500nm FWHM

target depth

1 nm accuracy for 1 keV ions possible


Summary single spin QC

  • Single electron and nuclear spin state read-out

    and coherent manipulation

  • 1 and 2 Qbit operation

    ( 3. Qbit 14N not used in experiment)

  • scaling requires coupling of defects (nm positioning)


Acknowledgment

3. Institute of Physics

University of Stuttgart

J. Wrachtrup

I. Popa

T. Gaebel,

M. Domhan

C.Wittmann

A. Gruber*

* currently at University of Chemnitz

In collaboration with:

S.Kilin, A. Nizovtsev (Minsk)

J. Twamley (University of Ireland)

J. Buttler (NRL Washington)

JD. Suter (Dortmund)

J. Meyer (Bochum)

J. Rabeau, S. Prawer (Melbourne)

DFG, EU(QIPDDF ROSES)

Landesstiftung BW


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