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 he 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
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Vorlesung Quantum Computing SS 08 1 A scalable system with well characterized qubits Long relevant decoherence times, much longer than the gate operation.
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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
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
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
Vorlesung Quantum Computing SS ‘08
4
Linear Trap
x
y
z
U1
RUac
Uac(t) = Ur + V0 cos Tteffective potential:
eff = x2 x2 + y
2 y2 + z2 z2
x = y >> z
(averaged over one rf cycle)
U2
z0
M. Sasura and V. Buzek: quant-ph/0112041
cmeyer
whether ions are trapped depends on rod diameter vs R and Ur only! (v does not come in!)
Vorlesung Quantum Computing SS ‘08
5
Potential
Vorlesung Quantum Computing SS ‘08
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Ions in a Linear Trap
z = 2qU12
mz02
typical operation parameters:
V0 = 300 – 800 VT/2 = 16 – 18 MHz
U12 = 2000 V
z0 = 5 mm
R = 1.2 mm
z/2 = 500 - 700 kHz
x,y/2 = 1.4 – 2 MHz (40Ca+)
70 m
40Ca+
24Mg+
Seidelin et al: Phys. Rev. Lett. 96, 253003 (2006)
Nägerl et al: Phys. Rev. A 61, 023405 (2000)
Vorlesung Quantum Computing SS ‘08
7
quantum computing with ions
H H-1
calculation
U
preparation
read-out
|A|
time
time
the ions are prepared to be in their ground state
Doppler cooling side band cooling
1st step 2nd step
kBT << ħz
Vorlesung Quantum Computing SS ‘08
8
Doppler cooling
when absorbing a photon, also the momentum is transferred
the net momentum of the spontaneousemission is zero
E = ħp = ħk
E = 0p = 0
E = ħp = ħk
k
absorption
for ions moving toward the laser beam the lightappears blue shifted → use a red detuned laser
= 0 + k ∙ v
Ca
Vorlesung Quantum Computing SS ‘08
9
side band cooling
Doppler cooling gets down to kBT ≈ ħ
internal electronic ground and excited state |g,|e