Download presentation

Presentation is loading. Please wait.

Published byNoah Schmidt Modified over 4 years ago

1
Vorlesung Quantum Computing SS 08 1 A scalable system with well characterized qubits Long relevant decoherence times, much longer than the gate operation time A qubit-specific measurement capability A A universal set of quantum gates U The ability to initialize the state of the qubits to a simple fiducial state, e.g. |00...0> DiVincenzo criteria DiVincenzo: Fortschr. Phys. 48 (2000) 9-11, pp. 771-783

2
Vorlesung Quantum Computing SS 08 2 Quantum Computing with Ions in Traps How to trap ions State preparation Qubit operations CNOT Deutsch – Jozsa Algorithm advantages/drawbacks

3
Vorlesung Quantum Computing SS 08 3 Paul Trap Nobel Prize 1989 centre is field free quadrupole field x and y motions not coupled! Chemnitz University

4
Vorlesung Quantum Computing SS 08 4 Linear Trap x y z U1U1 R U ac U ac (t) = U r + V 0 cos T t effective potential: eff = x 2 x 2 + y 2 y 2 + z 2 z 2 x = y >> z (averaged over one rf cycle) U2U2 z0z0 M. Sasura and V. Buzek: quant-ph/0112041

5
Vorlesung Quantum Computing SS 08 5 Potential

6
Vorlesung Quantum Computing SS 08 6 Ions in a Linear Trap z = 2 qU 12 mz 0 2 typical operation parameters: V 0 = 300 – 800 V T /2 = 16 – 18 MHz U 12 = 2000 V z 0 = 5 mm R = 1.2 mm z /2 = 500 - 700 kHz x,y /2 = 1.4 – 2 MHz ( 40 Ca + ) 70 m 40 Ca + 24 Mg + Seidelin et al: Phys. Rev. Lett. 96, 253003 (2006) Nägerl et al: Phys. Rev. A 61, 023405 (2000)

7
Vorlesung Quantum Computing SS 08 7 quantum computing with ions HH -1 calculation U preparation read-out |A| time the ions are prepared to be in their ground state Doppler coolingside band cooling 1st step2nd step k B T << ħ z

8
Vorlesung Quantum Computing SS 08 8 Doppler cooling when absorbing a photon, also the momentum is transferred the net momentum of the spontaneous emission is zero E = ħ p = ħk E = 0 p = 0 E = ħ p = ħk k absorption for ions moving toward the laser beam the light appears blue shifted use a red detuned laser = 0 + k v Ca

9
Vorlesung Quantum Computing SS 08 9 side band cooling Doppler cooling gets down to k B T ħ internal electronic ground and excited state |g,|e trapped ions moving in harmonic potential states |n, n= 0,1,2… cooling: |g,n |e,n-1 |e,n-1 |g,n-1

10
Vorlesung Quantum Computing SS 08 10 ions used as qubits electronic states as qubits (pseudo-spin) (CNOT, Deutsch-Jozsa Algorithm, Quantum-Byte) hyperfine states as qubits (CNOT, error correction, Grover Algorithm)

11
Vorlesung Quantum Computing SS 08 11 40 Ca + as qubit 4 2 S 1/2 4 2 P 1/2 4 2 P 3/2 3 2 D 3/2 3 2 D 5/2 397 nm 729 nm 854 nm 866 nm |0 |1 quadrupole transition used for Laser cooling quadrupole transition with relatively long relaxation time for cooling: 866 nm transition has to be irradiated as well, otherwise charge carriers will be trapped in 3 2 D 3/2 orbital fluorescence detection for read-out detection Nägerl et al: Phys. Rev. A 61, 023405 (2000) D 5/2 occupation P D red sideband blue sideband after Doppler cooling

12
Vorlesung Quantum Computing SS 08 12 9 Be + as qubit electron spin S = 1/2, m s = 1/2 nuclear spin I = 3/2, m I = 1/2, 3/2 F = I + S, m F 2 2 P 3/2 2 2 P 1/2 12 GHz 2 2 S 1/2 |F=2, m F =2 |F=1, m F =1 | | 1.25 GHz Doppler cooling hyperfine levels have long relaxation times sideband cooling |2,2 |n |1,1 |n-1 ; induced spontaneous Raman transition |1,1 |n-1 |2,2 |n-1 sideband cooling detection with fluorescence after + excitation + detection Monroe et al: Phys. Rev. Lett. 75, 4011 (1995) red blue after Doppler cooling after sideband cooling

13
Vorlesung Quantum Computing SS 08 13 quantum computing HH -1 calculation U preparation read-out |A| time quantum-bit (qubit) 0 1 a 1 0 + a 2 1 = a1a1 a2a2

14
Vorlesung Quantum Computing SS 08 14 qubit operations how does the system evolve with time? U (t) e ħ - iH QC t ^ ^ H QC = H trap + H ion + H man ^^^^ Splitting of S = ½ in external magnetic field: 2 2 S 1/2 |F=2, m F =2 |F=1, m F =1 | | s /2 = 1.25 GHz H ion = - ħ s 2 1 0 0 ^ B 0 = 0.18 mT H ion = - SB = - S z B 0 = - L S z ^ ^^

15
Vorlesung Quantum Computing SS 08 15 qubit coupling coulomb repulsion couples motional degrees of freedom H trap = ( x 2 x i 2 + y 2 y i 2 + z 2 z i 2 + ) + M 2 pi2pi2 M2M2 e2e2 4 0 |r i - r j | i=1 N N j>i trap potential eff E kin coulomb potential positions at rest 1 mode 2 modes A. Steane: quant-ph/9608011 ^

16
Vorlesung Quantum Computing SS 08 16 vibration modes as qubits (bus) centre of mass motion used as qubit A. Steane: quant-ph/9608011 i=1 H trap = ( z 2 z i 2 + ) = ħ i a i a i pi2pi2 M2M2 M 2 NN i z = 2 qU 12 mz 0 2 z z 3 J.F. Poyatos et al., Fortschr. Phys. 48, 785

17
Vorlesung Quantum Computing SS 08 17 9 Be + : the two qubit system 2 2 P 1/2 50 GHz 2 2 S 1/2 |F=2, m F =2 |F=1, m F =1 | | |1 | |0 |1 | |0 s /2 = 1.25 GHz z /2 = 11.2 MHz 2 2 P 3/2 |F=3, m F =3 |0 |aux |F=2, m F =0 vibrational state: control qubit hyperfine state: target qubit Raman transition + detection ~ 313 nm

18
Vorlesung Quantum Computing SS 08 18 spin dynamics dM x dt = (M y (t)B z M z (t)B y ) dM y dt = (M z (t)B x M x (t)B z ) dM z dt = (M x (t)B y M y (t)B x ) = M y (t)B z = - M x (t)B z = dM dt = M(t) x B = M y cos( L t) - M x sin( L t) = M x cos( L t) + M y sin( L t) B = 0 0 BzBz B 1 cos t B 1 sin t B0B0 magnetic field rotating in x,y-plane

19
Vorlesung Quantum Computing SS 08 19 spin flipping in lab frame http://www.wsi.tu-muenchen.de/E25/members/HansHuebl/animations.htm

20
Vorlesung Quantum Computing SS 08 20 rotating frame x y z x y z cos t sin t - sin t 001 0 0 = r z y x xrxr yryr t t cos t sin t - sin t 001 0 0 cos t sin t 0 B1B1 cos t -sin t 0 B1B1 + B rf = r cos 2 t 0 B rf = r 1 0 0 B1B1 -sin 2 t B1B1 + constant counter-rotating at twice RF applied RF generates a circularly polarized RF field, which is static in the rotating frame B 1 cos t 0 0 2 =

21
Vorlesung Quantum Computing SS 08 21 spin flip in rotating frame http://www.wsi.tu-muenchen.de/E25/members/HansHuebl/animations.htm

22
Vorlesung Quantum Computing SS 08 22 qubit manipulation: laser interaction H man = - B = m S B = B 1 x cos(kz- t+ ) ^ H man (S + e i + S - e -i ) = m B 1 /2ħ ħ 2 frame of reference: H 0 = ħ s S z + ħ z a a only spin state is changed i (S + ae i - S - a e -i ) ħ 2 for = s - z red side band i (S + a e i - S - ae -i ) ħ 2 for = s + z blue side band change of vibrational state always implies change of spin state Lamb-Dicke parameter: 2 d 0 / << for = s

23
Vorlesung Quantum Computing SS 08 23 qubit rotation 2 2 P 1/2 50 GHz 2 2 S 1/2 |F=2, m F =2 |F=1, m F =1 | | |1 | |0 |1 | |0 s /2 |0 |aux |F=2, m F =0 Qubit rotation on target qubit U /2,ion Raman transition with detuning s Duration of laser pulse: /2 rotation 2 e = i ħ S y cos /4 sin /4 - sin /4 1 1 1 1 2 = = U /2

24
Vorlesung Quantum Computing SS 08 24 /2- rotation matrix - - 1 2 U /2,ion = base vectors of the two–qubit register: Transformation matrix: U /2,ion = ( ) 1 2 1 2 1 2 1 2

25
Vorlesung Quantum Computing SS 08 25 CNOT operation - U ph = U ph transformation matrix: Transformation sequence: U /2,ion =U - /2,ion U ph - - 1 2 - - - = = U CNOT Monroe et al: Phys. Rev. Lett. 75, 4714 (1995)

26
Vorlesung Quantum Computing SS 08 26 phase rotation 2 2 P 1/2 50 GHz 2 2 S 1/2 |F=2, m F =2 |F=1, m F =1 | | |1 | |0 |1 | |0 s /2 |0 |aux |F=2, m F =0 Phase rotation on control qubit U ph Raman transition between and auxiliary state Full rotation by 2 U ph

27
Vorlesung Quantum Computing SS 08 27 quantum computing HH -1 calculation U preparation read-out |A| time quantum-bit (qubit) 0 1 a 1 0 + a 2 1 = a1a1 a2a2

28
Vorlesung Quantum Computing SS 08 28 Be ions: read-out spin state |F=2, m F =2 | |1 | |0 2 2 P 3/2 |F=3, m F =3 2 2 S 1/2 |F=1, m F =1 | |1 | |0 + detection read-out spin state via fluorescence prepare desired initial state using Raman pulses | on blue side band |1 on internal state |1 | perform CNOT cool system to | |0

29
Vorlesung Quantum Computing SS 08 29 Be ions: read out vibrational state |F=2, m F =2 | |1 | |0 2 2 P 3/2 |F=3, m F =3 2 2 S 1/2 |F=1, m F =1 | |1 | |0 + detection read-out spin state prepare same initial state and do CNOT convert vibrational into spin state on red side band for | on blue side band for | read-out spin state via fluorescence

Similar presentations

Presentation is loading. Please wait....

OK

SIMOCODE-DP Software.

SIMOCODE-DP Software.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google

Slideshare ppt on stress management Ppt on biodegradable and nonbiodegradable materials Ppt on class 10 hindi chapters books Ppt on popular social networking sites Ppt on safe abortion Ppt on natural resources land soil and water Ppt on types of forests in india Ppt on maggi in india Ppt on dry cell and wet cell battery Ppt on recycling of wastewater